Re: Reverberation Calculation/Modelling (Densil Cabrera )

```Subject: Re: Reverberation Calculation/Modelling
From:    Densil Cabrera  <d.cabrera@xxxxxxxx>
Date:    Sat, 4 Oct 2008 08:56:57 +1000
List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>

This is stating the obvious, but just in case it is useful, it may be worth recalling that simple statistical room acoustics may be used to estimate reverberation time and diffuse field level. If you know the volume of the rooms, the source-receiver distance, and you have recordings of the identical signals in each room with constant gain (i.e., same amplification in reproduction within each room, and same gain structure in recording the signals in the rooms), then you apply the following relationships:

L1, L2 = sound level of recording in room 1 or 2 in dB - i.e. measured from the sound files
Q = directivity factor of sound source (loudspeaker?), which could be estimated based on its size (e.g. Beranek's 'Acoustics')
R1, R2 = source-receiver distance in each room in metres
A1, A2 = absorption in each room, in square metres (a more subtle approach is to use room constant)
V1, V2 = room volume in cubic metres

L1 - L2 = 10 x log{ [Q/(4 x pi x R1^2) + 4/A1] / [Q/(4 x pi x R2^2) + 4/A2] }

Log is base 10

The diffuse field sound level is then 10 x log(4/A) for each room, while the  direct field level is 10 x log (Q/(4 x pi x R^2), so the difference between these gives an indication of the 'amount of reverberation' (i.e. the direct to reverberant ratio). For a given reverberation time, diffuse field level will be greater in a small room. Greater source-receiver distance, or lower Q, will reduce the direct field level.

Then if you want reverberation time, it may be estimated from RT = 0.16 x V / A, although again more subtle equations also exist (which would be advantageous in dry acoustical conditions).

There are many assumptions in such calculations, and you would have to take care that violations do not produce substantial errors.

Usually these calculations are done for octave band analysis.

Fingers crossed I got this right...
Densil
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From: AUDITORY - Research in Auditory Perception [mailto:AUDITORY@xxxxxxxx On Behalf Of John Spencer
Sent: Thursday, October 02, 2008 9:44 AM
To: AUDITORY@xxxxxxxx
Subject: Reverberation Calculation/Modelling

Dear List,

Im looking for some advice/help in relation to measuring or determining the amount of reverberation in a speech or audio signal. Ive been trying to see if there is any literature on this but I cannot find any way of measuring the amount of reverberation in a signal. Are there any mathematical models that can be used to calculate a "value" for revereration when given a speech/audio segment?

Also, I would intersted in finding out if there is a way of comparing two identical signals recorded in two different rroms to determine the revereration differences.

I don't suspect that much has been done in this area but thanks to anyone who can help me with information or advice.

John

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DAn Ellis <dpwe@ee.columbia.edu>
Electrical Engineering Dept., Columbia University