Matlab lookup table?

Using Matlab, I need some way to automatically find the point where an
arbitrary filter response crosses a threshold.  For example, given a low
pass filter, use freqz to find the response, then find the frequency that
where the magnitude most closely corresponds to -3dB.  If the response never
exactly hits -3dB, interpolation might be nice, but not really necessary as
I can generate enough points in the frequency response to make the error
negligibly small.  I would think this could be done with some sort of table
lookup function if there is such a thing.

Does anyone know if there are any built-in functions to help with this?  Or
should I just use a brute-force approach with a "for" loop looking for the
value?

--
Jon Harris
SPAM blocked e-mail address in use.  Replace the ANIMAL with 7 to reply.

Hello Jon,

A classic way to do this is inverse interpolation.  Just sample the filter's
frequency response at a bunch of points (spanning your desired point of
interest) creating f(w) and w pairs. Now feed these to your favorite
interpolation routine but with the f(w) and w values swapped. Now just feed
your desired f(w) value into the interpolator and out will pop the
corresponding w. The interpolation routine can be either a polynomial type
(I.e., Lagrange, Chebyshev, etc.) or a spline type (cubic, B, etc.). Matlab
should have some basic interpolation functions built in. For the case of low
polynomial order, you can directly do inverse interpolation with either
linear or quadratic forms.

Clay





"Jon Harris" <goldentully@hotmail.com> wrote in message
news:bp0nmh$1j70et$1@ID-210375.news.uni-berlin.de...
> Using Matlab, I need some way to automatically find the point where an
> arbitrary filter response crosses a threshold.  For example, given a low
> pass filter, use freqz to find the response, then find the frequency that
> where the magnitude most closely corresponds to -3dB.  If the response
never
> exactly hits -3dB, interpolation might be nice, but not really necessary
as
> I can generate enough points in the frequency response to make the error
> negligibly small.  I would think this could be done with some sort of
table
> lookup function if there is such a thing.
>
> Does anyone know if there are any built-in functions to help with this?
Or
> should I just use a brute-force approach with a "for" loop looking for the
> value?
>
> --
> Jon Harris
> SPAM blocked e-mail address in use.  Replace the ANIMAL with 7 to reply.
>
>

Jon Harris wrote:
> 
> Using Matlab, I need some way to automatically find the point where an
> arbitrary filter response crosses a threshold. For example, given a low
> pass filter, use freqz to find the response, then find the frequency that
> where the magnitude most closely corresponds to -3dB. 

You just have to solve the polynomial |H(Z)| = 1/sqrt(2).
Any numeric method will jump on solution after several iterations. 

> Does anyone know if there are any built-in functions to help with this?  Or
> should I just use a brute-force approach with a "for" loop looking for the
> value?

Use any of standard methods for solving equations.

Vladimir Vassilevsky

DSP and Mixed Signal Design Consultant

http://www.abvolt.com

On Thu, 13 Nov 2003 12:02:42 -0800, "Jon Harris"
<goldentully@hotmail.com> wrote:

>Using Matlab, I need some way to automatically find the point where an
>arbitrary filter response crosses a threshold.  For example, given a low
>pass filter, use freqz to find the response, then find the frequency that
>where the magnitude most closely corresponds to -3dB.  If the response never
>exactly hits -3dB, interpolation might be nice, but not really necessary as
>I can generate enough points in the frequency response to make the error
>negligibly small.  I would think this could be done with some sort of table
>lookup function if there is such a thing.
>
>Does anyone know if there are any built-in functions to help with this?  Or
>should I just use a brute-force approach with a "for" loop looking for the
>value?
>
>--
>Jon Harris

Hi John,
   If I understand your problem, maybe the 
following MATLAB code will help.  If you have 
the A & B coefficients of your lowpass filter:


[H,W] = freqz(B,A,N)
Hmag = abs(H);  % get the magnitude response
Hmag = 20*log10(Hmag/max(Hmag)); % Log with 0 dB being largest
I = find(Hmag<-3); % Find indices beyond end of passband
Wcutoff = W(min(I));  % Here's the lowpass -3 dB cutoff freq

Make N as large as you like.  The higher N, the 
better freq resolution you'll have in estimating 
the filter's -3 dB cutoff freq.

Good Luck,
[-Rick-]

Jon Harris wrote:
> Using Matlab, I need some way to automatically find the point where an
> arbitrary filter response crosses a threshold.  For example, given a low
> pass filter, use freqz to find the response, then find the frequency that
> where the magnitude most closely corresponds to -3dB.  If the response never
> exactly hits -3dB, interpolation might be nice, but not really necessary as
> I can generate enough points in the frequency response to make the error
> negligibly small.  I would think this could be done with some sort of table
> lookup function if there is such a thing.
> 
> Does anyone know if there are any built-in functions to help with this?  Or
> should I just use a brute-force approach with a "for" loop looking for the
> value?
> 
> --
> Jon Harris
> SPAM blocked e-mail address in use.  Replace the ANIMAL with 7 to reply.
> 
> 

something like this I think would give you the index in x where the 
value is closest to 3

find(abs(x-3) == min(abs(x-3)))


-Lasse

Thanks Rick.  The "find" function was what I was looking for.  Thanks also
to the rest of you who had good suggestions as well.

"Rick Lyons" <ricklyon@REMOVE.onemain.com> wrote in message
news:3fb404fd.48741156@news.west.earthlink.net...
> On Thu, 13 Nov 2003 12:02:42 -0800, "Jon Harris"
> <goldentully@hotmail.com> wrote:
>
> >Using Matlab, I need some way to automatically find the point where an
> >arbitrary filter response crosses a threshold.  For example, given a low
> >pass filter, use freqz to find the response, then find the frequency that
> >where the magnitude most closely corresponds to -3dB.  If the response
never
> >exactly hits -3dB, interpolation might be nice, but not really necessary
as
> >I can generate enough points in the frequency response to make the error
> >negligibly small.  I would think this could be done with some sort of
table
> >lookup function if there is such a thing.
> >
> >Does anyone know if there are any built-in functions to help with this?
Or
> >should I just use a brute-force approach with a "for" loop looking for
the
> >value?
> >
> >--
> >Jon Harris
>
> Hi John,
>    If I understand your problem, maybe the
> following MATLAB code will help.  If you have
> the A & B coefficients of your lowpass filter:
>
>
> [H,W] = freqz(B,A,N)
> Hmag = abs(H);  % get the magnitude response
> Hmag = 20*log10(Hmag/max(Hmag)); % Log with 0 dB being largest
> I = find(Hmag<-3); % Find indices beyond end of passband
> Wcutoff = W(min(I));  % Here's the lowpass -3 dB cutoff freq
>
> Make N as large as you like.  The higher N, the
> better freq resolution you'll have in estimating
> the filter's -3 dB cutoff freq.
>
> Good Luck,
> [-Rick-]
>
>

Not sure if this answers your question, I may have misunderstood what
you where trying to do?

b=[0.5263    0.4211    0.0526]; % define arbitrary filter
a=1;
N=100; % num points
[h,w]=freqz(b,a,N); % generate mag and phase
logh = 20*log10(abs(h)); % in logs
plot(w,logh) % lets make sure we have something sensible

now you want to find the point on the graph where it crosses -3dB
yeah?

val = -3; % this is the value that you want to get close to
index=find(logh<val); % find the indices of all elements in the vector
larger than our value

logh(index(1)), w(index(1)) % use the point where it first crosses our
threshold

et voila!

you can use the find function for all sorts of things, i mean if the
freq response decides it wants to come back up and hang aroud the 3 db
mark as the freq increases, then you'll have to do something clever to
find all the points that the logh vector crosses the -3db mark, or
gets within X% of the -3db point.  As far as that code goes, if you
know that it only crosses -3dB one time, then you can take the point
either side of the crossing and perform the interpolation that you
mentioned.   All the best.

col


"Jon Harris" <goldentully@hotmail.com> wrote in message news:<bp0nmh$1j70et$1@ID-210375.news.uni-berlin.de>...
> Using Matlab, I need some way to automatically find the point where an
> arbitrary filter response crosses a threshold.  For example, given a low
> pass filter, use freqz to find the response, then find the frequency that
> where the magnitude most closely corresponds to -3dB.  If the response never
> exactly hits -3dB, interpolation might be nice, but not really necessary as
> I can generate enough points in the frequency response to make the error
> negligibly small.  I would think this could be done with some sort of table
> lookup function if there is such a thing.
> 
> Does anyone know if there are any built-in functions to help with this?  Or
> should I just use a brute-force approach with a "for" loop looking for the
> value?