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I am currently tasked with optimizing FIR filters as lower order IIR
filters so that a micro-controller can perform the necessary DSP. This is
performed in the time domain rather than the frequency domain as the
computation time for the number of FFT's required would be too long,
preventing us from doing the other required processing.

I am aware of certain optimization techniques to perform the task such as
treating the optimization as a Conic or Quadratic programming problem and
constrained and unconstrained reduction techniques based on the BMT
method.

I am not a DSP expert and so the maths in these techniques is difficult to
understand and apply to my problem. Therefore is anyone aware of any
software or subset of software than can perform this task.

Many thanks in advance for any help you may give  

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On 28 Nov, 16:40, "luke999" <luke_hollingwo...@hotmail.com> wrote:
> I am currently tasked with optimizing FIR filters as lower order IIR
> filters so that a micro-controller can perform the necessary DSP. This is
> performed in the time domain rather than the frequency domain as the
> computation time for the number of FFT's required would be too long,
> preventing us from doing the other required processing.

I'm a bit confused. If you want to optimize the filters
'on the fly' as you process the data, that's what is known
as an 'adaptive filter', and there is a vast literature
on those.

The term 'optimize a filter' is used for the task of
designing a fixed-coefficient filter, which will not
change during operations. Since the optimization
of filter coefficients is a part of the system design
there are no constraints on computing power; you can
use your desktop computer to find the coefficients.

So you might want to clarify which of these contexts you
are working in.

> I am aware of certain optimization techniques to perform the task such as
> treating the optimization as a Conic or Quadratic programming problem and
> constrained and unconstrained reduction techniques based on the BMT
> method.
>
> I am not a DSP expert and so the maths in these techniques is difficult to
> understand and apply to my problem. Therefore is anyone aware of any
> software or subset of software than can perform this task.

The 'easy-to-get' software for filter design would be matlab
with filter design toolbox, which would set you back some
$2000-$2500.

There might be matlab clones out there that has similar
functionality, but I have no personal experience with those.

If you are into adaptive filters you might have no choise
but to deal with the problem from scratch. Or hire somebody
who can do that for you.

Rune

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luke wrote:

> I am currently tasked with optimizing FIR filters as lower order IIR
> filters so that a micro-controller can perform the necessary DSP.

I guess you mean that you want to approximate (not optimize) FIR
filters with IIR filters. I further assume that by IIR filter you
really mean filters with a rational transfer function (delayed sinc
filters are also IIR, but cannot be expressed with rational transfer
function with finite order).

This is always possible (consider that purely transversal filters are
a subset of filters with rational transfer functions). However,
whether you can actually reduce the number of coefficients depends on
how well you want the approximation to be. This is essentially a
filter design problem.

For the solution I would suggest FDLS (search the archives) modified
to minimize the l_infinity error (as opposed to the l_2 error). The
only difference lies in how you solve the linear regression equation.
For l_2 error minimization, you solve the normal equations. For
l_infinity minimization, you rewrite the regression equations into a
linear programming problem. Check out any book on robust regression on
how to do this.

If you want to search around a bit, try "order reduction" and "iir
filter design".

Regards,
Andor

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Andor <a...@gmail.com> writes:
> [...]
> For the solution I would suggest FDLS (search the archives) modified
> to minimize the l_infinity error (as opposed to the l_2 error). The
> only difference lies in how you solve the linear regression equation.
> For l_2 error minimization, you solve the normal equations. For
> l_infinity minimization, you rewrite the regression equations into a
> linear programming problem. Check out any book on robust regression on
> how to do this.

Hi Andor,

Would you please cite a reference or two that presents the theory of
l_infinity and l_2 minimization? My understanding is weak to
non-existent in this area and I'd like to bone up.
-- 
%  Randy Yates                  % "...the answer lies within your soul
%% Fuquay-Varina, NC            %       'cause no one knows which side
%%% 919-577-9882                %                   the coin will fall."
%%%% <y...@ieee.org>           %  'Big Wheels', *Out of the Blue*, ELO
http://www.digitalsignallabs.com

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On 28 Nov., 17:47, Randy Yates <ya...@ieee.org> wrote:
> Andor <andor.bari...@gmail.com> writes:
> > [...]
> > For the solution I would suggest FDLS (search the archives) modified
> > to minimize the l_infinity error (as opposed to the l_2 error). The
> > only difference lies in how you solve the linear regression equation.
> > For l_2 error minimization, you solve the normal equations. For
> > l_infinity minimization, you rewrite the regression equations into a
> > linear programming problem. Check out any book on robust regression on
> > how to do this.
>
> Hi Andor,
>
> Would you please cite a reference or two that presents the theory of
> l_infinity and l_2 minimization? My understanding is weak to
> non-existent in this area and I'd like to bone up.

Hi Randy

A nice article available online is [1]. It discusses numerical aspects
of l_1 and l_2 minimization (for small n, l_1 is actually faster than
l_2!). l_1 minimization is solved by reformulating the regression
equation as a linear programming problem. Finding the l_infinity
solution is done in exactly the same manner, except that the linear
programing reformulation is slightly different. I expanded on this
here some time ago:

http://groups.google.ch/group/comp.dsp/browse_frm/thread/d8aaa0438e620cf2/151a77cd29dc12c9?#151a77cd29dc12c9

Regards,
Andor

[1] S. Portnoy, R. Koeneker, The Gaussian hare and the Laplacian
tortoise: computability of squared-error versus absolute-error
estimators, Statistical Science, Vol. 12, Nr. 4, 279-300, 1997.

Online:
http://projecteuclid.org/DPubS?verb=Display&version=1.0&service=UI&handle=euclid.ss/1030037960&page=reco
rd

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On Fri, 28 Nov 2008 08:32:12 -0800 (PST), Andor
<a...@gmail.com> wrote:

>For the solution I would suggest FDLS (search the archives) modified
>to minimize the l_infinity error (as opposed to the l_2 error). The
>only difference lies in how you solve the linear regression equation.
>For l_2 error minimization, you solve the normal equations. For
>l_infinity minimization, you rewrite the regression equations into a
>linear programming problem. Check out any book on robust regression on
>how to do this.

I sure do wish that you'd publish this, for those of us who don't know
diddly about linear programming.

Greg

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Andor <a...@gmail.com> writes:

> On 28 Nov., 17:47, Randy Yates <ya...@ieee.org> wrote:
>> Andor <andor.bari...@gmail.com> writes:
>> > [...]
>> > For the solution I would suggest FDLS (search the archives) modified
>> > to minimize the l_infinity error (as opposed to the l_2 error). The
>> > only difference lies in how you solve the linear regression equation.
>> > For l_2 error minimization, you solve the normal equations. For
>> > l_infinity minimization, you rewrite the regression equations into a
>> > linear programming problem. Check out any book on robust regression on
>> > how to do this.
>>
>> Hi Andor,
>>
>> Would you please cite a reference or two that presents the theory of
>> l_infinity and l_2 minimization? My understanding is weak to
>> non-existent in this area and I'd like to bone up.
>
> Hi Randy
>
> A nice article available online is [1]. It discusses numerical aspects
> of l_1 and l_2 minimization (for small n, l_1 is actually faster than
> l_2!). l_1 minimization is solved by reformulating the regression
> equation as a linear programming problem. Finding the l_infinity
> solution is done in exactly the same manner, except that the linear
> programing reformulation is slightly different. I expanded on this
> here some time ago:
>
> http://groups.google.ch/group/comp.dsp/browse_frm/thread/d8aaa0438e620cf2/151a77cd29dc12c9?#151a77cd29dc12c9
>
> Regards,
> Andor
>
> [1] S. Portnoy, R. Koeneker, The Gaussian hare and the Laplacian
> tortoise: computability of squared-error versus absolute-error
> estimators, Statistical Science, Vol. 12, Nr. 4, 279-300, 1997.
>
> Online:
>
http://projecteuclid.org/DPubS?verb=Display&version=1.0&service=UI&handle=euclid.ss/1030037960&page=reco
rd

Thanks Andor! I'll have to take some time to digest this, so nothing
intelligent to respond with for now...
-- 
%  Randy Yates                  % "So now it's getting late,
%% Fuquay-Varina, NC            %    and those who hesitate
%%% 919-577-9882                %    got no one..."
%%%% <y...@ieee.org>           % 'Waterfall', *Face The Music*, ELO
http://www.digitalsignallabs.com

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Greg Berchin wrote:
(snip)

> I sure do wish that you'd publish this, for those of us who don't know
> diddly about linear programming.

Teaching linear programming doesn't seem very popular lately.
My daughter is learning it in high school, but I don't know how
many other schools are teaching it.

-- glen

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On Fri, 28 Nov 2008 16:12:10 -0700, Glen Herrmannsfeldt
<g...@ugcs.caltech.edu> wrote:

>Teaching linear programming doesn't seem very popular lately.
>My daughter is learning it in high school, but I don't know how
>many other schools are teaching it.

All the programming I know, I taught myself.  I may have to do the
same with linear programming.

Greg

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On 29 Nov, 00:12, Glen Herrmannsfeldt <g...@ugcs.caltech.edu> wrote:
> Greg Berchin wrote:
>
> (snip)
>
> > I sure do wish that you'd publish this, for those of us who don't know
> > diddly about linear programming.
>
> Teaching linear programming doesn't seem very popular lately.

'Genetic Algorithms' sounds so much more sexy. And GAs relieve
the 'analyst' from the burden of thinking... no wonder LP has
become a thing of the past.

> My daughter is learning it in high school, but I don't know how
> many other schools are teaching it.

Last week there was a suggestion from somebody to tighten
requirements to grades for 'teacher's students' (students
under education to become teachers.) In the Norwegian school
system the grades are from 0 to 6 (6 best) with 2 as the
lowest 'pass' grade. A few years ago the admissive grades
were restricted so that students needed grades of 3 or
better in a couple of the key subjects. At that time there
was all of a sudden 30% over-capacity in the 'teachers schools'
there were 30% more student slots than qualified applicants
under the new rules.

[Which means that we used to admit as teachers the most
incompetent graduating students! ]

Under last week's suggestion, requiring grades of 4 or
better in two or three key subjects, 50% of the present
students would not be qualified.

Seems things are moving in the right direction, but
30 years of negligence is not undone over night.

Rune

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