sauwen wrote:

> Hi all.  Does anyone know how to change the width of a feedback
> comb filter's teeth? From the general idea on wikipedia, it
> seems like it is only possible to change the delays and the
> gain. 

http://en.wikipedia.org/wiki/Comb_filter shows an unnormalized comb 
filter. Put a multiplier in series to keep the peaks at unit gain and 
the alpha coefficient will control Q; this is the same structure as 
Robert has shown.

But. That way shifts the strong dependence on alpha from peaks to 
troughs, which were pretty insensitive in the unnormalized version, 
as Wikipedia's graphs show. (Specifically, the minima will approach 
zero instead of 1/2 as |alpha| increases.) If that's fine with you, 
great. Otherwise describe in detail just what you wish the response 
to be across different settings -- what shall move and what is to 
stay put.

Martin

-- 
Why is 6 afraid of 7?
Because 7 8 9.

On Oct 10, 5:35 am, Andor <andor.bari...@gmail.com> wrote:
> robert bristow-johnson wrote:
> > On Oct 9, 5:21 pm, "sauwen" <sauwen...@gmail.com> wrote:
>
> > > Hi all.  Does anyone know how to change the width of a feedback comb
> > > filter's teeth? From the general idea on wikipedia, it seems like it is
> > > only possible to change the delays and the gain.
>
> > when you have a feedback comb filter (or even a feed-forward comb
> > filter), try to imagine replacing the delay element, z^-N, with a
> > quantitatively different delay element, z^-1.  then with that
> > feedback, you have a simple LPF where, depending on the feedback gain,
> > you can get an idea of how wide this single tooth is.  now replace
> > z^-1 with z^-N and you will see that your tooth is scrunched by a
> > factor of 1/N and there are N of these teeth from -Nyquist to just
> > under +Nyquist.
>
> But what to do if you have a comb filter where you are interested in N
> notches and now want to sharpen those notches without increasing their
> number?

what i intended was that one would do it the same way as
"sharpening" (perhaps not necessarily the same thing as what you are
referring to) the simple one-pole LPF by increasing the feedback coef
to get closer to 1.  but replace the z^-1 in the LPF prototype with z^-
N to get a comb.  as the coef (which happens to be the pole value)
gets closer to 1, the LPF cutoff gets lower (or closer to the center
of the tooth).

LPF:

             .-----.            .------.
    x[n] --->| 1-p |--->(+)---->| z^-1 |----------> y[n]
             '-----'     ^      '------'       |
                         |                     |
                         |      .-----.        |
                         '--<---|  p  |<-------'
                                '-----'

now ask, what happens when z^-1 is replaced by z^-N?

feedback comb:

             .-----.            .------.
    x[n] --->| 1-p |--->(+)---->| z^-N |----------> y[n]
             '-----'     ^      '------'       |
                         |                     |
                         |      .-----.        |
                         '--<---|  p  |<-------'
                                '-----'

i think it's pretty straight-forward and you sharpen the teeth by
increasing p (but |p| must remain less than 1).  that's how you
sharpen the single tooth of the LPF.  this was the simple answer that
i wanted to point to.  if you consider that even a simple LPF is a
sorta comb filter with teeth at every multiple of 2*pi, whatever you
can do with a LPF to lower the cutoff frequency (the difference
between the bandedge and the middle of the tooth at 0 Hz) is what you
do with a comb filter (where z^-1 is replaced by z^-N) to decrease the
frequency difference between the bandedge and the frequency of the
middle of the tooth.  but the frequency scale is itself scaled by 1/N
so the teeth are at multiples of 2*pi/N and the distance between tooth
center and edge is reduced by the same factor of 1/N.

you could make sharper comb filters (with more rectangular teeth) by
starting with a 2nd order (or higher order) LPF prototype (with z^-1)
and replacing those unit delays with a longer delay, z^-N.  you could
use the same concepts of Butterworth filters to make the teeth of the
comb filter look like little brick-wall rectangles with sharp corners
at the bandedges.

so now i'm gonna look more closely at Matt's pdf that you linked to.
i sorta think that this might correspond to transforming the
feedforward (FIR) LPF to a corresponding comb.  but i dunno yet.

r b-j

On Fri, 10 Oct 2008 02:35:04 -0700 (PDT), Andor
<andor.bariska@gmail.com> wrote:

>robert bristow-johnson wrote:
>> On Oct 9, 5:21&#4294967295;pm, "sauwen" <sauwen...@gmail.com> wrote:
>>
>> > Hi all. &#4294967295;Does anyone know how to change the width of a feedback comb
>> > filter's teeth? From the general idea on wikipedia, it seems like it is
>> > only possible to change the delays and the gain.
>>
>> when you have a feedback comb filter (or even a feed-forward comb
>> filter), try to imagine replacing the delay element, z^-N, with a
>> quantitatively different delay element, z^-1. &#4294967295;then with that
>> feedback, you have a simple LPF where, depending on the feedback gain,
>> you can get an idea of how wide this single tooth is. &#4294967295;now replace
>> z^-1 with z^-N and you will see that your tooth is scrunched by a
>> factor of 1/N and there are N of these teeth from -Nyquist to just
>> under +Nyquist.
>>
>> does that help you figger it out?
>
>But what to do if you have a comp filter where you are interested in N
>notches and now want to sharpen those notches without increasing their
>number? FIR filter sharpening to the rescue!
>
>Matthew's original DSP Guru article is now published (well done
>Matthew, whereever you are!) but still downloadable:
>
>http://www.dsprelated.com/showabstract/62.php
>
>Regards,
>Andor

Hi Andor,
  That's a good point you're making here.
Two items:

[1] I don't think Donadio's "filter sharpening" article 
was ever on the dspguru.com website.  It was, however, 
in the IEEE Sig. Proc. Magazine's "DSP Tip & Tricks" 
column in Sept. 2003 (pages 61-63).  A slightly expanded 
version of that article later became Chapoter 1 of the 
book "Streamlining Digital Signal Processing, a Tricks 
of the Trade Guidebook" (published by Wiley & Sons and 
the IEEE).  That PDF file, that you cited, is the 
book's Chapter 1. 

[2] In the first sentence of the last paragraph on 
page 6 of the PDF file, the phrase "half-power" should 
be changed to "half-amplitude".

Regards,
[-Rick-]

robert bristow-johnson wrote:
> On Oct 9, 5:21&#4294967295;pm, "sauwen" <sauwen...@gmail.com> wrote:
>
> > Hi all. &#4294967295;Does anyone know how to change the width of a feedback comb
> > filter's teeth? From the general idea on wikipedia, it seems like it is
> > only possible to change the delays and the gain.
>
> when you have a feedback comb filter (or even a feed-forward comb
> filter), try to imagine replacing the delay element, z^-N, with a
> quantitatively different delay element, z^-1. &#4294967295;then with that
> feedback, you have a simple LPF where, depending on the feedback gain,
> you can get an idea of how wide this single tooth is. &#4294967295;now replace
> z^-1 with z^-N and you will see that your tooth is scrunched by a
> factor of 1/N and there are N of these teeth from -Nyquist to just
> under +Nyquist.
>
> does that help you figger it out?

But what to do if you have a comp filter where you are interested in N
notches and now want to sharpen those notches without increasing their
number? FIR filter sharpening to the rescue!

Matthew's original DSP Guru article is now published (well done
Matthew, whereever you are!) but still downloadable:

http://www.dsprelated.com/showabstract/62.php

Regards,
Andor

>On Oct 9, 5:21=A0pm, "sauwen" <sauwen...@gmail.com> wrote:
>> Hi all. =A0Does anyone know how to change the width of a feedback comb
>> filter's teeth? From the general idea on wikipedia, it seems like it
is
>> only possible to change the delays and the gain.
>
>when you have a feedback comb filter (or even a feed-forward comb
>filter), try to imagine replacing the delay element, z^-N, with a
>quantitatively different delay element, z^-1.  then with that
>feedback, you have a simple LPF where, depending on the feedback gain,
>you can get an idea of how wide this single tooth is.  now replace
>z^-1 with z^-N and you will see that your tooth is scrunched by a
>factor of 1/N and there are N of these teeth from -Nyquist to just
>under +Nyquist.
>
>does that help you figger it out?
>
>r b-j
>
Hmm thanks for the insight..!

On Oct 9, 5:21&#4294967295;pm, "sauwen" <sauwen...@gmail.com> wrote:
> Hi all. &#4294967295;Does anyone know how to change the width of a feedback comb
> filter's teeth? From the general idea on wikipedia, it seems like it is
> only possible to change the delays and the gain.

when you have a feedback comb filter (or even a feed-forward comb
filter), try to imagine replacing the delay element, z^-N, with a
quantitatively different delay element, z^-1.  then with that
feedback, you have a simple LPF where, depending on the feedback gain,
you can get an idea of how wide this single tooth is.  now replace
z^-1 with z^-N and you will see that your tooth is scrunched by a
factor of 1/N and there are N of these teeth from -Nyquist to just
under +Nyquist.

does that help you figger it out?

r b-j