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From: gretzteam on 27 Apr 2010 08:52
Hi,
Say I generate a digital 2nd order notch filter. With the lattice
structure, one coefficient controls the notch frequency and the other the
bandwidth. I can get VERY good attenuation of the notch frequency, pretty
much only depending on wordlength used. The overall response looks like one
deep and narrow hole in a horizontal line with magnitude 1.

Now, if I generate the same order bandpass filter counterpart(either a new
design or by taking the complementary output of the lattice notch), I get a
sloppy looking response! The passband frequency is at 1, but the side lobes
don't give more than 30-60dB on either side.

I guess it has to do with poles not becoming zeros and vice versa, but I
can't quite figure it out.

Thanks!

From: Rune Allnor on 27 Apr 2010 09:09
On 27 apr, 14:52, "gretzteam" <gretzteam(a)n_o_s_p_a_m.yahoo.com> wrote:
> Hi,
> Say I generate a digital 2nd order notch filter. With the lattice
> structure, one coefficient controls the notch frequency and the other the
> bandwidth. I can get VERY good attenuation of the notch frequency, pretty
> much only depending on wordlength used. The overall response looks like one
> deep and narrow hole in a horizontal line with magnitude 1.
>
> Now, if I generate the same order bandpass filter counterpart(either a new
> design or by taking the complementary output of the lattice notch), I get a
> sloppy looking response! The passband frequency is at 1, but the side lobes
> don't give more than 30-60dB on either side.
>
> I guess it has to do with poles not becoming zeros and vice versa, but I
> can't quite figure it out.

This is pretty much like learning to read: At first you can't make
head or tail of the text; once you've learned how to read, you don't
understand why there was a problem at all.

You need to work through this in detail. Work through the magnitude
response formula for the biquad, and try and get a sense for how
the poles and zeros contribute to the overall response. Start out
with
the notch filter with a notch at w=pi/4. Then move the pole to some
other
location, w=3pi/4 (the zero remains at w = pi/4) and see the
difference.
Then contemplate the magnitude response formulas to find out what
happens.

Rune
From: gretzteam on 27 Apr 2010 12:15

>This is pretty much like learning to read: At first you can't make
>head or tail of the text; once you've learned how to read, you don't
>understand why there was a problem at all.
>
>You need to work through this in detail. Work through the magnitude
>response formula for the biquad, and try and get a sense for how
>the poles and zeros contribute to the overall response. Start out
>with
>the notch filter with a notch at w=pi/4. Then move the pole to some
>other
>location, w=3pi/4 (the zero remains at w = pi/4) and see the
>difference.
>Then contemplate the magnitude response formulas to find out what
>happens.
>
>Rune


Ok thank I will play around with a simple transfer function!
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