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Why do bandpass filters don't work like notch filters?

Started by gretzteam April 27, 2010
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!

On 27 apr, 14:52, "gretzteam" <gretzteam@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
>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!