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can we use butterworth and other such filters like chebyshev,elliptic etc with FIR

or they can be only used with IIR?

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  • $\begingroup$ There's a lot of beginners asking how to build Butterworth filters, without actually needing them. Why do you want to use a Butterworth FIR (which can't exist, sadly)? $\endgroup$ – Marcus Müller Dec 19 '18 at 20:19
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Filters according to those optimality criteria only exist as IIR filters. They are derived from the corresponding analog prototype filters via the bilinear transform, and this naturally results in IIR filters, i.e., filters with zeros and poles (away from the unit circle).

Of course, you can approximate these filters by FIR filters. The most straightforward way would be to truncate the infinite impulse response using some window function. But such an FIR filter is not optimal anymore since it can only approximate the optimal response.

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  • $\begingroup$ what are the optimality criteria? $\endgroup$ – Ben Dec 19 '18 at 18:14
  • $\begingroup$ @Ben: You mean how Butterworth, Chebyshev, etc., filters are defined? (because these are the optimality criteria). $\endgroup$ – Matt L. Dec 19 '18 at 18:15
  • $\begingroup$ Oh ok, thanks I thought you meant an optimality criterion on how to convert analog to digital filters. $\endgroup$ – Ben Dec 19 '18 at 18:17
  • $\begingroup$ @Ben: No, the bilinear transform preserves the optimality for these criteria (but not for others, e.g., a Bessel filter transformed via the bilinear transform is no optimal Bessel filter anymore). $\endgroup$ – Matt L. Dec 19 '18 at 18:18
  • $\begingroup$ also, abt, you can actually implement your FIR filter that approximates some IIR filter as a Truncated IIR (TIIR) filter. it might not be what you want, but it's a method to get some FIR properties (such as linear phase) with the lower computational cost of an IIR. it turns out, that to get linear phase with a TIIR, you have to do this filtfilt() thing in blocks. $\endgroup$ – robert bristow-johnson Dec 19 '18 at 19:20

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