Any shape IIR Filter

Let's say I have a particular freqeuncy response that I can draw out on
paper and I want an IIR filter to do just that.  What is the best approach
to this problem.  I know there are simpler ways to do this using FIR
filters but let's say my constraint was to only use the IIR form.

For example the frequency shape I need is a smiley face or a parabola. 
It's not a peak-notch type or a band-reject filter, but siomething kinda
inbetween.  How could I feed in this "desired frequency response" data to
generate coefficients for an any shape IIR filter?

Any ideas?

Regards,
Jeff 
DSP Engineer

sparafucile17 wrote:

> Let's say I have a particular freqeuncy response that I can draw out on
> paper and I want an IIR filter to do just that.  What is the best approach
> to this problem.  I know there are simpler ways to do this using FIR
> filters but let's say my constraint was to only use the IIR form.
> 
> For example the frequency shape I need is a smiley face or a parabola. 
> It's not a peak-notch type or a band-reject filter, but siomething kinda
> inbetween.  How could I feed in this "desired frequency response" data to
> generate coefficients for an any shape IIR filter?
> 
> Any ideas?

There is no universal solution.
The typical suboptimal approach is to split the response into the 
several frequency bands and equalize each band.

Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com

On 26 Okt., 19:33, "sparafucile17" <sparafucil...@hotmail.com> wrote:
> Let's say I have a particular freqeuncy response that I can draw out on
> paper and I want an IIR filter to do just that.  What is the best approach
> to this problem.  I know there are simpler ways to do this using FIR
> filters but let's say my constraint was to only use the IIR form.
>
> For example the frequency shape I need is a smiley face or a parabola.
> It's not a peak-notch type or a band-reject filter, but siomething kinda
> inbetween.  How could I feed in this "desired frequency response" data to
> generate coefficients for an any shape IIR filter?

You can use FDLS:

http://apollo.ee.columbia.edu/spm/external/tipsandtricks/files/TandT_Jan2007.zip

>On 26 Okt., 19:33, "sparafucile17" <sparafucil...@hotmail.com> wrote:
>> Let's say I have a particular freqeuncy response that I can draw out
on
>> paper and I want an IIR filter to do just that.  What is the best
approach
>> to this problem.  I know there are simpler ways to do this using FIR
>> filters but let's say my constraint was to only use the IIR form.
>>
>> For example the frequency shape I need is a smiley face or a parabola.
>> It's not a peak-notch type or a band-reject filter, but siomething
kinda
>> inbetween.  How could I feed in this "desired frequency response" data
to
>> generate coefficients for an any shape IIR filter?
>
>You can use FDLS:
>
>http://apollo.ee.columbia.edu/spm/external/tipsandtricks/files/TandT_Jan2007.zip
>
>

Wow, this is some intriguing information!  I will really have to stew on
this data for a while, but it looks very promising.  I used to be an IEEE
member and now I'm wishing that I still was!  That's cool that this was
published in Jan of this year.

I really appreciate the Matlab code that Gregory Berchin provided.  This
will really accelerate my ability to test this as a viable solution.

Any other ideas are still welcome.  

Thanks,
Jeff

On Fri, 26 Oct 2007 14:12:43 -0500, "sparafucile17"
<sparafucile17@hotmail.com> wrote:

>Any other ideas are still welcome.  

FDLS requires phase information in addition to magnitude; not always
easy to come by.  You can derive the minimum phase characteristic from
the magnitude, however, and FDLS should work fine with that.

If you only need to match magnitude, there are magnitude-only IIR least
squares techniques available.  For an example, see section 5.3.1 of the
original Oppenheim & Schafer for the method proposed by Steiglitz.

Greg Berchin

On Oct 26, 10:33 am, "sparafucile17" <sparafucil...@hotmail.com>
wrote:
> Let's say I have a particular freqeuncy response that I can draw out on
> paper and I want an IIR filter to do just that.  What is the best approach
> to this problem.  I know there are simpler ways to do this using FIR
> filters but let's say my constraint was to only use the IIR form.
>
> For example the frequency shape I need is a smiley face or a parabola.
> It's not a peak-notch type or a band-reject filter, but siomething kinda
> inbetween.  How could I feed in this "desired frequency response" data to
> generate coefficients for an any shape IIR filter?
>
> Any ideas?

Long long ago, when 8-bit home computers were just starting
to become popular, I wrote a program for a friend of mine who
was an analog designer.  Sort of like a video game, except
that the joystick selected and moved around poles and zeros
(conjugate pairs) on a complex plane, and the fire button
caused a frequency response plot to be updated (slowly, back
then).  Apparently this analog designer was using it to help
design some active filters for some unusual response curve
requirements.  Don't know if there is some digital z-plane
version of this kind of video game around, or whether it
might be useful to see if one can get "close enough" (high
score? :) by just "playing around".



IMHO. YMMV.
--
rhn A.T nicholson d.0.t C-o-M

On 26 Okt, 19:33, "sparafucile17" <sparafucil...@hotmail.com> wrote:
> Let's say I have a particular freqeuncy response that I can draw out on
> paper and I want an IIR filter to do just that.  What is the best approach
> to this problem.  I know there are simpler ways to do this using FIR
> filters but let's say my constraint was to only use the IIR form.
>
> For example the frequency shape I need is a smiley face or a parabola.
> It's not a peak-notch type or a band-reject filter, but siomething kinda
> inbetween.  How could I feed in this "desired frequency response" data to
> generate coefficients for an any shape IIR filter?
>
> Any ideas?

A couple of years ago I browsed some papers by Ken Steiglitz,
which appeared in the IEEE Transactions on Acoustics, Speech
and Signal Processing some time in the early -70s.

The articles described how to design IIR filters with more or
less arbitrary frequency response by means of optimization
methods.

It's been some time since I read those papers, but at the time
I got an impression that the design by optimization methdos
for FIRs and IIRs are based on different strategies, as the
FIR specification is a desired continuous response with
allowable ripple, whereas the IIR spec in the Steiglitz
papers were given in discrete points, with a result based
on a "connect the dots" approach.

Rune

"sparafucile17" <sparafucile17@hotmail.com> schrieb im Newsbeitrag 
news:yaidneqCALJ0ub_anZ2dnUVZ_qKgnZ2d@giganews.com...
> Let's say I have a particular freqeuncy response that I can draw out on
> paper and I want an IIR filter to do just that.  What is the best approach
> to this problem.  I know there are simpler ways to do this using FIR
> filters but let's say my constraint was to only use the IIR form.
>
> For example the frequency shape I need is a smiley face or a parabola.
> It's not a peak-notch type or a band-reject filter, but siomething kinda
> inbetween.  How could I feed in this "desired frequency response" data to
> generate coefficients for an any shape IIR filter?
>
> Any ideas?
>
> Regards,
> Jeff
> DSP Engineer


Hello Jeff,

You could try with Scilab's "yulewalk" function.
http://scilabsoft.inria.fr/product/man/html/eng/signal/yulewalk.htm
http://www.scilab.org/
yulewalk - least-square filter design



With Matlab: yulewalk
http://static.scribd.com/docs/5d5x34sksumje.pdf

Best regards,
Helmut

Helmut Sennewald wrote:

> "sparafucile17" <sparafucile17@hotmail.com> schrieb im Newsbeitrag 
> news:yaidneqCALJ0ub_anZ2dnUVZ_qKgnZ2d@giganews.com...
> 
>>Let's say I have a particular freqeuncy response that I can draw out on
>>paper and I want an IIR filter to do just that.  What is the best approach
>>to this problem.  I know there are simpler ways to do this using FIR
>>filters but let's say my constraint was to only use the IIR form.
>>
>>For example the frequency shape I need is a smiley face or a parabola.
>>It's not a peak-notch type or a band-reject filter, but siomething kinda
>>inbetween.  How could I feed in this "desired frequency response" data to
>>generate coefficients for an any shape IIR filter?
>>
>>Any ideas?
>>
>>Regards,
>>Jeff
>>DSP Engineer
> 
> 
> 
> Hello Jeff,
> 
> You could try with Scilab's "yulewalk" function.
> http://scilabsoft.inria.fr/product/man/html/eng/signal/yulewalk.htm
> http://www.scilab.org/
> yulewalk - least-square filter design
> 
> 
> 
> With Matlab: yulewalk
> http://static.scribd.com/docs/5d5x34sksumje.pdf
> 
> Best regards,
> Helmut
> 
> 

Don't know if solves his problem
Will probably do nicely for mine. And it's been sitting in front of me 
all along.
Thanks

On Fri, 26 Oct 2007 12:33:29 -0500, "sparafucile17"
<sparafucile17@hotmail.com> wrote:

>Let's say I have a particular freqeuncy response that I can draw out on
>paper and I want an IIR filter to do just that.  What is the best approach
>to this problem.  I know there are simpler ways to do this using FIR
>filters but let's say my constraint was to only use the IIR form.
>
>For example the frequency shape I need is a smiley face or a parabola. 
>It's not a peak-notch type or a band-reject filter, but siomething kinda
>inbetween.  How could I feed in this "desired frequency response" data to
>generate coefficients for an any shape IIR filter?
>
>Any ideas?
>
>Regards,
>Jeff 
>DSP Engineer

Hi Jeff,
  If you have access to the IEEE Signal Processing magazine,
there's an article in the "DSP Tips & Tricks" column,
in Jan. 2007, that 
might help you.  It's title is: "Precise Filter Design"
by Greg Berchin.

A slightly expanded version of that material is in the 
new IEEE Press book, "Streamlining Digital Signal Processing".

Good Luck,
[-Rick-]