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 3060dB 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 3060dB 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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