<html><head><meta http-equiv="Content-Type" content="text/html; charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><br class=""><div><blockquote type="cite" class=""><div class="">On Sep 15, 2018, at 11:44 AM, Tom Wiltshire <<a href="mailto:tom@electricdruid.net" class="">tom@electricdruid.net</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><div class="">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).<br class=""><br class="">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?<br class=""><br class="">What does the equation for a 4-pole notch look like? Can you do a 3-pole notch? What does that look like?<br class=""></div></div></blockquote><div><br class=""></div><div>Well, tell us more... :-)</div><div><br class=""></div><div>Yes, a 2-pole notch is: (s^2 + 1) / (s^2 + s + 1)</div><div><br class=""></div><div>A 3-pole notch is: (s^3 + s^2 + s + 1) / (s^3 + 2s^2 + 2s + 1)</div><div><br class=""></div><div>But it doesn't buy you anything over a 2-pole notch.</div><div><br class=""></div><div>A 4-pole filter can have a notch, but again, it doesn't buy you anything over a 2-pole notch.</div><div><br class=""></div><div>A 4-pole filter can have a double notch on a Butterworth response, like this:</div><div> (s^4 + 3.4s^2 + 1) / ((s^2 + 0.848s + 1)(s^2 + 0.765s + 1))</div><div><br class=""></div><div>But that's not very different from two 2-pole filters.</div><div><br class=""></div><div> -- Don</div></div><div class=""><div style="color: rgb(0, 0, 0); font-family: Menlo; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px;">--<br class="">Donald Tillman, Palo Alto, California<br class=""><a href="http://www.till.com" class="">http://www.till.com</a></div>
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