# Filter design with 'freqsamp' method?

Started by June 30, 2010
```I'm new to Matlab, so this is probably a really dumb question.
I'm trying to design an FIR where I can set the points.
I want a symmetric FIR.
I'm assuming that an N tap FIR gives me N/2 degrees of freedom
for an even number of taps, and (N + 1)/2 degrees of freedom
for an odd number of taps.
This should allow me to set the frequency response at a
number of points equal to the degrees of freedom, and
have the frequency response travel through these points
exactly. If I don't specify transitions that are too sharp
relative to the number of taps, then the frequency response
should be reasonably well controlled between the set points.

I had assumed that I could use the filter toolbox's freqsamp
method to do this, but it doesn't seem to work as I expected.
What am I doing wrong? I'd normally do this in Mathematica
or C, but I'm trying to get into the spirit of Matlab.

I would want to solve the point setting problem anyway, but
perhaps there's an easier way to do the immediate task that
I wanted it for. I want to implement a Butterworth amplitude
response in an FIR filter (to emulate some legacy equipment)
but I can't find an easy way of doing that in Matlab (hence the
point setting experiments).

Thanks

Pete

```
```
Pete Fraser wrote:

> I'm new to Matlab, so this is probably a really dumb question.
> I'm trying to design an FIR where I can set the points.
> I want a symmetric FIR.
> I'm assuming that an N tap FIR gives me N/2 degrees of freedom
> for an even number of taps, and (N + 1)/2 degrees of freedom
> for an odd number of taps.
> This should allow me to set the frequency response at a
> number of points equal to the degrees of freedom, and
> have the frequency response travel through these points
> exactly. If I don't specify transitions that are too sharp
> relative to the number of taps, then the frequency response
> should be reasonably well controlled between the set points.
>
> I had assumed that I could use the filter toolbox's freqsamp
> method to do this, but it doesn't seem to work as I expected.
> What am I doing wrong? I'd normally do this in Mathematica
> or C, but I'm trying to get into the spirit of Matlab.
>
> I would want to solve the point setting problem anyway, but
> perhaps there's an easier way to do the immediate task that
> I wanted it for. I want to implement a Butterworth amplitude
> response in an FIR filter (to emulate some legacy equipment)
> but I can't find an easy way of doing that in Matlab (hence the
> point setting experiments).

But why would anyone want to emulate Butterworth magnitude response in a
linear phase FIR filter whereas it is very straightforward to do the
(**exact) Butterworth as IIR filter?

** frequency warping

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

```
```"Vladimir Vassilevsky" <nospam@nowhere.com> wrote in message
news:0Jidnc3knONVbbbRnZ2dnUVZ_oSdnZ2d@giganews.com...

> But why would anyone want to emulate Butterworth magnitude response in a
> linear phase FIR filter whereas it is very straightforward to do the
> (**exact) Butterworth as IIR filter?

Butterworth will be one of several possible responses
from the same hardware.

I'd rather not deal with Butterworth's phase issues.

Pete

```
```On 6/30/2010 10:06 PM, Pete Fraser wrote:
> "Vladimir Vassilevsky"<nospam@nowhere.com>  wrote in message
> news:0Jidnc3knONVbbbRnZ2dnUVZ_oSdnZ2d@giganews.com...
>
>> But why would anyone want to emulate Butterworth magnitude response in a
>> linear phase FIR filter whereas it is very straightforward to do the
>> (**exact) Butterworth as IIR filter?
>
> Butterworth will be one of several possible responses
> from the same hardware.
>
> I'd rather not deal with Butterworth's phase issues.

What is so good about a Butterworth amplitude response that you want to
imitate it?

Jerry
--
Engineering is the art of making what you want from things you can get.
&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
```
```On 06/30/2010 06:21 PM, Pete Fraser wrote:
> I'm new to Matlab, so this is probably a really dumb question.
> I'm trying to design an FIR where I can set the points.
> I want a symmetric FIR.
> I'm assuming that an N tap FIR gives me N/2 degrees of freedom
> for an even number of taps, and (N + 1)/2 degrees of freedom
> for an odd number of taps.
> This should allow me to set the frequency response at a
> number of points equal to the degrees of freedom, and
> have the frequency response travel through these points
> exactly. If I don't specify transitions that are too sharp
> relative to the number of taps, then the frequency response
> should be reasonably well controlled between the set points.
>
> I had assumed that I could use the filter toolbox's freqsamp
> method to do this, but it doesn't seem to work as I expected.
> What am I doing wrong? I'd normally do this in Mathematica
> or C, but I'm trying to get into the spirit of Matlab.
>
> I would want to solve the point setting problem anyway, but
> perhaps there's an easier way to do the immediate task that
> I wanted it for. I want to implement a Butterworth amplitude
> response in an FIR filter (to emulate some legacy equipment)
> but I can't find an easy way of doing that in Matlab (hence the
> point setting experiments).

Make a vector that "draws" the frequency response that you want, then
take its FFT.

It may not be the entirely kosher way to do it, but it certainly works.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" was written for you.
See details at http://www.wescottdesign.com/actfes/actfes.html
```
```Tim Wescott  <tim@seemywebsite.com> wrote:

>Make a vector that "draws" the frequency response that you want, then
>take its FFT.
>
>It may not be the entirely kosher way to do it, but it certainly works.

Doesn't this give you a complex filter?

Can you just take the real part afterwards?

Steve
```
```On Jun 30, 10:39&#2013266080;pm, Tim Wescott <t...@seemywebsite.com> wrote:
> On 06/30/2010 06:21 PM, Pete Fraser wrote:
>
>
>
> > I'm new to Matlab, so this is probably a really dumb question.
> > I'm trying to design an FIR where I can set the points.
> > I want a symmetric FIR.
> > I'm assuming that an N tap FIR gives me N/2 degrees of freedom
> > for an even number of taps, and (N + 1)/2 degrees of freedom
> > for an odd number of taps.
> > This should allow me to set the frequency response at a
> > number of points equal to the degrees of freedom, and
> > have the frequency response travel through these points
> > exactly. If I don't specify transitions that are too sharp
> > relative to the number of taps, then the frequency response
> > should be reasonably well controlled between the set points.
>
> > I had assumed that I could use the filter toolbox's freqsamp
> > method to do this, but it doesn't seem to work as I expected.
> > What am I doing wrong? I'd normally do this in Mathematica
> > or C, but I'm trying to get into the spirit of Matlab.
>
> > I would want to solve the point setting problem anyway, but
> > perhaps there's an easier way to do the immediate task that
> > I wanted it for. I want to implement a Butterworth amplitude
> > response in an FIR filter (to emulate some legacy equipment)
> > but I can't find an easy way of doing that in Matlab (hence the
> > point setting experiments).
>
> Make a vector that "draws" the frequency response that you want, then
> take its FFT.
>
> It may not be the entirely kosher way to do it, but it certainly works.

Pete might want to use the "window method".  with an iFFT *larger*
than N, draw in the frequency response, he'll get an impulse response
that is longer than N, then window it to length N.  (then maybe FFT
back to see how bad the window mangled things.)

r b-j

```
```On 06/30/2010 08:10 PM, Steve Pope wrote:
> Tim Wescott<tim@seemywebsite.com>  wrote:
>
>> Make a vector that "draws" the frequency response that you want, then
>> take its FFT.
>>
>> It may not be the entirely kosher way to do it, but it certainly works.
>
> Doesn't this give you a complex filter?
>
> Can you just take the real part afterwards?

If the desired magnitude response is real and symmetric around the
frequency = 0 bin (element 1 in Matlab's indexing scheme) then the FFT
will be largely real, with only leftover numerical noise in the
imaginary part.  If the imaginary part has any weight to it at all, then
you've done something wrong.

Note that you want to be symmetric around frequency = 0 modulo the whole
thing; i.e. for a 256 element vector element 2 should equal element 256
with Matlab-style indexing, element 3 should equal element 255, etc.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" was written for you.
See details at http://www.wescottdesign.com/actfes/actfes.html
```
```Tim Wescott  <tim@seemywebsite.com> wrote:

>On 06/30/2010 08:10 PM, Steve Pope wrote:

>> Tim Wescott<tim@seemywebsite.com>  wrote:

>>> Make a vector that "draws" the frequency response that you want, then
>>> take its FFT.

>>> It may not be the entirely kosher way to do it, but it certainly works.

>> Doesn't this give you a complex filter?

>> Can you just take the real part afterwards?

>If the desired magnitude response is real and symmetric around the
>frequency = 0 bin (element 1 in Matlab's indexing scheme) then the FFT
>will be largely real, with only leftover numerical noise in the
>imaginary part.  If the imaginary part has any weight to it at all, then
>you've done something wrong.

That makes sense.  Thanks.

Steve
```
```"Jerry Avins" <jya@ieee.org> wrote in message