On Oct 10, 5:35 am, Andor <andor.bari...@[EMAIL PROTECTED]
> wrote:
> robert bristow-johnson wrote:
> > On Oct 9, 5:21 pm, "sauwen" <sauwen...@[EMAIL PROTECTED]
> 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
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