IIR filter design

Al Clark wrote:
> 
> Erik,
> 
> I don't have any suggestions but I am very interested in a filter program
> that does a good job at matching arbitrary responses. One of the filters
> that comes to mind is the standard A Weighting filter. It is defined (by
> standard) in the s plane and therefore does not map perfectly into the z
> plane.
> 
> Can your program accept a function written as H(s) as a target?

Not at the moment, but give any abritrary H(s) and a sample rate, 
it should be possible to turn that into a combined magnitude/phase 
response which can then be matched.

Erik
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  Erik de Castro Lopo  nospam@mega-nerd.com (Yes it's valid)
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"Erik de Castro Lopo" <nospam@mega-nerd.com> wrote in message
news:3F5A70C7.50C784DE@mega-nerd.com...
> Erik de Castro Lopo wrote:
> >
> > Hi all,
> >
> > As we all know, designing IIR filters is easy enough
> > for low filter order but is far more difficult when
> > higher order filters are required to meet design
> > contraints like low passband ripple, narrow transition
> > bands and high levels of attenuation in the stopband.
> >
> > I'm currently working on a program for designing IIR
> > filters and this software has recently produced a LP
> > filter with the following specs:
> >
> >      Order    : 18
> >      Passband : 0 - 0.2*fs   < 0.1 dB ripple
> >      Stopband : 0.25*fs - 0.5*fs  > 100 dB attenuation
>
> Another run of this program (4.5hrs) produced a 13th order
> filter meeting the same specs. Obviously, some more work
> is needed to find the minimum order for a given design
> spec.
>
> Erik

It looks to me like a standard 10th-order elliptic filter can meet your
specs, and actually have a stopband attenuation of over 104 dB.
Alternatively, it could get exactly 100 dB attenuation and have a passband
ripple of 0.035 dB.  I assume that matlab could generate these, though I
haven't tried it.  An elliptic filter can be generated very quickly using
standard techniques that don't require extensive search or iteration.  Is
there some other constraint or problem that makes a standard elliptical
filter not work here?

--
Eric Backus
R&D Design Engineer
Agilent Technologies, Inc.
425-356-6010 Tel

Erik de Castro Lopo wrote:

> Bernhard Holzmayer wrote:
>> ...
>> Matlab caused a lot of pain when I tried to design even lower
>> order filters (4th order Butterworth), when the relation between
>> cutoff-frequency and sampling frequency decreases:
>> try this: 4th order HPF and LPF (independently) at 1.5Hz
>> (Fs=48kHz).
>> ...
> 
> Is that a high pass or low pass filter?
> 
> Erik

Both.

I started with this (for LPF):
Fs = 48000;
qz = quantizer('single',[32,8]);
[b,a] = butter(4, fy / (Fs/2) );
[sos,g] = tf2sos(b,a);

The result was poor. Applying a hint from Mathworks, I changed to:
Fs = 48000;
qz = quantizer('single',[32,8]);
[z,p,k] = butter(4, fy / (Fs/2) );
[sos,g] = zp2sos(z,p,k);

Results were ok, except at 1.5Hz. 
At 1.5Hz I shifted the frequency to fy=1.495Hz until I succeeded.

Note: The internal stability method isstable() failed in my special 
situation and had to be replaced by a patched version from 
Mathworks. 

Bernhard
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Erik de Castro Lopo <nospam@mega-nerd.com> wrote in message news:<3F5C408D.A4753D8F@mega-nerd.com>...
> robert bristow-johnson wrote:
> > 
> > Erik de Castro Lopo <nospam@mega-nerd.com> wrote in message news:<3F592C33.DD349F59@mega-nerd.com>...
> > ...
> > > I'm therefore asking people here the following questions:
> > >
> > >    0) How big and how "difficult" are the IIR filters you
> > >       have designed?
> > 
> > i have chained together maybe 4 or 5 biquads in cascade.  the noise
> > starts to get to be a little bad by then.
> 
> Hi Robert,
> 
> Since its you saying this, i have to resume that you are
> talking about implementations using 24 bit fixed point
> arithmetic :-). Correct?

yes.  (for 4 or 5 biquads.)


long ago i implemented some filtering on the MC68000 (wasn't real time
but i wanted it done that day).  that was 16 bit, didn't know all of
the tricks i know now and it was pretty bad for more than 4th order.

r b-j

(remotely in North Dakota)