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I have a biquad filter, configuread as a low-pass filter (using Zolzer's formulas, similar to these). It does not overshoot and decays nicely in what I assume is -40dB/dec.

How can I device a calculation, that takes not only desired_cutoff_frequency as a parameter, but also desired_decay_slope?

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The decay is determined by the filter order. With a biquad (i.e., second order) filter you can't get more than approximately 40dB/decade (unless you're close to the Nyquist frequency where the frequency response has its zero). You can have less if you like, but not more. If you want less, then the only way to do that is to approximate a given slope by using some optimization method.

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  • $\begingroup$ Can you please expand on how to get less steep slope? Probably I can zero out some coefficients and assign a 1st order low-pass filter to the rest, but what about something less barbaric? $\endgroup$ – Vorac Mar 20 '15 at 8:45
  • $\begingroup$ @Vorac: What I meant is numerical optimization for approximating a prescribed slope, i.e. your filter coefficients are the result of some optimization procedure. $\endgroup$ – Matt L. Mar 20 '15 at 9:10

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