I am new to Signal Processing. From my understanding -- FIR/IIR just refer to the placement of poles and zeros in the z-domain helping us achieve convolution, if FIR and ??? in IIR.

Chebyshev and Butterworth define certain constraints under which a filter can be designed and is indicative of the ripple effect in the pass-band and stop band.

My question is - how are these two related. Can we design an IIR using the Chebyshev constraint. In real-time, is this constraint used using the Impulse Invariance Method or Bilinear Transform for IIR design?

Any answer to this would really help. Thanks


Chebychev and Butterworth filters can be transformed with the bilinear transform into IIR filters. The amplitude and phase responses will be warped according to the bilinear transform. This warp mainly makes for a higher cutoff rate than the corresponding analog filter (handwavingly, it's because the antialiasing filtering and sampling already does part of the work) which tends to be ok for most applications.

In contrast, using a bilinear transform on a Bessel filter is quite pointless since its salient design feature is a near constant phase delay in the pass band, and the bilinear transform warp messes this up. So there is a separate digital equivalent to Bessel filters that isn't related via simple bilinear transform.

FIR filters, in contrast, don't have straightforward connections to analog filter designs. Their design procedures are quite separate and only suitable for digital filters.

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    $\begingroup$ So Chebyshev filters are used for analog filter design and if we want analog to digital IIR filter, we use the bilinear transform? $\endgroup$ – Akhilesh Rao Aug 17 '17 at 21:48

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