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I'm writing a C++ application to extract four modulated carrier signals at four separate frequencies, from a single input signal. I've designed four FIR filters at t-filter.appspot.com but they run very slowly, even when I reduce # of taps to 80.

Is there a better option? People seem to point to biquad filters – are these different from FIR filters, and do they run more quickly in software?

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    $\begingroup$ Have you considered doing this in the frequency domain ? $\endgroup$ – Paul R May 7 '13 at 8:06
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    $\begingroup$ One biquad runs a lot faster than a FIR filter with 80 taps. A biquad filter has 5 coefficients, so it requires only 5 multiplications per sample. Your FIR filter requires 80 multiplications per sample (because it is linear phase it only requires 40 multiplications). $\endgroup$ – niaren May 7 '13 at 8:39
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    $\begingroup$ Paul R is right; this application could be a good candidate for frequency-domain filtering, for instance using the overlap-save technique. $\endgroup$ – Jason R May 7 '13 at 12:12
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    $\begingroup$ @niaren is right. A biquad is very fast and much less complicated than taking FFTs and worrying about edge effects. See www-users.cs.york.ac.uk/~fisher/mkfilter for an online design tool (very simple text interface, no graphing like t-filter.) You might try the "Chebyshev" or "resonator" options. $\endgroup$ – Wandering Logic May 7 '13 at 12:35
  • $\begingroup$ Discrete wavelet transforms could maybe help you. They are definitely fast enough anyway, but it will depend on how easy you can get the frequency and band-width to fit. $\endgroup$ – mathreadler Nov 24 '16 at 5:52
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Frequency domain filtering (FFT), as suggested by some comments, is definitely wrong -- it's even slower, or same speed at best! A recursive filter (IIR) is the fastes possible solution. If you choose a typical second order filter (called biquad in engineering slang) of Butterworth type and do your math right (factoring out coefficients) you only have 3 multiplications and five addition.

Edit: link to classics page: filter cookbook

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  • $\begingroup$ Whether an FFT filter is slower or faster depends on the number of filter taps. $\endgroup$ – Jim Clay May 7 '13 at 20:00
  • $\begingroup$ Yes sure, but your fft must have a window width of about as many samples as your filter has taps in order to get a simliar frequency resolution. But your fft is O(N log N) at best and you have to do two of them vs one O(N) fir filter. $\endgroup$ – André Bergner May 7 '13 at 20:09
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    $\begingroup$ Convolutions are O(NM), where M is the length of the filter. $\endgroup$ – Jim Clay May 7 '13 at 20:35
  • $\begingroup$ For a butterworth type filter you can even do it with two multiplications per sample if you're not constrained to a direct-form. Anyway, I also agree that the FFT seems a little overkill unless additional analysis or processing takes place... $\endgroup$ – niaren May 7 '13 at 20:36
  • $\begingroup$ Interesting answer! I was just getting a handle on how FIR filters worked, but I guess I'll have to dig even deeper and try to figure out IIR. Thanks! $\endgroup$ – Keith May 7 '13 at 20:56

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