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I know that Finite Impulse Response (FIR) filters can be equivalently expressed as aconvolution. The effect of convolution in frequency domain is well known. In conclusion it is easy to make sense of FIR filters.

My questions are:

- can also Infinite Impulse Response (IIR) filters be given a similar interpretation?

Are they convolution of some sort?

- There exists some digital IIR filters which manipulate the frequencies of the signal (e.g. low-pass, hi-pass, etc...).

How can one design an IIR filter which does specific operations to frequencies if we don't know how to handle it mathematically?

Alternatively, how can you prove that a low-pass IIR filter in time-domain, does indeed filter frequencies?

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# IIR filters question

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