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![Time-domain filter coefficients of the adjugate adj(P (z)) of a MIMO FDN with four delay lines (N = 4) and with a random orthogonal feedback matrix A. The delays are m = [977, 683, 981, 801] samples. The entire adjugate adj(P (z)) is displayed without truncation. Only the non-zero values are drawn with stems for better readability.](publication/373929728/figure/fig1/AS:11431281188777335@1694781262935/Time-domain-filter-coefficients-of-the-adjugate-adjP-z-of-a-MIMO-FDN-with-four-delay.png)
Time-domain filter coefficients of the adjugate adj(P (z)) of a MIMO FDN with four delay lines (N = 4) and with a random orthogonal feedback matrix A. The delays are m = [977, 683, 981, 801] samples. The entire adjugate adj(P (z)) is displayed without truncation. Only the non-zero values are drawn with stems for better readability.
Source publication
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 analysi...
Contexts in source publication
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... the following, we investigate the correlation of the filters in adj(P (z)). Fig. 2 shows an example adj(P (z)) for N = 4. The adjugate matrix adj(P (z)) can be expressed by co-factors, ...
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... illustrate the adjugate matrix by giving a small-scale example. Fig. 2 depicts the time-domain filter coefficients of the feedforward paths adj(P (z)) for an FDN with four delays, i.e., N = 4 and delays between 300 and 1000 samples. Each matrix entry is a sparse finite impulse response (FIR) filter, with 2 N −1 = 8 non-zero pulses (for the diagonal elements) and 2 N −2 = 4 non-zero pulses (for the ...
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... response (FIR) filter, with 2 N −1 = 8 non-zero pulses (for the diagonal elements) and 2 N −2 = 4 non-zero pulses (for the non-diagonal elements). For small N , the feedforward filters tend to be sparse. Figure 3 depicts the decomposition (11) of the feedforward and recursive portion of the FDN impulse response for the same MIMO FDN as shown in Fig. 2. The feedforward paths are the paths from the first input to the first output channel, the recursive response is the time-domain form of 1/p m,A (z), and the convolution of both sequences results in the impulse response between the respective input and output channels. We observe that the recursive response is denser, i.e., with more ...
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... adjugate adj(P (z)) is only a comparably short filter, and therefore it is not guaranteed to decorrelate the channels strongly. In the following, we study the inter-channel correlation of the FDN, particularly the feedforward paths. The Matlab-code for repeating the numerical results of this paper is available in GitHub 1 . Fig. 2. The white cell color indicates the maximum correlation for each pair of transfer function elements, whereas a darker color indicates a lower correlation, i.e., a better ...
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... ϕ ijkl is the cross-correlation between the two filters (adj P (z)) ij and (adj P (z)) kl . The diagonal contains the autocorrelations and is normalized to 1, whereas the remaining values are between 0 and 1. Fig. 4 shows the 16-by-16 inter-channel correlation matrix for the same FDN as in Fig. 2, which has the size N = 4. The range of the correlation values is between 0.70 and 0.95. For further summarized statistics, the median is applied to the non-diagonal elements of the inter-channel correlation matrix, ...
Citations
... The main use of velvet noise in audio engineering has been reverberation algorithms based on feedback [1][2][3][4] and feedforward structures [1,[5][6][7][8]]. Another application of velvet noise is the decorrelation of audio signals [9][10][11][12], a process that allows reducing the correlation of signals [13,14] and, for example, distributing processed copies of a mono signal to multiple loudspeakers to produce a diffuse sound field [15,16]. Velvet noise has also been used in sound [17][18][19][20] and speech synthesis [21,22]. ...
Velvet noise, a sparse pseudo-random signal, finds valuable applications in audio engineering , such as artificial reverberation, decorrelation filtering, and sound synthesis. These applications rely on convolution operations whose computational requirements depend on the length, sparsity, and bit resolution of the velvet-noise sequence used as filter coefficients. Given the inherent sparsity of velvet noise and its occasional restriction to a few distinct values, significant computational savings can be achieved by designing convolution algorithms that exploit these unique properties. This paper shows that an algorithm called the transposed double-vector filter is the most efficient way of convolving velvet noise with an audio signal. This method optimizes access patterns to take advantage of the processor's fast caches. The sequential sparse algorithm is shown to be always faster than the dense one, and the speedup is linearly dependent on sparsity. The paper also explores the potential for further speedup on multicore platforms through parallelism and evaluates the impact of data encoding, including 16-bit and 32-bit integers and 32-bit floating-point representations. The results show that using the fastest implementation of a long velvet-noise filter, it is possible to process more than 40 channels of audio in real time using the quad-core processor of a modern system-on-chip.
In real-time applications, like interactive virtual reality environments, there is a significant need for low-complexity simulation of room impulse responses in highly complex virtual scenes, but this remains a challenging issue. In particular, simulating late reverberation using physically based acoustic modeling requires much computational effort, contrary to the early reflections that can be modeled by simpler techniques, e.g., the image source method. To tackle this computational complexity issue, we propose a neural network-based hybrid artificial reverberation framework (Echo2Reverb) that generates late reverberation from given early reflections. The proposed model can control both temporal texture and frequency-dependent energy decay, i.e., echo density and spectral energy distribution, of the generated reverberations by extracting spectral and echo-related features and filtering sampled sparse sequences and Gaussian noises using estimated features. To support the end-to-end training with controlled echo density, a differentiable approximation of the normalized echo density profile is proposed. We train and test the model not only for nearly diffuse but also distinct echoes prominent in late reverberations, such as with flutter echoes in narrow corridors. Evaluation results demonstrate that the proposed model can accurately reproduce frequency-dependent energy decay and temporal texture of a room impulse response using only early reflections.
