Bandpass system identification using IIRs (audio)

Hello,

Surely somebody has already done this, using Matlab or Excel.

0. Providing Fs, the sampling frequency (usually 44100 Hz)
1. Providing a target structure like a 4-th order IIR highpass followed by
a 4-th order IIR lowpass. This is the most complicated scenario.
2. Providing F1 in Hertz, the high-pass cutoff rough indication
3. Providing F2 in Hertz, the low pass cutoff rough indication
4. Providing a 32-points amplitude plot in degrees from (F1)/2 untill
(F2)*2.
5. Providing a 32-points magnitude plot in decibels from (F1)/2 untill
(F2)*2.

Then Excel or Matlab would provide as output :

1. The IIR higpass numerator and denominator coefficients
2. The IIR lowpass numerator and denominator coefficients

This would be obtained by mimimizing the "area error" on the phase plot
and on the magnitude plot between (F1)/2 untill F2*(2). This is quite
tricky. Currently, I don't see how to do it practically using Excel or
Matlab.

For systems that are low-order than the specified 4th hi / 4th lo, Excel
or Matlab will output coefficients very close to zero.
Up to the user to finalize the calculation by putting the coefficients to
zero exacly. Or Excel and Matlab may assist him in doing this.

Application is audio with loudspeaker enclosure modelization prior to
correction and filtering. The 4th hi / 4th lo is the "Bose" tri-chamber
design. A 2th hi / 1st lo is the "closed enclosure" design. A 4th hi / 1st
lo is the "bass reflex" design. A 2th hi / 2nd lo" is the "dual chamber
bandpass" design.

Any suggestion welcome.
Students & applicants welcome if this is not available yet on Excel (thin
doubt !). Possible insertion in major enthusiast and semipro Electronics
publication - paper & web. Unique opportunity.

Steph

On Mar 17, 6:15&#4294967295;am, "steph_tsf" <stephanecnocka...@hotmail.com> wrote:

> Surely somebody has already done this, using Matlab or Excel.

FDLS will do approximately what you ask; I have occasionally used it
to model individual loudspeaker drivers.  Search comp.dsp for "FDLS"
with author "Berchin".  The article and the Matlab or C code are
available from various places on the Web, including from me directly
-- just ask.

Greg Berchin

Hello Greg,

are we talking about this :
http://groups.google.com/group/comp.dsp/msg/2c307e8e77fb5178

After this modelization - identification process, do we get "random"
high-order IIRs or can we inject a constraint like setting a simple
prototype structure like 4th-order highpass followed by a 1th-order
lowpass ?

Your work is very promising. Have you been published yet ?
Do you have experience on SynthMaker ?

Steph

Hello Greg,

Found this now : 

http://www.univ.trieste.it/~ramponi/teaching/DSP/materiale/ES_10_2.m

Should I start working on that using Matlab and Signal Processing Toolbox
?

Steph

Try 

hz = yulewalk(N, frq, mag);

matlab and scilab has this function and
can be used to design arbitrary shaped
iir filters given frequency and magnitude
response. 

N is the input order which in your case is
4.

Regards
Bharat Pathak

www.Arithos.com
~dsp Simplified

-------DSP DESIGN CONSULTANCY AND TRAINING--------

On Mar 17, 7:20&#4294967295;am, "steph_tsf" <stephanecnocka...@hotmail.com> wrote:

> are we talking about this :http://groups.google.com/group/comp.dsp/msg/2c307e8e77fb5178

Yes.

> After this modelization - identification process, do we get "random"
> high-order IIRs or can we inject a constraint like setting a simple
> prototype structure like 4th-order highpass followed by a 1th-order
> lowpass ?

You specify the numerator and denominator order, the algorithm
computes a least-squares fit to those orders.  From the coefficients
you can extract poles and zeroes and do with them whatever you please.

> Your work is very promising. Have you been published yet ?

Only in some ancient conference papers, and recently in a Signal
Processing Magazine article and as a chapter in Rick Lyons' book.

> Do you have experience on SynthMaker ?

No.

Greg

On Mar 17, 7:30&#4294967295;am, "steph_tsf" <stephanecnocka...@hotmail.com> wrote:

> Found this now :
>
> http://www.univ.trieste.it/~ramponi/teaching/DSP/materiale/ES_10_2.m

That's someone else's modification of my code.

> Should I start working on that using Matlab and Signal Processing Toolbox

You only need the Signal Processing Toolbox for the plotting
functions.  The rest is standard Matlab code.

Greg

Hello Greg,

Now I am using FLDS on Matlab with Signal Processing Toolbox.
I am using Order = 2 to start with something simple.
Therefore I am supplying data that is consistent with a 2nd-order IIR.

FDLS is working nice (very nice should I write !) when modelling a 2nd
order lowpass.

but ...

FDLS is not working nice when modelling a 2nd order highpass. 
FLDS is making big errors on highpass filter on low frequency. It doesn't
deliver a nice 12dB/octave attenuation curve at low frequencies.
  
Might this be caused by high frequencies having more weight in the
algorithm ?

Any suggestion welcome.

I would like to send to you some files I have prepared for you, to be
executed by Matlab.
I have improved the template, now the model IIR is plotted using thousands
of X points instead of the few points supplied at the input.
This way one can see how much the model IIR is deviant.

stephanecnockaertatremovehotmaildotcom

Steph

steph_tsf wrote:

> FLDS is making big errors on highpass filter on low frequency. It doesn't
> deliver a nice 12dB/octave attenuation curve at low frequencies.
>
> Might this be caused by high frequencies having more weight in the
> algorithm ?
>
> Any suggestion welcome.

First, try increasing the numerator and denominator orders.  If you
are attempting to match an s-domain frequency response with a z-domain
model, then because of the nonlinear mapping from s to z you will need
many extra degrees of freedom.

Second, how many input points are you using?  It is not uncommon to
use thousands.  A few tens or hundreds might not do the job.

Third, if all else fails, the FDLS Matlab program is capable of
weighted least squares.  Increase the weight on points where it is not
fitting well.

Good luck,
Greg

Hello Greg,

Now I am using FLDS on Matlab with Signal Processing Toolbox.
I am using Order = 2 to start with something simple.
Therefore I am supplying data that is consistent with a 2nd-order IIR.

FDLS is working nice (very nice should I write !) when modelling a 2nd
order lowpass.

but ...

FDLS is not working nice when modelling a 2nd order highpass. 
FLDS is making big errors on highpass filter on low frequency. It doesn't
deliver a nice 12dB/octave attenuation curve at low frequencies.
  
Might this be caused by high frequencies having more weight in the
algorithm ?

Any suggestion welcome.

I would like to send to you some files I have prepared for you, to be
executed by Matlab.
I have improved the template, now the model IIR is plotted using thousands
of X points instead of the few points supplied at the input.
This way one can see how much the model IIR is deviant.

stephanecnockaertatremovehotmaildotcom

Steph