Fig 8 - uploaded by Fritz Menzer
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Evolution of the two most extreme cases of mixing matrices for " reverberator " scenario. Top: 50 × 50 identity matrix. Bottom: 12 × 12 random unitary matrix.
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This paper presents different methods for designing unitary mixing matrices for Jot reverberators with a particular emphasis on cases where no early reflections are to be modeled. Possible applications include diffuse sound reverberators and decorrelators. The trade-off between effective mixing between channels and the number of multiply operations...
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Citations
... The primary criterion for choosing the feedback matrix for an FDN is ensuring losslessness of the structure, i.e., the energy of the system should not decay when the attenuation filters are not in use [202,203,250]. Apart from this, the matrices are also used to enhance specific properties of the FDN, such as the increase in the echo density, computational efficiency, and spectral flatness [26,225,226,251,252,253]. ...
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.
... The choice of the feedback matrix is crucial for the FDN algorithm to work correctly. The popular matrix types used in FDN implementations that fulfill the requirement of being unilossless are Hadamard [27], Householder [27], random orthogonal, and identity matrices [28]. Where the first three are chosen to enhance specific properties of the algorithm, e.g., density of the impulse response, the identity matrix, however, reduces the FDN to a Schroeder reverberator, or a parallel set of comb filters [6,28]. ...
... The popular matrix types used in FDN implementations that fulfill the requirement of being unilossless are Hadamard [27], Householder [27], random orthogonal, and identity matrices [28]. Where the first three are chosen to enhance specific properties of the algorithm, e.g., density of the impulse response, the identity matrix, however, reduces the FDN to a Schroeder reverberator, or a parallel set of comb filters [6,28]. The plugin presented in this study allows the user to choose between these four matrices through a drop-down menu and to learn about the differences in the sound obtained by changing this part of the FDN reverberator. ...
Reverberation is one of the most important effects used in audio production. Although nowadays numerous real-time implementations of artificial reverberation algorithms are available, many of them depend on a database of recorded or pre-synthesized room impulse responses, which are convolved with the input signal. Implementations that use an algorithmic approach are more flexible but do not let the users have full control over the produced sound, allowing only a few selected parameters to be altered. The real-time implementation of an artificial reverberation synthesizer presented in this study introduces an audio plugin based on a feedback delay network (FDN), which lets the user have full and detailed insight into the produced reverb. It allows for control of reverberation time in ten octave bands, simultaneously allowing adjusting the feedback matrix type and delay-line lengths. The proposed plugin explores various FDN setups, showing that the lowest useful order for high-quality sound is 16, and that in the case of a Householder matrix the implementation strongly affects the resulting reverberation. Experimenting with delay lengths and distribution demonstrates that choosing too wide or too narrow a length range is disadvantageous to the synthesized sound quality. The study also discusses CPU usage for different FDN orders and plugin states.
... The dense set of late reflections are added by a feedback network. Matrix theory has been invoked for the design of "good reverberation" [5][6][7][8]. ...
... To preserve the stability of the system, the matrix U d has to be a unitary matrix, which restricts the design of U in the s-domain to skew-hermitian matrices. For practical applications it is suitable to design the matrix U d directly [5][6][7]. ...
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.
... Various unitary feedback matrices have been proposed to enhance specific properties of the FDN: computational efficiency (circulant [1], sparse [171], Householder [161]), dense impulse response (Hadamard [161], circulant based on Gallois sequences [172]), fitness to measured impulse response with a genetic algorithm [95], spectral flatness [173] and approximating a geometric model [94,174]. • block triangular concatenation: By Theorem 8, two unilossless matrices E and F may be concatenated into a block triangular matrix E G 0 F where G is an arbitrary matrix. ...
... m N are the lengths of the N delays in samples. The echo density of the parallel comb-filter section is constant over time and it was soon realized that the echo density can be increased by interconnecting the feedback of the comb-filters resulting in the Feedback Delay Network (FDN)[161,171,172].In this chapter, we determine the echo density of an FDN over time and by this provide insight into the temporal evolution and the mixing time of an FDN's impulse response.Opposed to counting echoes in the impulse response, the presented prediction method gives means to determine the analytic properties of the echo density. It is shown that, under certain assumptions, the echo density follows a polynomial function. ...
In today's audio production and reproduction as well as in music performance practices it has become common practice to alter reverberation artificially through electronics or electro-acoustics. For music productions, radio plays, and movie soundtracks, the sound is often captured in small studio spaces with little to no reverberation to save real estate and to ensure a controlled environment such that the artistically intended spatial impression can be added during post-production. Spatial sound reproduction systems require flexible adjustment of artificial reverberation to the diffuse sound portion to help the reconstruction of the spatial impression. Many modern performance spaces are multi-purpose, and the reverberation needs to be adjustable to the desired performance style. Employing electro-acoustic feedback, also known as Reverberation Enhancement Systems (RESs), it is possible to extend the physical to the desired reverberation. These examples demonstrate a wide range of applications where reverberation is created and enhanced artificially employing signal processing techniques. A major challenge of designing artificial reverberators is the high complexity of the physical reverberation process. Even small office spaces of 40 m^3 exhibit more than 10^7 acoustic modes, in concert halls the number of acoustic modes can surpass 10^9 in the audible range. The room geometry, as well as the interaction with the boundary materials, can be as well fairly complex. Whereas these complex considerations are mandatory for simulations of specific spaces, used for example for the acoustic and architectural planning of a concert venue, they are somewhat misleading in the realm of artistic applications. The focus on perceptually convincing artificial reverberation algorithms provides the freedom to make some simplifications to the generation process, leading to the recursive systems, which play a central role in this dissertation. Two specific formulations of recursive systems for artificial reverberation are considered: Firstly, Feedback Delay Networks (FDNs) which are built around multiple delays which are fed back to their inputs and by this mimic the recursive process of sound waves bouncing back and forth in an acoustic space. And secondly, RESs, which are installed in rooms to extend the physical reverberation via electro-acoustic feedback between microphones and loudspeakers. The main objective of artificial reverberators is to recreate and enhance room impulse responses while considering three aspects: i) accurate recreation of physical spaces; ii) delivering perceptually convincing spaces; and iii) efficiency of processing and parameterization. The primary goal of this dissertation is to achieve better control over the evolution of the artificial reverberation over time, namely the evolution of normal modes and reflections over time. The decay rate of normal modes most importantly determines the stability of the system, but also the perceptual quality of the artificial reverberation. For this purpose, existing network topologies for artificial reverberation are unified in the general FDN framework. For the FDN, an analytic formulation of the polynomial governing the recursive behavior is presented from which analytic constraints on the angular distribution of the decaying modes are derived. Lossless FDNs are commonly used as a design prototype for artificial reverberation algorithms for which all normal modes neither decay nor rise. 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. This work presents the most general class of feedback matrices which constitutes lossless FDNs regardless the lengths of the delays. As a secondary goal, the temporal features of impulse responses produced by FDNs, i.e., the number of echoes per time interval and its evolution over time, are analyzed. This so-called echo density is related to known measures of mixing time and their psychoacoustic correlates such as perception of the room size. It is shown that the echo density of FDNs follows a polynomial function, whereby the polynomial coefficients can be derived from the lengths of the delays for which an explicit method is given. The mixing time of impulse responses can be predicted from the echo density, and conversely, the desired mixing time can be achieved by a derived mean delay length. In the last part of this dissertation, a novel time-variant reverberation algorithm is introduced. By modulating the feedback matrix nearly continuously over time, an intricate pattern of concurrent amplitude modulations of the feedback paths evolves. It is demonstrated that the perceived quality of the decaying normal modes can be enhanced by the feedback matrix modulation. The same technique of time-varying feedback matrices is applied in multichannel sound systems to improve the system's stability. It is shown with a statistical approach that time-varying mixing matrices can achieve optimal stability improvement for a higher number of channels. A listening test demonstrates the improved quality of time-varying mixing matrices over comparable existing techniques.
... Notice the absorption filters in the feedforward path that allow controlling the decay rate at different frequencies, and a tonal correction filter that is used to equalize the reverberator frequency response so that the generated reverberation sounds more natural. 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.
... This can be accounted to the FDN's flexibility in design, computational efficiency, and independent control over energy decay, amount of diffusion and total energy in each frequency band [13]. Further work has been done to maximize the echo density of FDNs by using specific feedback matrices [18]- [20]. ...
Feedback delay networks (FDNs) are frequently used to generate artificial reverberation. This contribution discusses the temporal features of impulse responses produced by FDNs, i.e., the number of echoes per time unit and its evolution over time. This so-called echo density is related to known measures of mixing time and their psychoacoustic correlates such as auditive perception of the room size. It is shown that the echo density of FDNs follows a polynomial function, whereby the polynomial coefficients can be derived from the lengths of the delays for which an explicit method is given. The mixing time of impulse responses can be predicted from the echo density, and conversely, a desired mixing time can be achieved by a derived mean delay length. A Monte Carlo simulation confirms the accuracy of the derived relation of mixing time and delay lengths.
... Various unitary feedback matrices have been proposed to enhance specific properties of the FDN: computational efficiency (circulant [10], sparse [31], Householder [14]), dense impulse response (Hadamard [14], circulant based on Gallois sequences [32]), fitness to measured impulse response with a genetic algorithm [33], spectral flatness [34] and approximating a geometric model [35], [36]. All those examples of feedback matrices are unitary and therefore by Lemma 1 unilossless. ...
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.
... There are also works which proposed novel feedback delay structures [Dahl and Jot, 2000] or feedback matrices [Menzer and Faller, 2010;Rocchesso, 1997]. [Frenette, 2000] [Välimäki et al., 2012]. ...
There is an increasing interest in creating interactive virtual worlds due to the wide variety of potential applications in entertainment and education. The 3D acoustic scene can be synthesized from two perspectives : the physical approaches and the perceptual approaches. Acoustic radiance transfer method is an efficient ray-based method to model the diffuse reflections and the late reverberation. An extension of the Radiance Transfer Method (RTM) is proposed in this thesis, which allows modeling the early part of specular reflections while keeping the advantage of the original model for the late reverberation simulation. Feedback delay networks are widely used structures to generate the late reverberation. A new method is presented in this thesis, which inherits the efficiency of the Feedback Delay Network (FDN) structure, but aims at linking the parameters of the FDN directly to the geometries of the modeled environment. The relation is achieved by assigning a physical meaning to each delay line and studying the sound energy exchange between them. Then the physical approachand the perceptual approach are combined. The simplified acoustic Radiance Transfer Method, with extension for both specular and diffuse reflections, is incorporated with the Feedback Delay Networks. The new reverberator, despite of modeling the diffuse and late reverberation, is also capable of simulating the early and specular reflections with accuracy.
... To achieve a high-quality late reverberation, the feedback loop should be lossless, i.e. energypreserving, hence typically the feedback matrix A is designed to be unitary. Each particular choice of the feedback matrix has corresponding implications on subjective or objective qualities of the reverberator [32]; e.g. in the particular case of the identity matrix, A = I, the FDN structure reduces to N comb filters connected in parallel and acts as the Schroeder reverberator [3]. Note, however that unitary matrices are only a subset of possible lossless feedback matrices [10], [33]; we elaborate on this point in the next subsection. ...
An acoustic reverberator consisting of a network of delay lines connected via
scattering junctions is proposed. All parameters of the reverberator are
derived from physical properties of the enclosure it simulates. It allows for
simulation of unequal and frequency-dependent wall absorption, as well as
directional sources and microphones. The reverberator renders the first-order
reflections exactly, while making progressively coarser approximations of
higher-order reflections. The rate of energy decay is close to that obtained
with the image method (IM) and consistent with the predictions of Sabine and
Eyring equations. The time evolution of the normalized echo density, which was
previously shown to be correlated with the perceived texture of reverberation,
is also close to that of IM. However, its computational complexity is one to
two orders of magnitude lower, comparable to the computational complexity of a
feedback delay network (FDN), and its memory requirements are negligible.
... Algorithms based on delay networks are comprised of delays, filters, and feedback paths and they are characterized by low memory requirements, low computational complexity, and good parameterization but often lacking realism. The original algorithms by Schroeder and Logan, which were subsequently improved by Moorer [4], and the feedback delay networks (FDN) originally proposed by Jot and Chaigne are popular examples of delay network algorithms [5,6,7,8]. ...
An efficient algorithm approximating the late part of room reverberation is proposed. The algorithm partitions the impulse response tail into variable-length segments and replaces them with a set of sparse FIR filters and lowpass filters, cascaded with several Schroeder allpass filters. The sparse FIR filter coefficients are selected from a velvet noise sequence, which consists of ones, minus ones, and zeros only. In this application, it is sufficient perceptually to use very sparse velvet noise sequences having only about 0.1 to 0.2% non-zero elements, with increasing sparsity along the impulse response. The algorithm yields a parametric approximation of the late part of the impulse response, which is more than 100 times more efficient computationally than the direct convolution. The computational load of the proposed algorithm is comparable to that of FFT-based partitioned convolution techniques, but with nearly half the memory usage. The main advantage of the new reverberator is the flexible parameterization.
