Reply by Angelo Campanella●November 25, 20052005-11-25

Emile wrote:

>> Ok, i found that the matlab function

etc.
I have a hard time understanding your question, let alone the answers
given.
Are you trying to model the sound absorption of unspecified materials?
Or do you want to model the impulse response of a proposed space?
Can you be a little more specific?
For the convenience of mathematical treatment in a manner that matches
our pshychoacoustic perceptions, the referenced frequency bands are
enumerated on a factor-of-2 scale ("octave") basis, centering on 1,000
Hz. That same scale is sometimes further subdivided for frequency
analysis into 1/3-octaves on a finer scale as increments of 2 to the 1/3
power.
Otherwise: My experience is that most firm surface materials have
little absorption below 100 Hz, and that high frequency absorption
depends on the depth of the porous material comprising that surface.
If you are looking for a general approximation of the effect of
surfaces in a room, then represent the surface at its position x, y, z,
the surface normal as a vector, and presume an absorption of o.5 when it
is thought to be absorptive, and 0 if it is thought to be reflective.
The resulting mathematical sound decay and reflections after a
mathematical sound impulse will fairly well typify the room; this
impulse response will be close to reality. Then you can mathematically
vary the respective areas, their location and their orientation to
produce the space impulse response that you want.
Angelo Campanella.

Reply by Emile●November 25, 20052005-11-25

Emile wrote:

> Emile wrote:
>
>> Hi,
>>
>> Can anybody point me to a paper/book/site/algorithm/tool on how to
>> desing a low order filter to model the absorption coefficients of
>> materials. I have found that these coefficients usually are given for
>> 6 octave bands (125,250,500,1000,2000,4000Hz). More information on
>> this subject is greatly appreciated.
>>
>>
>
> Ok, i found that the matlab function
>
> [a,b] = invfreqz(h,w,n,m)
>
> should do the trick, but i have some trouble with the w input param. h
> is a vector with the complex frequency response at the frequency points
> specified in vector w, but these frequency points are specified in
> radians between 0 and Pi.
>
> I dont really understand how to specify these octave bands (expressed in
> Hz) in radians between 0 and Pi. Should i do some sort of mapping like
> [0 - samplingfrequency] -> [0 - Pi]?
>

I have found the right expression is in radians/sample (oops). I was
thinking in radians/sec, and then i could only specify frequencies up to
0.5Hz
so the mapping should be imo:
1 Hz (cycle/second) = 1/fs * 2*Pi rad/sample

>
>
>> Emile Vrijdags

Reply by Rune Allnor●November 25, 20052005-11-25

Emile wrote:

> Emile wrote:
> > Hi,
> >
> > Can anybody point me to a paper/book/site/algorithm/tool on how to
> > desing a low order filter to model the absorption coefficients of
> > materials. I have found that these coefficients usually are given for 6
> > octave bands (125,250,500,1000,2000,4000Hz). More information on this
> > subject is greatly appreciated.

Most attempts I have seen to solve this problem, use modeling programs
for whatever physics is involved in the acoustic propagation. Which
basically
is avery messy approach if the numerical model does not fit the physics
"sufficiently well". Others use empirical models, presumably based on
some statistical fitting of experimental data.
The problem is that most parameters change, and depend on all sorts of
factors. Is there a structure on texture on the surface where the sound
hits?
If so, the reflection coefficient will probably depend on both
frequency
and incidence angle, perhaps even azimuth angle.
Is the body infinitely thick, like the earth, or is there a finite
depth of, say,
a wall in a room? The sound is likely to penetrate a wall of finite
thickness
at some combination of angle and frequency.
Do you measure in free space, like outdoors, or in an enclosed cavity,
like a small room? In the former case you need to account for Lloyd
mirror effects, in the latter you may be dealing with normal modes.
There are so many factors to consider that it is not possible to come
up with a general answer your question.

> Ok, i found that the matlab function
>
> [a,b] = invfreqz(h,w,n,m)
>
> should do the trick, but i have some trouble with the w input param. h
> is a vector with the complex frequency response at the frequency points
> specified in vector w, but these frequency points are specified in
> radians between 0 and Pi.
>
> I dont really understand how to specify these octave bands (expressed in
> Hz) in radians between 0 and Pi. Should i do some sort of mapping like
> [0 - samplingfrequency] -> [0 - Pi]?

Almost correct. You need to map it as
[0 - samplingfrequency] -> [0 - 2*Pi]
(a factor 2 in the last interval). Make sure you use a calibrated
microphone,
calibrated amplifiers and calibrated ADCs. Or the results of your
analysis
will not be very useful.
Rune

Reply by Emile●November 24, 20052005-11-24

Emile wrote:

> Hi,
>
> Can anybody point me to a paper/book/site/algorithm/tool on how to
> desing a low order filter to model the absorption coefficients of
> materials. I have found that these coefficients usually are given for 6
> octave bands (125,250,500,1000,2000,4000Hz). More information on this
> subject is greatly appreciated.
>
>

Ok, i found that the matlab function
[a,b] = invfreqz(h,w,n,m)
should do the trick, but i have some trouble with the w input param. h
is a vector with the complex frequency response at the frequency points
specified in vector w, but these frequency points are specified in
radians between 0 and Pi.
I dont really understand how to specify these octave bands (expressed in
Hz) in radians between 0 and Pi. Should i do some sort of mapping like
[0 - samplingfrequency] -> [0 - Pi]?

> Emile Vrijdags

Reply by Emile●November 23, 20052005-11-23

Hi,
Can anybody point me to a paper/book/site/algorithm/tool on how to
desing a low order filter to model the absorption coefficients of
materials. I have found that these coefficients usually are given for 6
octave bands (125,250,500,1000,2000,4000Hz). More information on this
subject is greatly appreciated.
Emile Vrijdags