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Time-Varying Feedback Matrices in Feedback Delay Networks and Their Application in Artificial Reverberation
Abstract
This paper introduces a time-variant reverberation algorithm as an extension of the feedback delay network (FDN). By modulating the feedback matrix nearly continuously over time, a complex pattern of concurrent amplitude modulations of the feedback paths evolves. Due to its complexity, the modulation produces less likely perceivable artifacts and the time-variation helps to increase the liveliness of the reverberation tail. A listening test, which has been conducted, confirms that the perceived quality of the reverberation tail can be enhanced by the feedback matrix modulation. In contrast to the prior art time-varying allpass FDNs, it is shown that unitary feedback matrix modulation is guaranteed to be stable. Analytical constraints on the pole locations of the FDN help to describe the modulation effect in depth. Further, techniques and conditions for continuous feedback matrix modulation are presented.
... They can be implemented in various ways: Fig. 1(a) shows the original form [1] and Fig. 1(c) and 1(d) show the two most commonly seen (e.g., [3,4]). Schroeder allpass filters are also "nested" in cascade with delay lines inside of Feedback Delay Networks (FDNs) [5][6][7][8][9][10] or another Schroeder allpass [2,[11][12][13][14][15][16]. Time-varying first-order allpass filters (Schroeder allpasses with length-one delay lines) have also been explored in digital audio effect and synthesizer design [10,[17][18][19][20][21][22][23][24][25]. ...
... Although reverb algorithms are almost always designed from a linear time-invariant (LTI) prototype, it is common to vary gains over time to break up resonances [5,8,11,[26][27][28][29][30]. It is essential in varying these gains that the structure's stability be preserved, which can be accomplished by preserving the signal energy during variation. ...
... It is essential in varying these gains that the structure's stability be preserved, which can be accomplished by preserving the signal energy during variation. Unfortunately the standard Schroeder allpass filter has been shown not to preserve energy as its coefficient is changed [8]. ...
... [27] stacked the differentiable PEQs and nonlinearities (again, it is a cascaded Wiener-Hammerstein model) to mimic an analog distortion pedal. Upon these works, we clarify the reliability of the FSM, provide a general differentiable LTI filter based on a state-variable filter (SVF) parameterization [28], [29], and build the DAR models with it. ...
... B. Differentiable Feedback Delay Network 1) Feedback Delay Network: The most widely used class of AR models is the delay network, which recursively interconnects long delay lines [4]. Among numerous delay network models, we implement Feedback Delay Network (FDN) [12] differentiably since it can express any other delay networks [28], [43]. Indeed, its difference equation can be expressed in a general delayed state-space form. ...
... • Pre and Post Filter Matrix. Following most previous works [19], [28], [44], B is set to a (constant) gain vector b. C is composed of a gain vector c and a common filter C 1 , i.e., C = C 1 c. ...
We propose differentiable artificial reverberation (DAR), a family of artificial reverberation (AR) models implemented in a deep learning framework. Combined with the modern deep neural networks (DNNs), the differentiable structure of DAR allows training loss gradients to be back-propagated in an end-to-end manner. Most of the AR models bottleneck training speed when implemented "as is" in the time domain and executed with a parallel processor like GPU due to their infinite impulse response (IIR) filter components. We tackle this by further developing a recently proposed acceleration technique, which borrows the frequency-sampling method (FSM). With the proposed DAR models, we aim to solve an artificial reverberation parameter (ARP) estimation task in a unified approach. We design an ARP estimation network applicable to both analysis-synthesis (RIR-to-ARP) and blind estimation (reverberant-speech-to-ARP) tasks. And using different DAR models only requires slightly a different decoder configuration. This way, the proposed DAR framework overcomes the previous methods' limitations of task-dependency and AR-model-dependency.
... Both SISO and MIMO allpass FDNs were applied to a wide range of roles including: 1) increasing the echo density as preprocessing to an artificial reverberator [2,16]; 2) increasing echo density of in the feedback loop of reverberators [17][18][19][20]; 3) decorrelation for widening the auditory image of a sound source [21][22][23]; 4) as reverberator in electro-acoustic reverberation enhancement systems [15,18,24,25]; 5) linear dynamic range reduction [26,27] ; and 6) dispersive system design [28][29][30]. In the broader context of control theory, allpass FDNs are strongly related to Schur diagonal stability [31], e.g., stability properties of asynchronous networks. ...
... To demonstrate system properties of an FDN independent from delays m, we have earlier developed a representation of p m,A pzq based on the principal minors of A [6,19]. This representation is also useful to derive the uniallpass property of FDNs. ...
... If the FDN is stable and uniallpass, then it is also allpass for m " 1. Therefore, Theorem 1 applies and due to (19) and (20), we have det V "˘1 and A is non-singular if and only if D is non-singular. According to (8), if the FDN is allpass then the determinant of the transfer function det Hpzq is allpass. ...
In the 1960s, Schroeder and Logan introduced delay line-based allpass filters, which are still popular due to their computational efficiency and versatile applicability in artificial reverberation, decorrelation, and dispersive system design. In this work, we extend the theory of allpass systems to any arbitrary connection of delay lines, namely feedback delay networks (FDNs). We present a characterization of uniallpass FDNs, i.e., FDNs, which are allpass for an arbitrary choice of delays. Further, we develop a solution to the completion problem, i.e., given an FDN feedback matrix to determine the remaining gain parameters such that the FDN is allpass. Particularly useful for the completion problem are feedback matrices, which yield a homogeneous decay of all system modes. Finally, we apply the uniallpass characterization to previous FDN designs, namely, Schroeder's series allpass and Gardner's nested allpass for single-input, single-output systems, and, Poletti's unitary reverberator for multi-input, multi-output systems and demonstrate the significant extension of the design space.
... However, smearing problems have been reported for transient sounds [19]. Other ways to improve the FDN include introducing time-varying elements in the structure, such as modulated delay lines [20], allpass filters [3], or a time-varying feedback matrix [21,22,23]. Time-varying delay lines lead to imprecise control of the decay time, whereas an FDN with time-varying allpass filters is not guaranteed to be stable [23]. ...
... Other ways to improve the FDN include introducing time-varying elements in the structure, such as modulated delay lines [20], allpass filters [3], or a time-varying feedback matrix [21,22,23]. Time-varying delay lines lead to imprecise control of the decay time, whereas an FDN with time-varying allpass filters is not guaranteed to be stable [23]. Since a time-varying feedback matrix is less likely to cause artifacts in the reverberation sound, this method has been found to improve the sound quality of the reverberation tail [23]. ...
... Time-varying delay lines lead to imprecise control of the decay time, whereas an FDN with time-varying allpass filters is not guaranteed to be stable [23]. Since a time-varying feedback matrix is less likely to cause artifacts in the reverberation sound, this method has been found to improve the sound quality of the reverberation tail [23]. Another approach is to introduce short delays in the feedback matrix, so that each matrix element consists of a gain and a delay [24]. ...
Artificial reverberation is an audio effect used to simulate the acoustics of a space while controlling its aesthetics, particularly on sounds recorded in a dry studio environment. Delay-based methods are a family of artificial reverberators using recirculating delay lines to create this effect. The feedback delay network is a popular delay-based reverberator providing a comprehensive framework for parametric reverberation by formalizing the recirculation of a set of interconnected delay lines. However, one known limitation of this algorithm is the initial slow build-up of echoes, which can sound unrealistic, and overcoming this problem often requires adding more delay lines to the network. In this paper, we study the effect of adding velvet-noise filters, which have random sparse coefficients, at the input and output branches of the reverberator. The goal is to increase the echo density while minimizing the spectral coloration. We compare different variations of velvet-noise filtering and show their benefits. We demonstrate that with velvet noise, the echo density of a conventional feedback delay network can be exceeded using half the number of delay lines and saving over 50% of computing operations in a practical configuration using low-order attenuation filters.
... Both SISO and MIMO allpass FDNs were applied to a wide range of roles including: 1) increasing the echo density as preprocessing to an artificial reverberator [2,17]; 2) increasing echo density of in the feedback loop of reverberators [18][19][20]; 3) decorrelation for widening the auditory image of a sound source [21][22][23]; 4) as reverberator in electro-acoustic reverberation enhancement systems [16,19,24,25]; 5) linear dynamic range reduction [26,27] ; and 6) dispersive system design [28,29]. In the broader context of control theory, allpass FDNs are strongly related to Schur diagonal stability [30], e.g., stability properties of asynchronous networks. ...
... The transfer function matrix (2) can be stated as a rational polynomial [5,20], i.e., ...
... To demonstrate system properties of an FDN independent from delays m, we have earlier developed a representation of p m,A pzq based on the principal minors of A [6,20]. This representation is also useful to derive the uniallpass property of FDNs. ...
In the 1960s, Schroeder and Logan introduced delay-based allpass filters, which are still popular due to their computational efficiency and versatile applicability in artificial reverberation, decorrelation, and dispersive system design. In this work, we extend the theory of allpass systems to any arbitrary connection of delay lines, namely feedback delay networks (FDNs). We present a complete characterization of uniallpass FDNs, i.e., FDNs, which are allpass for an arbitrary choice of delays. Further, we develop a solution to the completion problem, i.e., given an FDN feedback matrix to determine the remaining gain parameters such that the FDN is allpass. Particularly useful for the completion problem are feedback matrices, which yield a homogeneous decay of all system modes. Finally, we apply the uniallpass characterization to previous FDN designs, namely, Schroeder's series allpass and Gardner's nested allpass for single-input, single-output systems, and, Poletti's unitary reverberator for multi-input, multi-output systems and demonstrate the significant extension of the design space.
... Feedforward-feedback allpass filters have been introduced with the delay lines to increase the short-term echo density [9,10]. Alternatively, allpass filters may be placed after the delay lines [11,12], which in turn doubles the effective size of the FDN [13]. Alternatively, scattering filters can be introduced in series to the FDN. ...
... We have tested various other strategies for choosing vectors v i to no avail. In the following, we present alternative characterizations based on (13), which results in more intuitive designs. ...
... 2) Cascade Multiplication: Alternatively, the FIR FFM can directly implement the cascaded form in (13) with alternating processing of delays D m k (z) and mixing U k . The diagonal delay matrix D m k (z), implemented with ring buffers, require N delay read and write operations plus circular pointer shifts. ...
Feedback delay networks (FDNs) are recursive filters, which are widely used for artificial reverberation and decorrelation. One central challenge in the design of FDNs is the generation of sufficient echo density in the impulse response without compromising the computational efficiency. In a previous contribution, we have demonstrated that the echo density of an FDN can be increased by introducing so-called delay feedback matrices where each matrix entry is a scalar gain and a delay. In this contribution, we generalize the feedback matrix to arbitrary lossless filter feedback matrices (FFMs). As a special case, we propose the velvet feedback matrix, which can create dense impulse responses at a minimal computational cost. Further, FFMs can be used to emulate the scattering effects of non-specular reflections. We demonstrate the effectiveness of FFMs in terms of echo density and modal distribution.
... However, an inherent disadvantage of Schroeder allpass filters is the dependency between the dry-wet-ration and the decay time. Nonetheless, allpass filters were applied to with a wide range of roles including: (1) increasing the echo density as preprocessing to an artificial reverberator [1,7,8]; (2) increasing echo density of in the feedback loop of reverberators [5,[9][10][11][12][13]; ...
... While for a scalar gain g, (13) and (15) are identical, they are subtly different for frequency-dependent gain g(z). The original formulation (13) is only directly realizable for scalar gains because g * (z) is non-causal for FIR filters or unstable for IIR filters. ...
... In other words, g(z) needs to be a maximum phase IIR filter. While this is a step forward, also the computational cost increased: the Gerzon formulation (15) requires about three times of the operations of the Schroeder formulation (13). A further drawback with the IIR filter formulation is that the filter g(z) itself introduces new poles that are independent of the filter response design. ...
Since the introduction of feedforward–feedback comb allpass filters by Schroeder and Logan, its popularity has not diminished due to its computational efficiency and versatile applicability in artificial reverberation, decorrelation, and dispersive system design. In this work, we present an extension to the Schroeder allpass filter by introducing frequency-dependent feedforward and feedback gains while maintaining the allpass characteristic. By this, we directly improve upon the design of Dahl and Jot which exhibits a frequency-dependent absorption but does not preserve the allpass property. At the same time, we also improve upon Gerzon’s allpass filter as our design is both less restrictive and computationally more efficient. We provide a complete derivation of the filter structure and its properties. Furthermore, we illustrate the usefulness of the structure by designing an allpass decorrelation filter with frequency-dependent decay characteristics.
... Feedforward-feedback allpass filters have been introduced with the delay lines to increase the short-term echo density [9,10]. Alternatively, allpass filters may be placed after the delay lines [11,12], which in turn doubles the effective size of the FDN [13]. Alternatively, scattering filters can be introduced in series to the FDN. ...
... It can be shown that for any V (z), there are U 1 , m 1 , and, [22, p. 733]. Thus, any paraunitary FIR FFM can be factored into form (13). In this formulation, the FFM mainly introduces K delay and mixing stages within the main FDN loop (see Figure 3). ...
... We have tested various other strategies for choosing vectors v i to no avail. In the following, we present alternative characterizations based on (13), which results in more intuitive designs. ...
Feedback delay networks (FDNs) are recursive filters, which are widely used for artificial reverberation and decorrelation. One central challenge in the design of FDNs is the generation of sufficient echo density in the impulse response without compromising the computational efficiency. In a previous contribution, we have demonstrated that the echo density of an FDN can be increased by introducing so-called delay feedback matrices where each matrix entry is a scalar gain and a delay. In this contribution, we generalize the feedback matrix to arbitrary lossless filter feedback matrices (FFMs). As a special case, we propose the velvet feedback matrix, which can create dense impulse responses at a minimal computational cost. Further, FFMs can be used to emulate the scattering effects of non-specular reflections. We demonstrate the effectiveness of FFMs in terms of echo density and modal distribution.
... We first review two standard methods for the modal decomposition [17,18]. Let A be an invertible matrix, then adj(A) = det(A)A −1 is the adjugate of the matrix A [19]. ...
... where the coefficients c i are derived from the principal minors of A [18]. The system poles are the roots of the scalar polynomial. ...
... For FDNs, however, the matrix polynomial P (z) in (7) is improper because det(P K ) = 0. In fact, if det(A) = 0, the number of finite roots is N which is also the degree of the scalar polynomial in (9) [18]. ...
Feedback delay networks (FDNs) belong to a general class of recursive filters which are widely used in sound synthesis and physical modeling applications. We present a numerical technique to compute the modal decomposition of the FDN transfer function. The proposed pole finding algorithm is based on the Ehrlich-Aberth iteration for matrix polynomials and has improved computational performance of up to three orders of magnitude compared to a scalar polynomial root finder. The computational performance is further improved by bounds on the pole location and an approximate iteration step. We demonstrate how explicit knowledge of the FDN's modal behavior facilitates analysis and improvements for artificial reverberation. The statistical distribution of mode frequency and residue magnitudes demonstrate that relatively few modes contribute a large portion of impulse response energy.
... We first review two standard methods for the modal decomposition [17,18]. Let A be any invertible matrix, then ...
... where the coefficients c i are derived from the principal minors of A [18]. The system poles are the roots of the scalar polynomial. ...
... For FDNs, however, P K is singular such that the actual number of roots is lower, respectively, many roots are infinite. In fact, if det(A) = 0, the number of finite roots is N which is also the degree of the scalar polynomial in (10) [18]. ...
Feedback delay networks (FDNs) belong to a general class of recursive filters which are widely used in sound synthesis and physical modeling applications. We present a numerical technique to compute the modal decomposition of the FDN transfer function. The proposed pole finding algorithm is based on the Ehrlich-Aberth iteration for matrix polynomials and has improved computational performance of up to three orders of magnitude compared to a scalar polynomial root finder. We demonstrate how explicit knowledge of the FDN's modal behavior facilitates analysis and improvements for artificial reverberation. The statistical distribution of mode frequency and residue magnitudes demonstrate that relatively few modes contribute a large portion of impulse response energy.
... Delay modulation reduces detuning, but is less robust at lower frequencies. [14][15][16] The authors have introduced a further technique based on time-varying mixing matrices 17,18 in the context of artificial reverberation and RESs. ...
... In compliance with Eq. (10), the eigenvectors U are chosen to be unitary. The time-domain processing matrix XðtÞ is real if the eigenvectors and eigenvalues appear in complex conjugate pairs, 18 i.e., there is a disjunct pairing of i and j such that ...
... For odd N, there is an additional fixed eigenvalue with a modulation frequency of zero. 18 For simplicity N is assumed to be even in the following. We show that XðxÞ is Hermitian symmetric for MM ...
Various time-varying algorithms have been applied in multichannel sound systems to improve the system's stability and, among these, frequency shifting has been demonstrated to reach the maximum stability improvement achievable by time-variation in general. However, the modulation artifacts have been found to diminish the gain improvement unusable for a higher number of channels and high-quality applications such as music reproduction. This paper proposes alternatively time-varying mixing matrices, which is an efficient algorithm corresponding to symmetric up and down frequency shifting. It is shown with a statistical approach that time-varying mixing matrices can as well achieve maximum stability improvement for a higher number of channels. A listening test demonstrates the improved quality of time-varying mixing matrices over frequency shifting.
... FDNs have been proposed by Stautner and Puckette [1] and gained popularity as an efficient and flexible way to model and process artificial reverberation [2]. Many parametric reverberation algorithms like Schroeder's Cascaded Allpass and Moorer's extension [3], [4], Dattorro's Allpass Feedback Network [5], Dahl and Jot's Absorbent Allpass FDN [6], can be expressed by an FDN [7], [8]. Other physical modeling structures like digital waveguide networks (DWN), digital waveguide mesh (DWM), scattering delay networks (SDN) and finite difference time domain (FDTD) simulation are in close relation to the FDN structure [9]- [12]. ...
... In a more general approach, Gerzon described unitary networks, i.e., frequencydependent unitary matrices of filters, in a feedback loop to constitute a lossless FDN [16]. However, a non-unitary, nontriangular feedback matrix can constitute a lossless FDN as well [8]. It has been shown that if an FDN is lossless then the feedback matrix has only eigenvalues on the unit circle [9]. ...
... , C m N ,g N (z)] is a diagonal matrix of allpass filters. In [8], the authors showed that any allpass FDN can be represented as a standard FDN with twice the delay lines and the feedback matrix Figure 5 depicts a single delay line allpass FDN and an equivalent two delay line standard FDN. It has been shown in [6] that the allpass FDN is lossless if all |g i | ≤ 1. ...
Lossless Feedback Delay Networks (FDNs) are commonly used as a design prototype for artificial reverberation algorithms. The lossless property is dependent on the feedback matrix, which connects the output of a set of delays to their inputs, and the lengths of the delays. Both, unitary and triangular feedback matrices are known to constitute lossless FDNs, however, the most general class of lossless feedback matrices has not been identified. In this contribution, it is shown that the FDN is lossless for any set of delays, if all irreducible components of the feedback matrix are diagonally similar to a unitary matrix. The necessity of the generalized class of feedback matrices is demonstrated by examples of FDN designs proposed in literature.
... The theory of time-varying mixing matrices for artificial reverberation have been recently developed by the authors [16] and its design and efficient implementation have been discussed in [17]. The mixing matrix is designed to be unitary and energy-conserving at every time instance. ...
... For the regenerative approach, the microphone-toloudspeaker path G ML is realized by a time-varying mixing matrix A(n), where n is the instance of time. It has been shown that unitary time-varying mixing matrices in a feedback loop are stable under arbitrary time-variation, if it is stable at every time instance [16]. For time-domain processing, A(n) is typically real-valued and therefore orthogonal, i.e. ...
... A direct implementation of the time-varying allpass gains may become unstable under strong variation [22], whereas the stability of the time-varying feedback matrix was shown for arbitrary variation [16]. More advanced allpass structures can ensure stability under timevariation [23], but also increases the complexity of the design. ...
... The theory of time-varying feedback matrices in FDNs has been outlined by the authors in [4]. The 9255 ...
... The feedback delay network (FDN) is a general structure that has been the superior choice in recent years to generate artificial reverberation [1]. To further account for physical acoustic changes [2], to reduce the computational requirements [3] or to enhance the perceived quality [4], various techniques have been developed to incorporate temporal variations into artificial reverberation. In the context of reverberation enhancement systems, which are formally related to FDNs [5], time-variation has been successfully employed to improve the system's stability and coloration [6][7][8][9]. ...
... In the context of reverberation enhancement systems, which are formally related to FDNs [5], time-variation has been successfully employed to improve the system's stability and coloration [6][7][8][9]. In [4], the authors proposed the use of time-varying feedback matrices in FDNs, and demonstrated that it provides an attractive alternative to time-varying delay lines or allpass filters. This contribution investigates practical considerations in parameterization and computational efficiency of the implementation of time-varying feedback matrices. ...
Feedback delay networks (FDNs) can be efficiently used to generate parametric artificial reverberation. Recently, the authors proposed a novel approach to time-varying FDNs by introducing a time-varying feedback matrix. The formulation of the time-varying feedback matrix was given in the complex eigenvalue domain, whereas this contribution specifies the requirements for real valued time-domain processing. In addition, the computational costs of different time-varying feedback matrices, which depend on the matrix type and modulation function, are discussed. In a performance evaluation, the proposed orthogonal matrix modulation is compared to a direct interpolation of the matrix entries.
... The transfer function matrix (2) can be stated as a rational polynomial [2,33], i.e., ...
... where the (N − 1) × (N − 1) submatrix M ij (z) results from deleting row i and column j of P (z). A determinant of the form det D m z -1 − A is given by [33] det ...
The feedback delay network (FDN) is a popular filter structure to generate artificial spatial reverberation. A common requirement for multichannel late reverberation is that the output signals are well decorrelated, as too high a correlation can lead to poor reproduction of source image and uncontrolled coloration. This article presents the analysis of multichannel correlation induced by FDNs. It is shown that the correlation depends primarily on the feedforward paths, while the long reverberation tail produced by the recursive path does not contribute to the inter-channel correlation. The impact of the feedback matrix type, size, and delays on the inter-channel correlation is demonstrated. The results show that small FDNs with a few feedback channels tend to have a high inter-channel correlation, and that the use of a filter feedback matrix significantly improves the decorrelation, often leading to the lowest inter-channel correlation among the tested cases. The learnings of this work support the practical design of multichannel artificial reverberators for immersive audio applications.
... Recent research on FDNs has focused on mixing matrix design to increase echo density [5], modal analysis [6], [7], time-varying FDNs [8], allpass FDNs for colorless reverberation [9] and scattering FDNs for dense reverberation [10]. Grouping of delay lines to control direction-dependent energy decay, known as the Directional Feedback Delay Network, was proposed by Alary et al. in [11]. ...
... Room 1 has the shortest T 60 , and Room 3 has the longest. The maximum error in the GFDN's T 60 by using a nearly paraunitary coupling matrix, calculated according to (8), is shown in Fig. 8b by solid lines. The dashed lines show the the Just Noticeable Difference (JND) in reverberation time, 5% [37]. ...
Feedback Delay Networks are one of the most popular and efficient means of generating artificial reverberation. Recently, we proposed the Grouped Feedback Delay Network (GFDN), which couples multiple FDNs while maintaining system stability. The GFDN can be used to model reverberation in coupled spaces that exhibit multi-stage decay. The block feedback matrix determines the inter- and intra-group coupling. In this paper, we expand on the design of the block feedback matrix to include frequency-dependent coupling among the various FDN groups. We show how paraunitary feedback matrices can be designed to emulate diffraction at the aperture connecting rooms. Several methods for the construction of nearly paraunitary matrices are investigated. The proposed method supports the efficient rendering of virtual acoustics for complex room topologies in games and XR applications.
... In the current study, RAZR was adapted to generate six, 12, 24, 48, or 96 VRS, equivalent to one, two, four, eight, and 16 VRS per surface of the underlying shoebox room. To ensure similar spectro-temporal characteristics of the FDN output throughout evaluation and avoiding subtle timbre changes in the resulting reverberant tail due to a variation of the number of FDN channels [44,45], the FDN always operated with the highest number of 96 channels, independent of the number of rendered VRS. The 96 FDN outputs were directly used for 96 VRS and downmixes with 48, 24, 12, and six VRS were generated in a sequential procedure by adding pairs of the FDN output channels. ...
... For real-time applications, a perceptually optimal choice of FDN parameters for a low number of FDN channels has to be found. Although several studies optimized FDNs using, e.g., time-varying parameters or considering mode density (e.g., [64,44]), RAZR uses a physically-based design of the FDN, in which the delays are derived from the dimensions of the room. This is also motivated by interpreting the FDN as a rough approximation of radiance transfer [65]. ...
... Recently, many extensions of the FDN have been proposed, such as the directional feedback delay network (DFDN) (Alary and Politis, 2020;Alary, Politis, et al., 2019) which operates onto an Ambisonics signal (see section 2.3.2.2), or a grouped feedback delay network (GFDN) where the FDN channels are parametrized in two distinct groups such that double slopes behavior can be achieved (Das, Abel, and Canfield-Dafilou, 2020;. Furthermore, Schlecht and Habets (2015) proposed a time varying FDN, where a unitary feedback matrix is regularly rotated such that time-variability of real rooms are imitated. This has the advantage of "breaking" periodic temporal patterns, hence making the reverberation more natural (Schlecht and Habets, 2015). ...
... Furthermore, Schlecht and Habets (2015) proposed a time varying FDN, where a unitary feedback matrix is regularly rotated such that time-variability of real rooms are imitated. This has the advantage of "breaking" periodic temporal patterns, hence making the reverberation more natural (Schlecht and Habets, 2015). The introduction of filters within the feedback loop has also been studied in order to increase the echo density (Schlecht, 2020). ...
This thesis takes place within the RASPUTIN project and focuses on the development, evaluation and use of immersive acoustic virtual reality simulation tools for the purpose of helping blind individuals prepare in-situ navigations in unfamiliar reverberant environments. While several assistive tools, such as sensory substitution devices, can provide spatial information during navigation, an alternative approach is to devise a real-time room acoustic simulation and auralization engine for use by blind individuals at home to enable them to virtually navigate in unfamiliar environments under controlled circumstances, hence building mental representations of these spaces prior to in-situ navigation. In this thesis, I tackle three aspects of this subject. The first part focuses on efficient simulations and auralizations of coupled volumes, which occur in many buildings of interest for navigation preparation (e.g. city halls, hospitals, or museums) and whose simulation and auralization can be challenging. The second part focuses on the individualization of head related transfer functions, which is a necessary step in providing individualized and convincing auditory experiences. Finally, the last part investigates some aspects of the space cognition following use of different learning paradigms, such as tactile maps.
... To assess the required spatial resolution of late reverberation rendering, in the current study RAZR was adapted to generate either 6, 12, 24, 48, or 96 VRS, equivalent to 1, 2, 4, 8, and 16 VRS per surface of the underlying shoebox room. To ensure similar spectro-temporal characteristics of the FDN output throughout evaluation and avoiding timbre changes in the resulting reverberant tail due to a variation of the number of FDN channels ( [34], [35]), the FDN always operated with the highest number of 96 channels, independent of the number of rendered VRS. The 96 FDN outputs were directly used for 96 VRS and the spatial resolution of the late reverberation was adjusted by using a set of downmixes for 48, 24, 12, and 6 VRS generated in a sequential procedure by adding pairs of the FDN output channels. ...
... For real-time applications, a perceptually optimal choice of FDN parameters for a low number of FDN channels has to be found. While several studies optimized FDNs using, e.g., time-varying parameters or optimization of mode density (e.g., [43], [34]), RAZR uses a physically-based design of the FDN, where the delays are derived from the dimensions of the room. This is also motivated by interpreting the FDN as a rough approximation of radiance transfer [44]. ...
For 6-DOF (degrees of freedom) interactive virtual acoustic environments (VAEs), the spatial rendering of diffuse late reverberation in addition to early (specular) reflections is important. In the interest of computational efficiency, the acoustic simulation of the late reverberation can be simplified by using a limited number of spatially distributed virtual reverb sources (VRS) each radiating incoherent signals. A sufficient number of VRS is needed to approximate spatially anisotropic late reverberation, e.g., in a room with inhomogeneous distribution of absorption at the boundaries. Here, a highly efficient and perceptually plausible method to generate and spatially render late reverberation is suggested, extending the room acoustics simulator RAZR [Wendt et al., J. Audio Eng. Soc., 62, 11 (2014)]. The room dimensions and frequency-dependent absorption coefficients at the wall boundaries are used to determine the parameters of a physically-based feedback delay network (FDN) to generate the incoherent VRS signals. The VRS are spatially distributed around the listener with weighting factors representing the spatially subsampled distribution of absorption coefficients on the wall boundaries. The minimum number of VRS required to be perceptually distinguishable from the maximum (reference) number of 96 VRS was assessed in a listening test conducted with a spherical loudspeaker array within an anechoic room. For the resulting low numbers of VRS suited for spatial rendering, optimal physically-based parameter choices for the FDN are discussed.
... Since then, FDNs have gained popularity for creating efficient artificial reverberation. Some important contributions in FDN research include [6,7] in which the authors propose a circulant feedback matrix for efficient implementation and maximum diffusion, and those by Schlecht [8,9] which deal with time-varying FDNs and their practical implementation. Schlecht also studied the properties of mixing matrices that produce lossless FDNs [10]. ...
... A slow and continuous change from one function to another is known as homotopy [12]. In [8], the authors create a feedback matrix evolution equivalent to a recursive update using linear modulation functions. In this paper, we parameterize M as a function of θ. ...
The mixing matrix of a Feedback Delay Network (FDN) reverberator is used to control the mixing time and echo density profile. In this work, we investigate the effect of the mixing matrix on the modes (poles) of the FDN with the goal of using this information to better design the various FDN parameters. We find the modal decomposition of delay network reverberators using a state space formulation, showing how modes of the system can be extracted by eigenvalue decomposition of the state transition matrix. These modes, and subsequently the FDN parameters, can be designed to mimic the modes in an actual room. We introduce a parameterized orthonormal mixing matrix which can be continuously varied from identity to Hadamard. We also study how continuously varying diffusion in the mixing matrix affects the damping and frequency of these modes. We observe that modes approach each other in damping and then deflect in frequency as the mixing matrix changes from identity to Hadamard. We also quantify the perceptual effect of increasing mixing by calculating the normalized echo density (NED) of the FDN impulse responses over time.
... The modification of systems based on state-space descriptions by feedback structures is a widely used method, e.g., in control theory [1,2], in the adjustment of boundary behavior of physical systems [13,14,29] and in the creation of artificial reverberation with feedback delay networks [31,32]. ...
... But, according to the real-time algorithms in [17,18,33], the system in (23) can be implemented in terms of 2nd order filters. Alternatively, the matrix powers in (23) can be performed efficiently on the eigenvalue decomposition of D d and U d [31,32]. The parameters γD, γU in (23) may be time varying for practical applications. ...
The attachment of feedback loops to physical or musical systems
enables a large variety of possibilities for the modification of the
system behavior. Feedback loops may enrich the echo density of
feedback delay networks (FDN), or enable the realization of complex
boundary conditions in physical simulation models for sound
synthesis. Inspired by control theory, a general feedback loop is attached
to a model of a vibrating membrane. The membrane model
is based on the modal expansion of an initial-boundary value problem
formulated in a state-space description. The possibilities of the
attached feedback loop are shown by three examples, namely by
the introduction of additional mode wise damping; modulation and
damping inspired by FDN feedback loops; time-varying modification
of the system behavior.
... Losses are then incorporated by multiplying the unilossless matrix by a diagonal matrix of scalars designed to achieve a pre-set reverberation time, T 60 . While it is possible to design feedback matrices as time varying and/or frequency dependent [7,24], this paper focuses on the time-invariant and frequency-independent case. With this assumption, the stability of the system can be easily enforced throughout the training, thanks to the model reparameterization strategies discussed later in Section 4. ...
Over the past few decades, extensive research has been devoted to the design of artificial reverberation algorithms aimed at emulating the room acoustics of physical environments. Despite significant advancements, automatic parameter tuning of delay-network models remains an open challenge. We introduce a novel method for finding the parameters of a feedback delay network (FDN) such that its output renders target attributes of a measured room impulse response. The proposed approach involves the implementation of a differentiable FDN with trainable delay lines, which, for the first time, allows us to simultaneously learn each and every delay-network parameter via backpropagation. The iterative optimization process seeks to minimize a perceptually motivated time-domain loss function incorporating differentiable terms accounting for energy decay and echo density. Through experimental validation, we show that the proposed method yields time-invariant frequency-independent FDNs capable of closely matching the desired acoustical characteristics and outperforms existing methods based on genetic algorithms and analytical FDN design.
... Is the highest degree of envelopment elicited by a stationary and isotropic diffuse sound field, or by a sound field that exhibits audible spatio-temporal fluctuations/modulations? These questions are relevant in the technical design and creative application of artificial reverberators [21][22][23][24][25], spatial sound synthesis techniques [4,26,27], and spatial up-mixing algorithms [28,29]. ...
... Is the highest degree of envelopment elicited by a stationary and isotropically diffuse sound field, or by a sound field that exhibits audible spatio-temporal fluctuations / modulations? These questions are relevant in the technical design and creative application of artificial reverberators [19,20,21,22,23], spatial sound synthesis techniques [3,24,25], and spatial upmixing algorithms [26,27]. ...
Listener envelopment refers to the sensation of being surrounded by sound, either by multiple direct sound events or by a diffuse reverberant sound field. More recently, a specific attribute for the sensation of being covered by sound from elevated directions has been proposed by Sazdov et al. and was termed listener engulfment. This contribution investigates the effect of the temporal and directional density of sound events on listener envelopment and engulfment. A spatial granular synthesis technique is used to precisely control the temporal and directional density of sound events. Experimental results indicate that a directionally uniform distribution of sound events at time intervals Δt < 20 milliseconds is required to elicit a sensation of diffuse envelopment, whereas longer time intervals lead to localized auditory events. It shows that elevated loudspeaker layers do not increase envelopment, but contribute specifically to listener engulfment. Lowpass-filtered stimuli increase envelopment, but lead to a decreased control over engulfment. The results can be exploited in the technical design and creative application of spatial sound synthesis and reverberation algorithms.
... The issue of stability is discussed in the context of accurate synthesis of sound-energy decay in multiple frequency bands. An attenuation filter is, in the case of this dissertation, realized as a time-invariant infiniteimpulse-response (IIR) filter, which requires all of its poles to lie within the unit circle in order to maintain stability [235,236,237,238]. If this condition is met in the overall magnitude of the attenuation filter (which can include several low-order filters), the IR of the reverberator will decay instead of being sustained or amplified. ...
In this dissertation, the discussion is centered around the sound energy decay in enclosed spaces. The work starts with the methods to predict the reverberation parameters, followed by the room impulse response measurement procedures, and ends with an analysis of techniques to digitally reproduce the sound decay.
The research on the reverberation in physical spaces was initiated when the first formula to calculate room's reverberation time emerged. Since then, finding an accurate and reliable method to predict reverberation has been an important area of acoustic research. This thesis presents a comprehensive comparison of the most commonly used reverberation time formulas, describes their applicability in various scenarios, and discusses their accuracy when compared to results of measurements. The common sources of uncertainty in reverberation time calculations, such as bias introduced by air absorption and error in sound absorption coefficient, are analyzed as well. The thesis shows that decreasing such uncertainties leads to a good prediction accuracy of Sabine and Eyring equations in diverse conditions regarding sound absorption distribution.
The measurement of the sound energy decay plays a crucial part in understanding the propagation of sound in physical spaces. Nowadays, numerous techniques to capture room impulse responses are available, each having its advantages and drawbacks. In this dissertation, the majority of commonly used measurement techniques are listed, whereas the exponential swept-sine is described in more detail. This work elaborates on the external factors that may impair the measurements and introduce error to their results, such as stationary and non-stationary noise, as well as time variance. The dissertation introduces Rule of Two, a method of detecting nonstationary disturbances in sweep measurements. It also shows the importance of using median as
a robust estimator in non-stationary noise detection.
Artificial reverberation is a popular sound effect, used to synthesize sound energy decay for the purpose of audio production. This dissertation offers an insight into artificial reverberation algorithms based on recursive structures. The filter design proposed in this work offers precise control over the decay rate while being efficient enough for real-time implementation. The thesis discusses the role of the delay lines and feedback matrix in achieving high echo density in feedback delay networks. It also shows that four velvet-noise sequences are sufficient to obtain smooth output in interleaved velvet noise reverberator. The thesis shows that the accuracy of reproduction increases the perceptual similarity between measured and synthesised impulse responses.
The insights collected in this dissertation offer insights into the intricacies of reverberation prediction, measurement and synthesis. The results allow for reliable estimation of parameters related to sound energy decay, and offer an improvement in the field of artificial reverberation.
... Average correlation coefficients < 0.03 between the VRS signals enable the approximation of isotropic late reverberation as superposition of spatially distributed incoherent sound sources (see also Jacobsen & Roisin, 2000). By using the fixed, high number of 96 channels in the FDN, independent of the number of VRSs, the spatial resolution of the late reverberation can be adjusted while maintaining the spectro-temporal characteristics and thus avoiding timbre changes in the resulting reverberant tail (see, e.g., Schlecht & Habets, 2015, 2017. Polyhedra centered around the listener were used to determine the directions for spatialization of the VRSs, where the number of vertices corresponded to the number of VRSs (see Figure 1). ...
Late reverberation involves the superposition of many sound reflections, approaching the properties of a diffuse sound field. Since the spatially resolved perception of individual late reflections is impossible, simplifications can potentially be made for modelling late reverberation in room acoustics simulations with reduced spatial resolution. Such simplifications are desired for interactive, real-time virtual acoustic environments with applications in hearing research and for the evaluation of hearing supportive devices. In this context, the number and spatial arrangement of loudspeakers used for playback additionally affect spatial resolution. The current study assessed the minimum number of spatially evenly distributed virtual late reverberation sources required to perceptually approximate spatially highly resolved isotropic and anisotropic late reverberation and to technically approximate a spherically isotropic sound field. The spatial resolution of the rendering was systematically reduced by using subsets of the loudspeakers of an 86-channel spherical loudspeaker array in an anechoic chamber, onto which virtual reverberation sources were mapped using vector base amplitude panning. It was tested whether listeners can distinguish lower spatial resolutions of reproduction of late reverberation from the highest achievable spatial resolution in different simulated rooms. The rendering of early reflections remained unchanged. The coherence of the sound field across a pair of microphones at ear and behind-the-ear hearing device distance was assessed to separate the effects of number of virtual sources and loudspeaker array geometry. Results show that between 12 and 24 reverberation sources are required for the rendering of late reverberation in virtual acoustic environments.
... A popular method to increase the modal density in delay networks is to vary slightly the length of delay lines over time thus producing more modes [182,192,116,178], which requires the use of fractional delay lines [193]. In [194], a time-varying recirculating matrix is used to modulate the recirculation coefficients that changes the amplitude of modes over time. To reproduce the frequency-response of real rooms, the absorbent filters require precise design, usually through the use of a set of high-order equalization filters [195,183,196,197,198]. ...
Available online with the related articles at: http://urn.fi/URN:ISBN:978-952-64-0472-1
In this dissertation, the reproduction of reverberant sound fields containing directional characteristics is investigated. A complete framework for the objective and subjective analysis of directional reverberation is introduced, along with reverberation methods capable of producing frequency- and direction-dependent decay properties. Novel uses of velvet noise are also proposed for the decorrelation of audio signals as well as artificial reverberation. The methods detailed in this dissertation offer the means for the auralization of reverberant sound fields in real-time, with applications in the context of Immersive sound reproduction such as virtual and augmented reality.
... Since then, FDNs have become one of the most popular structures for synthesizing reverberation due to the relative efficiency of the approach. Recent research on FDNs has focused on mixing matrix design to increase echo density [6], modal analysis [7,8], time-varying FDNs [9], scattering FDNs [10], and reverberation time control by accurate design of the decay filters [11,12]. ...
Delay Network reverberators are an efficient tool for synthesizing reverberation. We propose a novel architecture, called the Grouped Feedback Delay Network (GFDN) reverberator, with groups of delay lines sharing different target decay rates, and use it to simulate coupled room acoustics. Coupled spaces are common in apartments, concert halls, and churches where two or more volumes with different reverberation characteristics are linked via an aperture. The difference in reverberation times (T60s) of the coupled spaces leads to unique phenomena, such as multi-stage decay. Here the GFDN is used to simulate coupled spaces with groups of delay line filters representing the T60 s of the coupled rooms. A parameterized, orthonormal mixing matrix is presented that provides control over the mixing times of the rooms and amount of coupling between the rooms. As an example application we measure a coupled bedroom and bathroom system separated by a door in an apartment and use the GFDN to synthesize the late field for different openings of the door separating the two rooms, thereby varying coupling between the rooms.
... In Fig. 1, we show the difference between non-smooth and smooth mixing matrices in terms of coherence error and spectral smoothness, for CðxÞ I, K ¼ 1024 and N ¼ 4. The non-smooth solution is generated from random unitary matrices at each frequency instance x k . For the smooth solution, we applied the method used in Schlecht and Habets (2015), originally derived to achieve continuous feedback matrix modulation. We imposed smooth transitions, i.e., similar unitary matrices across frequency, between Cðx 0 Þ ¼ I and Cðx K=2 Þ ¼ H= ffiffiffi ffi N p ...
The spatial properties of a noise field can be described by a spatial coherence function. Synthetic multichannel noise signals exhibiting a specific spatial coherence can be generated by properly mixing a set of uncorrelated, possibly non-stationary, signals. The mixing matrix can be obtained by decomposing the spatial coherence matrix. As proposed in a widely used method, the factorization can be performed by means of a Choleski or eigenvalue decomposition. In this work, the limitations of these two methods are discussed and addressed. In particular, specific properties of the mixing matrix are analyzed, namely, the spectral smoothness and the mix balance. The first quantifies the mixing matrix-filters variation across frequency and the second quantifies the number of input signals that contribute to each output signal. Three methods based on the unitary Procrustes solution are proposed to enhance the spectral smoothness, the mix balance, and both properties jointly. A performance evaluation confirms the improvements of the mixing matrix in terms of objective measures. Furthermore, the evaluation results show that the error between the target and the generated coherence is lowered by increasing the spectral smoothness of the mixing matrix.
... Feedforward-feedback allpass filters have been introduced with the delay lines to increase the short-term echo density [40,7]. Alternatively, allpass filters may be placed after the delay lines [35,36], which in turn doubles the effective size of the FDN [29]. Gardner proposed the nested allpass structure by [8], which recursively replaces the delay in the allpass with another allpass. ...
Feedback delay networks (FDNs) are recursive filters, which are widely used for artificial reverberation and decorrelation. While there exists a vast literature on a wide variety of reverb topologies, this work aims to provide a unifying framework to design and analyze delay-based reverberators. To this end, we present the Feedback Delay Network Toolbox (FDNTB), a collection of the MAT-LAB functions and example scripts. The FDNTB includes various representations of FDNs and corresponding translation functions. Further, it provides a selection of special feedback matrices, topologies, and attenuation filters. In particular, more advanced algorithms such as modal decomposition, time-varying matrices, and filter feedback matrices are readily accessible. Furthermore, our toolbox contains several additional FDN designs. Providing MATLAB code under a GNU-GPL 3.0 license and including illustrative examples, we aim to foster research and education in the field of audio processing.
... Since then, FDNs have become one of the most popular structures for synthesizing reverberation due to the relative efficiency of the approach. Recent research on FDNs has focused on mixing matrix design to increase echo density [4], modal analysis [5,6], time-varying FDNs [7], directional FDNs [8], and reverberation time control by accurate design of the decay filters [9,10]. ...
Feedback delay network reverberators have decay filters associated with each delay line to model the frequency dependent reverberation time (T60) of a space. The decay filters are typically designed such that all delay lines independently produce the same T60 frequency response. However, in real rooms, there are multiple , concurrent T60 responses that depend on the geometry and physical properties of the materials present in the rooms. In this paper, we propose the Grouped Feedback Delay Network (GFDN), where groups of delay lines share different target T60s. We use the GFDN to simulate coupled rooms, where one room is significantly larger than the other. We also simulate rooms with different materials , with unique decay filters associated with each delay line group, designed to represent the T60 characteristics of a particular material. The T60 filters are designed to emulate the materials' absorption characteristics with minimal computation. We discuss the design of the mixing matrix to control inter-and intra-group mixing , and show how the amount of mixing affects behavior of the room modes. Finally, we discuss the inclusion of air absorption filters on each delay line and physically motivated room resizing techniques with the GFDN.
... Feedforward-feedback allpass filters have been introduced in series to increase the short-term echo density [9,10]. Alternatively, allpass filters may be placed after the delay lines [11] which in turn doubles the effective size of the FDN [12]. Instead of allpass filters, FIR filters with pseudo-random exponentially decaying coefficients were proposed [13]. ...
This paper received the best paper award at WASPAA 2019. Feedback delay networks (FDNs) belong to a general class of re-cursive filters which are widely used in artificial reverberation and decorrelation applications. One central challenge in the design of FDNs is the generation of sufficient echo density in the impulse response without compromising the computational efficiency. In a previous contribution, we have demonstrated that the echo density of an FDN grows polynomially over time, and that the growth depends on the number and lengths of the delays. In this work, we introduce so-called delay feedback matrices (DFMs) where each matrix entry is a scalar gain and a delay. While the computational complexity of DFMs is similar to a scalar-only feedback matrix, we show that the echo density grows significantly faster over time, however, at the cost of non-uniform modal decays.
... Another modeling approach for the AIR is using a combined poles and zeros system model, i.e., Infinite Impulse Response (IIR) filter, see [7], [8], [9], [10], [11]. This model is capable of capturing the infinite AIR with a finite model order. ...
Acoustic echo cancellation and system identification in reverberant environments have been thoroughly studied in the literature. Theoretically, in a reverberant environment the Acoustic Impulse Response (AIR) relating the loudspeaker signal, denoted reference, with the corresponding signal component at the microphone, denoted echo, is of an infinite length and can be modeled as an Infinite Impulse Response (IIR) filter. Correspondingly, the echo signal can be modeled as an Auto Regressive Moving Average (ARMA) process. Yet, most methods for this problem adopt a Finite Impulse Response (FIR) system model or equivalently a Moving Average (MA) echo signal model due to their favorable simplicity and stability. Latter methods, denoted FIR-Acoustic Echo Canceller (AEC), employ an Adaptive Filter (AF) for tracking a possibly time-varying system and cancelling echo. Some contributions adopt an IIR system model and utilize it to derive a time-domain AEC and accurately analyze the room behaviour. An IIR system model has also been successfully applied in the Short Time Fourier Transform (STFT) domain for the dereverberation problem. In this contribution we consider an IIR model in the STFT domain and propose a novel online AEC algorithm, denoted IIR-AEC, which tracks the model parameters and cancels echo. The order of the feedback filter, equivalent to the order of the Auto Regressive (AR) part of the echo signal model, can be designed to fit the acoustic model and the order of the feed-forward filter, equivalent to the order of the MA part of the echo signal model, is limited to a single tap, thereby requiring that the STFT window is longer than the early part of the AIR. The computational complexity of proposed IIR-AEC is comparable to a Recursive Least Squares (RLS) implementation of FIR-AEC. These methods are evaluated using real measured AIRs drawn from a recording campaign and the IIR-AEC is shown to outperform the FIR-AEC.
... The original design uses a Householder matrix for the feedback path, however other unitary matrices can also be used [90]. These matrices can also be time-varying, resulting in improved perceptual characteristics [91]. ...
Developments in immersive audio technologies have been evolving in two directions: physically motivated systems and perceptually motivated systems. Physically motivated techniques aim to reproduce a physically accurate approximation of desired sound fields by employing a very high equipment load and sophisticated, computationally intensive algorithms. Perceptually motivated techniques, however, aim to render only the perceptually relevant aspects of the sound scene by means of modest computational and equipment load. This article presents an overview of perceptually motivated techniques, with a focus on multichannel audio recording and reproduction, audio source and reflection culling, and artificial reverberators.
Spatial audio systems are designed to control the perceived direction (and distance) of sounds. Depending on the sound scene, sensations can range from localized auditory events to listener envelopment ('being surrounded by sound') and engulfment ('being covered by sound'). This thesis consists of publications on localization, envelopment, and engulfment in real and virtualized loudspeaker environments. Concerning real, surrounding loudspeaker arrangements, the first part of the thesis investigates the effects of the spatio-temporal density of sound events on envelopment and engulfment. Listening experiments and auditory models reveal how envelopment can be preserved at off-center listening positions: when horizontally surrounding loudspeakers each provide a 3 dB sound pressure level (SPL) decay per doubling of distance (line sources), the interaural level difference is minimized across the entire listening area, which preserves the perceived directional balance. Regarding temporal density, experiments using a spatial granular synthesis approach suggested that surrounding sound events at random intervals of Δt < 20 milliseconds create a diffusely enveloping auditory event, which can be explained by the temporal integration of localization cues in the auditory system with time constants of 50 to 200 milliseconds. Moreover, experiments using a hemispherical loudspeaker arrangement demonstrate that envelopment and engulfment are perceptually distinct spatial attributes.
Whether localization, envelopment, and engulfment can be reproduced in a binaurally virtualized loudspeaker environment is investigated in the second part of the thesis. The dynamic virtualization developed for the experiments uses a six-degrees-of-freedom direct-sound rendering and a measurement-based three-degrees-of-freedom room acoustic auralization. Experiments were conducted in a studio environment using acoustically transparent headphones. This `in situ' methodolody allows for a direct comparison between the virtualized and the real loudspeaker environment, revealing spatial mapping errors caused by the binaural rendering. While the high-level sensations of envelopment and engulfment could be reproduced well using non-individual head-related transfer functions (HRTFs), vertical localization errors in the frontal area were found to notably distort the directional mapping in the virtualized loudspeaker environment.
This habilitation outlines the scientific works and methods undertaken to free virtual acoustic rendering based on the spherical harmonic basis functions (Ambisonics) from excessive wiggles, blur or poor robustness, and efforts undertaken to liberate the rendering of measured or recorded virtual environments of interest from fixed source and receiver directivities, or source and receiver locations. As a collection of works, the habilitation attempts to provide context and an overview of the papers, works, software, the contributions to the book Ambisonics, and projects accomplished to realize these goals, in many cases within a collaborative effort with master and doctoral students, and esteemed colleagues. (Works collected here in are nearly all available per given URL or DOI links).
Artificial reverberation (AR) models play a central role in various audio applications. Therefore, estimating the AR model parameters (ARPs) of a reference reverberation is a crucial task. Although a few recent deep-learning-based approaches have shown promising performance, their non-end-to-end training scheme prevents them from fully exploiting the potential of deep neural networks. This motivates the introduction of differentiable artificial reverberation (DAR) models, allowing loss gradients to be back-propagated end-to-end. However, implementing the AR models with their difference equations “as is” in the deep learning framework severely bottlenecks the training speed when executed with a parallel processor like GPU due to their infinite impulse response (IIR) components. We tackle this problem by replacing the IIR filters with finite impulse response (FIR) approximations with the frequency-sampling method. Using this technique, we implement three DAR models—differentiable Filtered Velvet Noise (FVN), Advanced Filtered Velvet Noise (AFVN), and Delay Network (DN). For each AR model, we train its ARP estimation networks for analysis-synthesis (RIR-to-ARP) and blind estimation (reverberant-speech-to-ARP) task in an end-to-end manner with its DAR model counterpart. Experiment results show that the proposed method achieves consistent performance improvement over the non-end-to-end approaches in both objective metrics and subjective listening test results.
Late reverberation involves the superposition of many sound reflections resulting in a diffuse sound field. Since the spatially resolved perception of individual diffuse reflections is impossible, simplifications can potentially be made for modelling late reverberation in room acoustics simulations with reduced spatial resolution. Such simplifications are desired for interactive, real-time virtual acoustic environments with applications in hearing research and for the evaluation of hearing supportive devices. In this context, the number and spatial arrangement of loudspeakers used for playback additionally affect spatial resolution. The current study assessed the minimum number of spatially evenly distributed virtual late reverberation sources required to perceptually approximate spatially highly resolved isotropic and anisotropic late reverberation and to technically approximate a spherically isotropic diffuse sound field. The spatial resolution of the rendering was systematically reduced by using subsets of the loudspeakers of an 86-channel spherical loudspeaker array in an anechoic chamber. It was tested whether listeners can distinguish lower spatial resolutions for the rendering of late reverberation from the highest achievable spatial resolution in different simulated rooms. Rendering of early reflections was kept fixed. The coherence of the sound field across a pair of microphones at ear and behind-the-ear hearing device distance was assessed to separate the effects of number of virtual sources and loudspeaker array geometry. Results show that between 12 and 24 reverberation sources are required.
A series of experiments was performed to analyze the linked activity of neurons recorded simultaneously in the sensorimotor and visual areas of the cortex in rabbits with a defensive dominant in the CNS. The dominant focus was formed in the CNS using threshold electrical stimulation of the left paw at a frequency of 0.5 Hz. The analysis showed that trained animals responded to the tone by twitching the paw only when functional connections formed closed circuits, with a variety of different configurations, providing for circulation of rhythmic information, in the intervals between tests. In addition, these studies showed that this information was retained for weeks.
Recent research related to artificial reverberation is reviewed. The focus is on research published during the past few years after the writing of an overview article on the same topic by the same authors. Advances in delay networks, convolution-based techniques, physical room models, and virtual analog reverberation models are described. Many new developments are related to the feedback delay network, which is still the most popular parametric reverberation method. Additionally, three specific methods are discussed in detail: velvet-noise reverberation methods, scattering delay networks, and a modal architecture for artificial reverberation. It becomes evident that research on artificial reverberation and related topics continues to be as active as ever. The related conference paper is available from the AES E-Library at http://www.aes.org/e-lib/browse.cfm?elib=18061.
Time-varying components are used in some multichannel sound systems
designed for the enhancement of room acoustics. Time-variation can
usefully reduce the risk of producing ringing tones and improve
stability margins, provided that any modulation artefacts are inaudible.
Frequency-shifting is one form of time-variation which provides the best
case improvement in loop gain, and for which the single channel
stability limit has been derived. This paper determines the stability
limit for multiple channel systems with frequency-shifting by
generalizing the previous single-channel analysis. It is shown that the
improvement in stability due to frequency-shifting reduces with the
number of channels. Simulations are presented to verify the theory. The
stability limits are also compared with those of time-invariant systems,
and preliminary subjective assessments are carried out to indicate
useable loop gains with frequency-shifting.
Image methods are commonly used for the analysis of the acoustic properties
of enclosures. In this paper we discuss the theoretical and practical
use of image techniques for simulating, on a digital computer, the
impulse response between two points in a small rectangular room.
The resulting impulse response, when convolved with any desired input
signal, such as speech, simulates room reverberation of the input
signal. This technique is useful in signal processing or psychoacoustic
studies. The entire process is carried out on a digital computer
so that a wide range of room parameters can be studied with accurate
control over the experimental conditions. A FORTRAN implementation
of this model has been included.
The feedback delay network (FDN) has been proposed for digital
reverberation, The digital waveguide network (DWN) is also proposed with
similar advantages. This paper notes that the commonly used FDN with an
N×N orthogonal feedback matrix is isomorphic to a normalized
digital waveguide network consisting of one scattering junction joining
N reflectively terminated branches. Generalizations of FDNs and DWNs are
discussed. The general case of a lossless FDN feedback matrix is shown
to be any matrix having unit-modulus eigenvalues and linearly
independent eigenvectors. A special class of FDNs using circulant
matrices is proposed. These structures can be efficiently implemented
and allow control of the time and frequency behavior. Applications of
circulant feedback delay networks in audio signal processing are
discussed
This paper presents a new time-variant reverberation algorithm that can be used in reverberation enhancement systems. In these systems, acoustical feedback is always present and time variance can be used to obtain more gain before instability (GBI). The presented time-variant reverberation algorithm is analyzed and results of a practical GBI test are presented. The proposed reverberation algorithm has been used successfully with an electro-acoustically enhanced rehearsal room. This particular application is briefly overviewed and other possible applications are discussed.
If a Banach space is endowed with the additional geometric structure of an inner product, one obtains a Hilbert space, which preserves many further properties of a finite-dimensional vector space. In particular, one has the useful tools of orthogonal projections and orthonormal bases.
The problem of the bounded-input/bounded-output stability of time-varying recursive filters is discussed. While simple, well-known criteria exist for the stability of time-invariant filters, guaranteeing stability when the filter coefficients are allowed to vary is much more difficult. Better insight into the causes for instability can be gained by using the state-space representation of the filter and examining the singular values of the state transition matrix. Two simple criteria based on the state transition matrix can be derived that guarantee the stability of the time-varying filter. Moreover, in the second-order case the singular values of this matrix provide a useful estimate of the maximum and average signal gains that result from the modification of the filter coefficients. These estimates can be used in practice to keep a time-varying filter from blowing up. It is also shown that some filter topologies are better suited to time-varying filtering than others, and a few techniques are presented that can be used to stabilize an otherwise unstable time-varying filter.
An artificial reverberator is described which has a flat amplitude‐frequency response and therefore does not alter the spectral balance or “color” of the reverberated sound. Neither does the reverberator add any extraneous hollow, reedy, or metallic qualities or flutter echoes of its own. The number of echoes per second increases with time according to the same law governing the echo statistics of a real room. Thus, it is compatible with the most exacting fidelity requirements in sound recording, home use, and the electroacoustic conversion of auditoriums and theaters, designed primarily for speech, into concert halls. In the last application, the flat amplitude‐frequency response of the reverberator minimizes acoustic feedback problems associated with other artificial reverberation devices.
Comb filters composed in a parallel or a serial way are a popular part of delay-line based artificial reverberators. Because the analysis of a complex comb filter structure can be tedious, there is a need for transforming such a structure into a compact and general representation. For this a transformation into the feedback delay network (FDN) filter structure is proposed as it is a general and well established framework to investigate the acoustic properties of the filter and therefore allows to compare different approaches. Index Terms ?? comb filter, feedback delay network, artificial reverberation
In reverberation enhancement systems (RESs), sound is constantly fed back from multiple microphones to multiple loudspeakers to enhance reverberation artificially in the target room. This contribution shows that such a system can be understood as an extended feedback delay network (FDN). A tuning process, similar to that of the FDN is presented, allowing arbitrary frequency-dependent reverberation elongation. The cross-talk between the loudspeakers and the microphones leads to comb filtering and isolated ringing modes in the RES, which produce undesired metallic and rough sounds. To mitigate these undesired effects, a cross-talk cancellation system is integrated in the RES. In a simulation example, the benefits of cross-talk cancellation is evaluated.
Some linear time-varying (LTV) components used to control feedback in sound systems were tested experimentally in real-time simulators and rooms with and without external reverberation. Gain before instability (GBI) was measured in single channels employing frequency shifting (FS), phase modulation (PM), and delay modulation (DM) implemented on a digital signal processor. FS performed according to the established theory. For PM GBI increased almost monotonically with modulation index beta, except for cases with large loop gain irregularities which displayed a reduced GBI for values of beta that corresponded to low carrier suppression. Also, GBI was practically independent of the modulation frequency f(m) already from 0.5 Hz even when this was much lower than the correlation distance of the loop gain transfer function. Rooms with different reverberation times gave different initial (time-invariant) GBI values but these differences decreased by the use of modulation. The GBI increase was larger for cases with external reverberation than for cases without clue to increased loop gain irregularity, and the GBI results depended on f(m). Since the possible GBI increase is determined by the initial GBI, LTV system performance should be measured in terms of GBI and not GBI increase alone. Robustness increased by equalizing the loop gain before employing LTV components. DM gave little protection for low frequencies but was efficient at high frequencies. (C) 1999 Acoustical Society of America. [S0001-4966(99)03407-4].
A comprehensive review of FIR (Finite Impulse Response) and allpass filter design techniques for bandlimited approximation of a fractional digital delay is presented. Emphasis is on simple and efficient methods that are well suited for fast coefficient update or continuous control of the delay value. Several new approaches are proposed and numerous examples are provided that illustrate the performance of the methods.
A new method for the calculation of room acoustical impulse responses is described, which is based on two well‐known computer algorithms, the ray‐tracing and the image‐source models. With the new method, the procedure of sieving the ‘‘visible’’ image sources out of the enormous quantity of possible sources is carried out by examination of the histories of sound particles. From the obtained list of visible image sources, the impulse response of the enclosure is easily constructed. The new method combines the advantages of the ray‐tracing process, namely, the relatively slow increase of computation time with the length of the impulse response, with the accuracy inherent to the image‐source model, which is even sufficient to calculate the Fourier transform, i.e., the steady‐state transmission function of the room, or to convolve the impulse response with sound signals.
The paper is a tutorial intended to serve as a reference in the field of digital audio effects in the electronic music industry for those who are new to this specialization of digital signal processing. The effects presented are those that are demanded most often, hence they will serve as a good toolbox. The algorithms chosen are of such a fundamental nature that they will find application ubiquitously and often.
The paper is a tutorial intended to serve as a reference in the field of digital audio effects in the electronic music industry for those who are new to this specialization of digital signal processing. The effects presented are those that are demanded most often, hence they will serve as a good toolbox. The algorithms chosen are of such a fundamental nature that they will find application ubiquitously and often.
A general approach is proposed to the problem of realizing a recursive digital display network capable of simulating in real time the perceptively relevant characteristics of the reverberation decay in a room. The analysis/synthesis method presented makes it possible to imitate the late reverberation of a given room by optimizing some of the reverberant filter's parameters. The analysis phase is based on a time-frequency representation of the energy decay, computed from an impulse response measured in the room. The energy decay relief is proposed as a spectral development of the integrated energy decay curve introduced by Schroeder. Its three-dimensional representation allows perceptively relevant visual comparison of two room responses (measured or artificial) and accurate calculation of some widely used objective criteria of room acoustic quality.
The first artificial reverberation algorithms were proposed in the early 1960s, and new, improved algorithms are published regularly. These algorithms have been widely used in music production since the 1970s, and now find applications in new fields, such as game audio. This overview article provides a unified review of the various approaches to digital artificial reverberation. The three main categories have been delay networks, convolution-based algorithms, and physical room models. Delay-network and convolution techniques have been competing in popularity in the music technology field, and are often employed to produce a desired perceptual or artistic effect. In applications including virtual reality, predictive acoustic modeling, and computer-aided design of acoustic spaces, accuracy is desired, and physical models have been mainly used, although, due to their computational complexity, they are currently mainly used for simplified geometries or to generate reverberation impulse responses for use with a convolution method. With the increase of computing power, all these approaches will be available in real time. A recent trend in audio technology is the emulation of analog artificial reverberation units, such as spring reverberators, using signal processing algorithms. As a case study we present an improved parametric model for a spring reverberation unit.
Artificial reverberator topologies making use of all-pass filters in a feedback loop are popular, but have lacked accurate control of decay time and energy level. This paper reviews a general theory of artificial reverberators based on Unitary-Feedback Delay Networks (UFDN), which allow accurate control of the decay time at multiple frequencies in such topologies. We describe the design of an efficient reverberator making use of chains of elementary filters, called "absorbent all-pass filters", in a feedback loop. We show how, in this particular topology, the late reverberant energy level can be controlled independently of the other control parameters. This reverberator uses the I3DL2 control parameters, which have been designed as a standard interface for controlling reverberators in interactive 3D audio.
This chapter discusses reverberation algorithms, with emphasis on algorithms that can be implemented for realtime performance.
The chapter begins with a concise framework describing the physics and perception of reverberation. This includes a discussion
of geometrical, modal, and statistical models for reverberation, the perceptual effects of reverberation, and subjective and
objective measures of reverberation. Algorithms for simulating early reverberation are discussed first, followed by a discussion
of algorithms that simulate late, diffuse reverberation. This latter material is presented in chronological order, starting
with reverberators based on comb and allpass filters, then discussing allpass feedback loops, and proceeding to recent designs
based on inserting absorptive losses into a lossless prototype implemented using feedback delay networks or digital waveguide
networks.
This paper illustrates the use of a numerical time-domain simulation based on the finite-difference time-domain (FDTD) approximation for studying low- and middle-frequency room acoustic problems. As a direct time-domain simulation, suitable for large modeling regions, the technique seems a good ''brute force'' approach for solving room acoustic problems. Some attention is paid in this paper to a few of the key problems involved in applying FDTD: frequency-dependent boundary conditions, non-Cartesian grids, and numerical error. Possible applications are illustrated with an example. An interesting approach lies in using the FDTD simulation to adapt a digital filter to represent the acoustical transfer function from source to observer, as accurately as possible. The approximate digital filter can be used for auralization experiments. (C) 1995 Acoustical Society of America.
Many recent publications in audio research present subjective evaluations of audio quality based on the Recommendation ITU-R BS.1534-1 (MUSHRA, MUltiple Stimuli with Hidden Reference and Anchor). This is a very welcome trend because it enables researchers to assess the implications of their developments. The evaluation of listening tests, however, sometimes sufers from an incomplete understanding of the underlying statistics. The present paper aims at identifying the causes for the pitfalls and misconceptions in MUSHRA evaluations. It exemplifes the impact of falsely used or even misused statistics. Subsequently, schemes for evaluating the listeners' judgments that are well-grounded on statistical considerations comprising an understanding of the concepts of statistical power and efect size are proposed.
Electronic devices are widely used to introduce in sound signals an artificial reverberation subjectively similar to that caused by multiple reflections in a room. Attention is focused on those devices employing delay loops. Usually, these devices have a comb-like frequency response which adds an undesired "color" to the sound quality. Also, for a given reverberation time, the density of echoes is far below that encountered in a room, giving rise to a noticeable flutter effect in transient sounds. A class of all-pass filters is described which may be employed in cascade to obtain "colorless" reverberation with high echo density.
A unitary n-input n-output linear network preserves the total energy of all input signals. Using the functional calculus of normal matrices, it is proved that feedback round a unitary circuit plus a direct path with suitable gain yields another unitary circuit. This has applications to the design of electronic reverberation units.
A fractional delay filter is a device for bandlimited
interpolation between samples. It finds applications in numerous fields
of signal processing, including communications, array processing, speech
processing, and music technology. We present a comprehensive review of
FIR and allpass filter design techniques for bandlimited approximation
of a fractional digital delay. Emphasis is on simple and efficient
methods that are well suited for fast coefficient update or continuous
control of the delay value. Various new approaches are proposed and
several examples are provided to illustrate the performance of the
methods. We also discuss the implementation complexity of the
algorithms. We focus on four applications where fractional delay filters
are needed: synchronization of digital modems, incommensurate sampling
rate conversion, high-resolution pitch prediction, and sound synthesis
of musical instruments.
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Splitting the unit delay—Tools for fractional delay filter design
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Delay line modulation and chorus
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Norms, inner products, and orthogonality
Reveberation algorithms
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