[sdiy] Multimode pole-mixing - building notch responses

[Tom Wiltshire]

Hi All,

Can anyone explain pole-mixing notch responses to me in a way that I can “get”?

Most of the responses from a multimode pole-mixing filter I understand, but I’m struggling with notches.

The bandpass responses, for example, are the same as the highpass responses, but “shifted right” to effectively make them into a highpass and a lowpass in series - a bandpass. That’s easy to understand. Intuitive, even.

I guess the trouble is I don’t really know what a notch filter looks like in terms of the s-domain equations, so it’s hard to see how the pole-mixing leads to that result. Even the Allpass responses are easier, but in that case, I *do* know what the s domain equation is supposed to look like (s-1/s+1 for the one-pole, s^2-s+1 / s^2+s+1 for the two-pole, right?).

Any pointers appreciated. I’m trying to fill in a few of the blanks!

Thanks,
Tom