Engineering
Sample
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Digital Signal Processing: Schroeder Reverberator 203***
1.
PROGRAM DESIGN
A reverberator was developed according to Schroder’s
design [4]. The main program code can be found in
Appendix A1.
1.1.
Comb Filters
The term ‘comb filter’ comes from the resemblance of
the filter response to that of a comb, with peaks and
valleys caused by destructive interference. Schroeder
notes that this filter behaviour reflects the typical
response of a room, which can fluctuate in sound
pressure by an average of 10 dB, and up to 40dB in
severe cases. He cites research by Bell Laboratories:
‘Extreme response irregularities are imperceptible when
the density of peaks and valleys on the frequency scale
is high enough.’ Therefore, as long as the reflection
density is high enough, the uneven response of the comb
filter should not be an issue.
Four comb filters were created with the function ‘Comb
Filter’ (Appendix A2). They were connected in parallel
and output to the all-pass filters.
1.2.
All-pass Filters
All-pass filters have a ‘flat amplitude-frequency
response’ [5]. This avoids the undesirable effect of
colouration mentioned previously. This is achieved with
the ‘addition of a suitably proportioned undelayed path’
[6]. It may be deduced that the signal is only altered in
phase, and not in frequency. This may be described as
‘smeared’ over time.
A pair of all-pass filters were created with the function
‘All Pass’ (Appendix A3). These were connected in
series to the output of the comb filter bank, resulting in
a multiplication in reflection density [7].
1.3.
T60 Gain Calculator
A MATLAB function ‘t60 Gain Calculator’ (Appendix
A4) was created to allow the user to input a required
T60 decay time in seconds. This is defined as the time
taken for the impulse to decay to -60dB with respect to
its initial amplitude. This was achieved by adjusting the
gains of the comb filters. A separate function was
created to convert seconds in to samples (Appendix
A5). Schroeder gives the T60 gain formula as:
T  3 n / ( log gn ) (1)
Transposing:
g  10
 (3 /T )
(2)
Where:
g = Gain
T = T60 (seconds)

= Delay (seconds
1.4.
Low-pass Filter
A simple low-pass filter function was created by using a
small delay to cause destructive interference (Appendix
A6). At low frequencies, this had a negligible effect on
phase. However, with increasing frequency, the phase
differences became more significant, leading to
attenuation. This would have simulated the natural
attenuation of high frequency reverberated sound. The
low-pass filter was not implemented in the final design
due to time constraints. It should have been connected
to a feedback loop from the output of the filter, feeding
back into the inputs of the comb filter bank.
1.5.
Schroeder Curve
The function ‘Schroeder Curve’ was created to plot the
Schroeder reverse integration of the filter impulse
response (Appendix A7). This was done by looping
from the end of the output array and summing all
values.
Digital Signal Processing: Schroeder Reverberator 203***
RESULTS
Figure 1: Impulse Response
20
X: 0.24
Y: -5.007
0
X: 0.7353
Y: -35.14
-20
Level (dB)
-40
-60
-80
-100
-120
-140
-160
0
0.5
1
1.5
Time (s)
Figure 2: Schroder T60 Reverberation Time
9
3
x 10
2.5
X: 1
Y: 1.804e+009
2
Reflections
2.
1.5
1
0.5
0
0
0.5
1
Time (seconds)
Figure 3: Reflection Density
1.5