[sdiy] Multimode pole-mixing - building notch responses

[Donald Tillman]

> On Sep 15, 2018, at 11:44 AM, Tom Wiltshire <tom at electricdruid.net> wrote:
> 
> Sorry, I didn’t explain myself well enough. I’m talking about a pole-mixing filter like the Xpander (multimode that way) not a state-variable filter (multimode a different way).
> 
> State variable I get well enough, but I hadn’t really considered the notch response there either, so thanks for the explanation. The S domain maths is the same for the pole-mixing case, so I’m looking for  (s^2 + 1) / (s^2 + s + 1) for a 2-pole notch, right?
> 
> What does the equation for a 4-pole notch look like? Can you do a 3-pole notch? What does that look like?

Well, tell us more...  :-)

Yes, a 2-pole notch is: (s^2 + 1) / (s^2 + s + 1)

A 3-pole notch is: (s^3 + s^2 + s + 1) / (s^3 + 2s^2 + 2s + 1)

But it doesn't buy you anything over a 2-pole notch.

A 4-pole filter can have a notch, but again, it doesn't buy you anything over a 2-pole notch.

A 4-pole filter can have a double notch on a Butterworth response, like this:
    (s^4 + 3.4s^2 + 1) / ((s^2 + 0.848s + 1)(s^2 + 0.765s + 1))

But that's not very different from two 2-pole filters.

  -- Don
--
Donald Tillman, Palo Alto, California
http://www.till.com

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