A New Reverberator Based on Variable Sparsity Convolution

Abstract

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.

Full text

Proc. of the 16th Int. Conference on Digital Audio Effects (DAFx-13), Maynooth, Ireland, September 2-6, 2013
A NEW REVERBERATOR BASED ON VARIABLE SPARSITY CONVOLUTION
Bo Holm-Rasmussena,b
aAcoustic Technology
Department of Electrical Engineering
Technical University of Denmark
Kgs. Lyngby, Denmark
Heidi-Maria Lehtonenband Vesa Välimäkib
bDepartment of Signal Processing and Acoustics
School of Electrical Engineering
Aalto University
Espoo, Finland
ABSTRACT
An efficient algorithm approximating the late part of room rever-
beration is proposed. The algorithm partitions the impulse re-
sponse 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 se-
lected from a velvet noise sequence, which consists of ones, minus
ones, and zeros only. In this application, it is sufficient perceptu-
ally 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 approxima-
tion of the late part of the impulse response, which is more than
100 times more efficient computationally than the direct convolu-
tion. The computational load of the proposed algorithm is compa-
rable 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.
1. INTRODUCTION
Artificial reverberation has been a popular audio effect since the
early studio recordings almost a century ago. Rooms and halls
are considered being both linear and time-invariant (LTI) systems,
regarding sound in the audible range. Therefore the sonic char-
acteristic of a specific concert hall can be replicated by an LTI
system having the same impulse response. Impulse responses of
concert halls normally contain three important phases: the direct
(a.k.a. dry) sound, the early reflections, and the late reverberation
which has dense reflections [1].
Many artificial digital reverberation algorithms have been de-
scribed since Schroeder and Logan published the first one in the
early 1960s [2, 3]. The realtime algorithms are often categorized
as based on either delay networks, convolution or a hybrid [1].
Algorithms based on delay networks are comprised of delays, fil-
ters, and feedback paths and they are characterized by low mem-
ory requirements, low computational complexity, and good pa-
rameterization 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 net-
work algorithms [5, 6, 7, 8].
Convolution by the desired room impulse response (RIR) re-
sults in very realistic reverberation but is difficult to parameterize;
the partitioned fast convolution method reduces the computational
complexity considerably compared to direct (FIR filter) convolu-
tion and avoids the delay introduced by full-length FFT convolu-
tion [9, 10]. A recent article by Välimäki et al. provides a thorough
overview of the development of artificial reverberation [1].
In this paper a novel hybrid late reverberation algorithm based
on convolution, implemented as sparse FIR (SFIR) filters, and op-
timized with delay network elements is presented. The SFIR co-
efficients are extracted from a specific kind of white noise known
as velvet noise [11, 12]. Schroeder allpass (SAP) filters [2] are
used to allow SFIR filters with greater sparsity to be used. The
motivations for this work have been the desire to find a compu-
tationally efficient and flexible reverb algorithm, which would be
easy to control and to calibrate to a recorded RIR.
The SFIR filters in the proposed algorithm can be seen as
an unwrapped FIR version of the late reverberation algorithms
based on a single SFIR filter and a feedback loop first proposed by
Rubak and Johansen [13, 14]. Later Karjalainen and Järveläinen
refined the algorithm both sonically and in terms of lower com-
putational complexity by using sparse coefficients extracted from
velvet noise, and by continuously updating the sparse coefficients
[11]. Recently Lee et al. [15] have proposed several ways of im-
proving the sonic qualities of this kind of algorithm further, mainly
by how the update of the sparse coefficients takes place. The soni-
cally most promising of these algorithms sounds reasonably good
for most input signals but the performance of the algorithm is diffi-
cult to foresee because of its time variance. Moreover, it can only
replicate RIRs with strictly exponentially decaying reverberation
times because the filter attenuator is in a feedback loop.
The proposed reverberator provides high-quality zero-delay
diffuse late reverberation sonically comparable to convolution and
with similar computational complexity, latency, and approximately
half the memory requirements compared to the partitioned fast
convolution. The spectral coloration and decay can easily be indi-
vidually controlled by a set of filters and attenuators for artistic fine
tuning and abstract reverberation effects, e.g. non-exponentially
decaying reverberation as in [16]. All elements of the proposed
algorithm are LTI which means that the common linear signal pro-
cessing theory can be applied without approximations as opposed
to the time-varying algorithms, e.g. [11, 15, 17]. This kind of re-
verberator is suitable for many applications for example in game
audio, live music, and music production.
The following section of this paper describes velvet noise.
Section 3 presents the proposed algorithm. Section 4 shows how
well the algorithm can fit the reverberation of a real concert hall.
Section 5 compares the computational complexity and memory us-
age with other algorithms, finalizing this paper with a conclusion
in Section 6.
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Figure 1: Velvet noise generator. (a) The algorithm is initiated with
an impulse, (b) which is converted into an endless pulse train, next
(c) the variable delay line adds jitter to the distance between the
neighboring pulses, and finally (d) the switch changes the sign of
some of the pulses. The outcome of these phases are illustrated in
Figure 2 (a) to (d), respectively.
2. VELVET NOISE
2.1. Generation of velvet noise
The specific kind of sparse white noise known as velvet noise was
introduced in 2007 by Karjalainen and Järveläinen [11]. A more
recent study [12] explains the generation of velvet noise as a jit-
tered pulse train with randomly selected sign which gives a se-
quence of zeros with few +1 or −1sample values. The pulse
locations are defined as
k(m) = round[m Td+r1(m) (Td−1)] ,(1)
where mis the integer pulse counter, r1(m)is a random value
uniformly distributed in the range from 0 to 1, and Tdis the aver-
age distance between pulses. The −1in equation (1) is to avoid
coinciding pulses [12]. The sign of each pulse is chosen by the
following definition
s(n) = 2round[r2(m)] −1, if n=k(m)
0, otherwise (2)
where nis the integer sample counter and r2(m)is another ran-
dom value again uniformly distributed in the range from 0 to 1.
This means that velvet noise has one parameter besides its level
that is the average distance between pulses, Td.
Generation of velvet noise can be described by the block dia-
gram implementation shown in Figure 1. Figure 2 shows a signal
at the four different positions, (a) to (d), of Figure 1. Both fig-
ures illustrate that (a) the algorithm is initiated by an impulse, (b)
which the non-attenuating feedback loop converts into an endless
pulse train, (c) the variable delay line triggered by the pulses adds
jitter uniformly distributed between the pulses in the pulse train
avoiding coinciding pulses, and (d) the random-controlled switch
also triggered by the pulses changes the sign of some of the pulses
resulting in velvet noise. The shown signal is 500 samples long
with an average pulse density, 1/Td, of 2205 pulses/s and 44.1 kHz
sample frequency corresponding to an average pulse period of 20
samples1. The block diagram corresponds to reformulating (1) as
k(m) = round[m Td] + round[r1(m) (Td−1)]
  
c(m)
,(3)
where the second half corresponds to c(m)in Figure 1. The gen-
erator produces velvet noise in integer values of Td.
1Td= 20 samples results in exactly 25 non-zero samples for a velvet
noise sequence 500 samples long.
(a)
(b)
(c)
(d)
Time [samples]
Figure 2: Generation of 500 samples of velvet noise. The signal is
shown for the four different positions in the velvet noise generator
illustrated in Figure 1; (a) the initiating impulse, (b) pulse train,
(c) jittered pulse train, and (d) the resulting velvet noise sequence.
Only the non-zero samples are shown.
2.2. Properties of velvet noise
Listening tests [11, 12] showed that broadband velvet noise with
average pulse densities above approximately 2000 pulses/s sounds
even smoother (i.e., less rough) than Gaussian white noise pre-
sented at the same RMS level. Another conclusion from [11] was
that lowpass filtered (fc= 1.5 kHz) velvet noise sounds smoother
than Gaussian white noise even down to the lowest tested average
pulse density of 600 pulses/s. In the more recent study [12] lis-
tening tests showed that velvet noise is the noise perceived as the
smoothest among six comparable algorithms with average pulse
densities at or below 2000 pulses/s further indicating that velvet
noise is a well suited sparse noise for efficient late reverberation.
Two important properties of velvet noise make it very suit-
able for direct convolution artificial late reverberation, namely its
extremely low average pulse density (meaning very few non-zero
filter coefficients), which makes it computationally efficient, and
its perceptible smoothness, which makes it still sound realistic. Di-
rect convolution with velvet noise (or any other sparse sequence) is
known as SFIR filtering. Velvet noise SFIR filters smears the input
through time but is spectrally flat with small variations throughout
the spectrum as the velvet noise. Comparable spectral variations
are found for the parallel feedback comb filters in [4].
Convolution of a signal by SFIR filtering having velvet-noise
coefficients can be implemented efficiently without multiplications.
Most of the coefficients of the SFIR filter are zero and they must
not be computed at all. Instead, the input signal is propagated in
the delay line of the filter, and only those input signal samples,
which coincide with the non-zero coefficients are added together
to produce the output. One idea is to separately run through the
indices of coefficient values +1 and −1, add the corresponding
sample values taken from the delay line, and finally subtract the
two sums. This convolution process can be formulated as
x(n)∗s(n) = 
m+
x[n+k(m+)] −
m−
x[n+k(m−)] ,(4)
where x(n)is the input signal, ∗denotes the convolution process,
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Figure 3: Proposed late reverb algorithm. An impulse response
example signal at the five places in the algorithm, (a) to (e), is
shown in Figure 4(a) to (e), respectively.
s(n)is the velvet noise sequence, k(m+)is the index of the posi-
tive pulses, and k(m−)is the index of the negative pulses.
For example, when 1% of the SFIR coefficients are non-zero
(meaning +1 or −1) and the filter length is Psamples, computing
an output sample requires 0.01Padditions and no multiplications.
For comparison, a regular FIR filter of the same length needs P−1
additions and Pmultiplications per output sample.
3. NOVEL REVERBERATION MODEL
Figure 3 shows a block diagram of the proposed late reverberator.
In the following, a description of how an input impulse turns into
a realistic, dense late impulse response by the algorithm is given.
First the input impulse is fed to the first velvet noise filter, SFIR1,
and at the same time its copy is delayed by the length of the SFIR
filter, z−L1. The white noise output of SFIR1is sonically colored
by the H1filter and attenuated by factor G1. One sequence of
SFIR filter, coloration filter, and attenuator is referred to as a sin-
gle path. When the impulse has gone through the first path it will
immediately start producing an output of the second path and so
on; this is caused by neighboring SFIR filters and z−Ldelays hav-
ing the same length. In other words, the input to each SFIR filter is
delayed corresponding to the length of all the previous SFIR filters
starting with zero delay for SFIR1and ending with a delay cor-
responding to the accumulated length of SFIR1to SFIRM−1for
SFIRM. The summed signal is fed through a cascade of KSAP
filters to allow SFIR filters with greater sparsity to be used and to
smear the transition between them.
To illustrate this, Figures 4(a) to (e) show an example impulse
response at the corresponding, (a) to (e), positions of Figure 3. The
signal is followed through the second path and all the way to the
output. Both Figures 3 and 4 illustrate that (a) for the second path
the impulse is delayed L1samples (which corresponds to L1/Fs
seconds), (b) the impulse response of SFIR2is a velvet noise se-
quence, (c) lowpass filtering and attenuation according to H2and
G2, (d) summation of the signal from all the paths, and (e) SAP
filtered dense output signal. The figure only shows the first 300 ms
of the impulse response which in this example exactly corresponds
−1
0
1
(a)
L /F
1 s L /F
2 s L /F
3 s
−1
0
1
(b)
−0.1
0
0.1
(c)
−0.1
0
0.1
(d)
0 50 100 150 200 250 300
−0.1
0
0.1
(e)
Time [ms]
Figure 4: Example impulse response shown for the five positions,
(a) to (e), in the reverberation algorithm in Figure 3; (a) impulse
delayed by L1samples, (b) velvet noise, (c) lowpass filtered and
attenuated, (d) the signals from all paths are added up, and (e) the
resulting output impulse response.
to the length of the first three paths; the signal in Figure 4(d) con-
tinues until the Mth path and Figure 4(e) continues even longer
because of the recursive nature of the SAP filters. The length of
the SFIR filters and the attenuation factor Gincrease gradually for
each path while the SFIR pulse density and the cutoff frequency of
filters Hdecrease for each path; see Figure 4(d).
The SFIR filters and their corresponding neighboring delay
line can share the same memory space. The memory usage for
all the SFIR filters corresponds to the length of the target impulse
response. The length of each SFIR filter must be chosen shorter
when the frequency characteristic of the target impulse response
changes more rapidly (often in the beginning). The output of each
SFIR filter is filtered and attenuated corresponding to the spectral
content and level of the target impulse response at the correspond-
ing point. Lower average pulse densities are used for the SFIR
filters where the coloration filter has a more lowpassed character-
istic (normally towards the end of the impulse response).
The Nth order SAP filter is given by the transfer function [18]
A(z) = g+z−N
1 + g z−N,(5)
where gis the allpass coefficient which for all the SAP filters is
0.618, derived from the golden ratio, to maximally reduce the peak
power of impulses [19, 20]. The order of the SAP filters are dis-
tributed as integer values between 1 (first order) and the overall
average pulse period2. The number of cascaded SAP filters and
2The overall average pulse period is calculated as the mean of all SFIR
average pulse periods.
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Figure 5: Complete reverberator containing direct sound, early
reflections, and late reverberation; and mixing of the three signals.
The content of the block named “Reverb” is shown in Figure 3.
their orders are selected so that they together fill out the gaps of
the SFIR filters; meaning that increasing sparsity of SFIR filters
demands more SAP filters to make up for the missing SFIR pulses.
A sufficient number of SAP filters and their orders are selected so
that the probability distribution of a SAP filtered velvet noise sig-
nal with the overall average pulse density approximates a Gaus-
sian distribution. An SFIR average pulse density starting at 100
pulses/s and a cascade of seven SAP filters has been found to be a
good compromise for a diffuse concert hall; this configuration will
be used in the reverberator example presented in the next section.
The algorithm produces late reverberation. The early reflec-
tions can be approximated in many ways, e.g. as described in [11,
21, 22]. A simple example of a complete reverberator contain-
ing direct sound, early reflections, and late reverberation is shown
in Figure 5. The early reflections are reproduced by convolution
(FIRE) of the first part of the impulse response excluding the di-
rect sound impulse. The input signal is delayed, z−D, and passed
through the late reverberation algorithm before mixing with the di-
rect sound and early reflections. The mixing can include additional
filtering, delay etc. of the signals; in the complete reverberator used
in the next Section the mixing procedure is just an addition of the
three signals. FIREand z−Dcan share the same delay-line mem-
ory.
The impulse response of a cascade of several SAP filters is
more sparse in the beginning and grows more dense as the am-
plitude decays and the peak power is delayed, as seen in Figure
4(e). To camouflage this sparsity and to make up for the delay,
z−Dis less than the length of FIRE; more exactly FIREminus the
amount of samples as the sum of all the SAP filter orders. Hereby
the sparse part of the SAP filter impulse response occurs while the
early reflections still sounds. The SAP filters of course only smear
the signal forward in time, making the output of each path overlap.
The first path is lacking an overlap which is compensated for by a
slight amplification of G1, depending on the sum of the order of
the SAP filters.
4. MODELING EXAMPLE
4.1. Measured impulse response
As an example of how well the reverberator can replicate real
world impulse responses we have used a good quality well doc-
umented impulse response recorded from the concert hall in the
Finnish city Pori as our target impulse response [23]. The chosen
impulse response was recorded with the source on the stage, re-
ceiver at the floor far from the stage, and with an omni-directional
microphone. The impulse response is named s1_r3_o.wav in
Time [s]
Frequency [kHz]
(b)
[dB]
0 0.5 1 1.5 2
15
10
5
0
−60
−30
0
(a)
Figure 6: (a) Time signal and (b) spectrogram of measured im-
pulse response from the concert hall in Pori, Finland [23].
1 5 10 15 20
(a)
0 0.5 1 1.5 2
40
60
80
100
(b)
Time [s]
Density [pulses/s]
Figure 7: (a) Gradually increasing length of the 20 frames starting
from 100 milliseconds, (b) decreasing pulse density with increas-
ing filter number.
[23]; the same impulse response has been used to test the perfor-
mance of the reverberator described in [11]. Figure 6 shows the
time signal and spectrogram of the impulse response. The sam-
ple frequency of the measured and replicated impulse response is
44.1 kHz.
4.2. Replicated impulse response
We consider the late reverberation of the impulse response from
Pori to span from 100 milliseconds to when the impulse response
reaches zero amplitude after approximately 2.1 seconds3. Filters
are fitted by linear predictive coding (LPC) to Mnon-overlapping
rectangular windows of the measured late reverberation. The length
of the analyzed windows corresponds to the length of the SFIR fil-
ters and thereby selects the input to each path. The number and
length of windows was chosen based on inspection of the spectro-
gram in Figure 6(b). In the beginning of the signal the rapid change
of frequency characteristics motivated for shorter windows, while
3The signal reaches zero amplitude (no noise-floor) because it has been
de-noised, see [23] for details. For a non-denoised impulse response the
signal should be faded out when all frequency regions have reached the
noise floor to avoid convolution with the noise floor.
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125 250 500 1000 2000 4000 8000 16000
−60
−40
−20
0
Frequency [Hz]
Magnitude [dB]
H1
H17
Figure 8: Magnitude response of every second LPC filter ranging
from the first to the seventeenth.
at the end larger window lengths are sufficient. Figure 7(a) il-
lustrates the gradually increasing window length for higher filter
numbers resulting in M= 20 LPC filters and paths4. The LPC fil-
ters gave a good fit down to order 10 which was chosen as the LPC
filter order. Figure 8 shows the magnitude response for a selec-
tion of the fitted LPC filters including attenuation; the tendency is
clearly a gradually increasing lowpass characteristic and increas-
ing attenuation for higher filter numbers. The increasing lowpass
characteristic was exploited by lowering the average pulse density
of the higher filter numbers as shown in Figure 7(b); the average
pulse density was linearly distributed from 100 to 40 pulses/s for
the 20 filters.
The number of cascaded SAP filters was chosen to be K= 7
by the procedure described in Section 3 (approximating a Gaussian
amplitude distribution). The order ranges from 1 to the overall
mean of the average pulse period, Fs
(100+40)/2= 630 samples. The
exact order of the SAP filters are 1, 64, 140, 209, 442, 555, and
630. The attenuation for the paths, G1to GM, was calculated as
the average power of a one-second velvet noise sequence with the
same average pulse density as the SFIR in that path filtered by the
LPC filter and the cascade of SAP filters. The lack of smearing in
the first path is compensated for by an amplification; +3 dB has
shown to be sufficient for the chosen SAP filters.
The direct sound and early reflections are generated by con-
volution of the first 100 milliseconds of the original impulse re-
sponse. The time signal and spectrogram of the replicated impulse
response is shown in Figure 9, which closely resembles Figure
6. Figure 10 shows a comparison of the reverberation times of
the measured and generated impulse response from Figure 6 and
9, respectively. The reverberation times are calculated as T30 . The
generated impulse response varies in any octave band no more than
±7% relative to the measured impulse response.
Informal listening tests revealed that the perceived properties
of the impulse response and artificial reverberation of sounds gen-
erated from the algorithm were very similar to the original. The
generated impulse response and sound examples are available on
the Internet5. The sonic performance of the algorithm can easily
be evaluated for other sounds by convolution with the impulse re-
sponse because the algorithm is linear and time-invariant.
4The border sample indexes of the 20 windows are as follows: 4411,
5672, 7214, 9044, 11171, 13602, 16343, 19400, 22779, 26484, 30521,
34895, 39609, 44669, 50077, 55837, 61954, 68431, 75271, 82477 and
90053.
5http://www.acoustics.hut.fi/go/dafx13-vscreverb/
Time [s]
Frequency [kHz]
(b)
[dB]
0 0.5 1 1.5 2
15
10
5
0
−60
−30
0
(a)
Figure 9: (a) Time signal and (b) spectrogram of the algorithm-
generated impulse response; compare with Figure 6.
125 250 500 1000 2000 4000 8000
0
0.5
1
1.5
2
2.5
3
Octave Band [Hz]
Reverberation Time [s]
Measured
Generated
Figure 10: Comparison of T30 reverberation times in octave bands
for the measured and the generated impulse response.
4.3. Abstract reverberation effect
The settings for the generated impulse response shown in Figure 9
has been altered to illustrate how well the algorithm also works for
producing abstract reverberation effects. In this example only the
20 attenuators, G1to G20, have been manipulated6to give an im-
pulse response that has an increasing amplitude. Figure 11 shows
the resulting time signal and spectrogram. The shown abstract re-
verberation effect sounds somewhat similar to a compressed and
gated reverb. Many other kinds of abstract effects can easily be
made with this algorithm including time-reversed RIR and other
non-decaying or pulsating impulse responses.
5. IMPLEMENTATION COST COMPARISON
The implementation cost of the algorithm is compared to direct
convolution and partitioned fast convolution. Table 1 shows the
6The exact G-values used for the abstract reverb effect are relative to
the values found in Subsection 4.2. The relative values increases +3.47 dB
for each path starting with 0 dB for G1.
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Time [s]
Frequency [kHz]
(b)
[dB]
0 0.5 1 1.5 2
15
10
5
0
−60
−30
0
(a)
Figure 11: (a) Time signal and (b) spectrogram of the abstract
reverb impulse response.
number of floating point operations (FLOPs) per sample and the
number of signal memory samples required for the three reverber-
ation algorithms for a 2-second long impulse response, as in the
previous section. The listed values for the direct convolution are
based on the direct form implementation. The values for the parti-
tioned fast convolution are taken from the recent improvement of
the algorithm by Wefers and Vorländer [10, Table 1]. The settings
for replicating the impulse response in Section 4 was used for the
computational cost and memory usage calculations listed for the
proposed algorithm. The implementation cost of the early reflec-
tions is not included in the calculations. Table 1 shows that the
proposed algorithm is approximately as efficient computationally
as the partitioned convolution and over 100 times more efficient
than the direct convolution. The memory consumption of the new
method is approximately equivalent to that of the direct convolu-
tion and approximately 50% smaller than that of the partitioned
convolution algorithm.
Table 2 specifies what kind of operations (multiplication or ad-
dition) and from which part of the algorithm the 527 FLOPs orig-
inates. denotes the summation before the SAP filters. Note
that the SFIR filter uses zero multiplications and that approxi-
mately 73% of the operations (400 FLOPs) are spend on the spec-
tral coloration filterbank. The computational complexity listed is
for FLOPs only, ignoring any branching operations, specialized
signal processing instructions etc. The memory usage listed is for
the signal memory only, ignoring any memory needed for filter
coefficients.
6. CONCLUSION
This paper presented a novel algorithm for simulating the late part
of room reverberation. The idea is to use a bank of sparse FIR
(SFIR) filters followed by spectral coloration filters, from which
the summed output is fed through a cascade of several Schroeder
allpass (SAP) filters. The coefficients for the SFIR filters are ob-
tained from velvet noise sequences, which are proven to provide
smooth responses even with very low pulse densities (down to 0.1-
Table 1: Comparison of computational complexity and memory
usage for the three reverberation algorithms (impulse response
length: 2 s, sample rate: 44.1 kHz).
Direct Partitioned Proposed
Convolution Convolution Algorithm
FLOPs /sample: 176401 399 527
Signal memory: 88200 176400 90442
Table 2: Detailed specification of the 527 FLOPs computed for
every sample in the proposed algorithm. Operations are specified
as additions or multiplications for each part of the algorithm.
SFIR H G SAP
Additions: 160 200 0 19 14
Multiplications: 0 200 20 0 14
0.2% non-zero elements). Moreover, the sparsity of the SFIR fil-
ters varies along the reverberation tail with sparser filters towards
the end where the impulse response has a more lowpassed char-
acteristic. The coloration filters can be designed by fitting LPC
filters to partitioned variable-length segments of a target impulse
response in order to obtain realistic coloration for the reverb, and
the SAP filters are used to smooth out the transition between SFIR
filters. The inclusion of SAP filters allows for using even sparser
SFIR filters; this principle can also be used in similar algorithms to
lower the computational cost considerably, e.g. [13, 14, 11, 15, 17].
The performance of the proposed algorithm was demonstrated
with a modeling example, and the results showed that the algo-
rithm is able to model the overall characteristics of the target con-
cert hall impulse response. The design procedure allows a flexible
parametric approximation of the target late part of the impulse re-
sponse, and additionally, the proposed reverb is computationally
efficient providing a clear advantage over the direct convolution
and comparable to the FFT-based partitioned convolution method,
but with nearly half the memory usage. Sound examples are avail-
able online at
http://www.acoustics.hut.fi/go/dafx13-vscreverb/.
7. ACKNOWLEDGMENTS
This work was conducted when Bo Holm-Rasmussen was a vis-
iting student at Aalto University, Espoo, Finland. The work of
Heidi-Maria Lehtonen was supported by the Finnish Cultural Foun-
dation.
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