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I am very familiar with IIR and FIR filters for processing digital signals (audio is my main interest). I am keen to know if there are alternative filters based on different mathematical models to IIR and FIR?

I have a degree in maths but learning about DSP is just a hobby (I didn't study it at university) so I haven't a clue whether this is a stupid question or not :-)

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  • $\begingroup$ Note that FIR filters can be considered a subset of IIR filters. $\endgroup$ – endolith Jan 25 '16 at 19:21
  • $\begingroup$ or maybe the other way around, @endolith. consider Truncated IIR filters. $\endgroup$ – robert bristow-johnson Jan 25 '16 at 20:55
  • $\begingroup$ @robertbristow-johnson How is that the other way around? You're still making FIR filters as a special case of IIR filters, no? $\endgroup$ – endolith Jan 25 '16 at 21:06
  • $\begingroup$ well, the way i look at it is that TIIR filters are really FIR. they are a subset of FIR filters. a means of implementing an FIR filter. not unlike fast-convolution, as another means of implementing an FIR. $\endgroup$ – robert bristow-johnson Jan 26 '16 at 0:29
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FIR and IIR filters are discrete-time linear time-invariant (LTI) filters. There are also (linear) time-varying systems, which could be implemented just like FIR or IIR filters, but with time-varying coefficients. Audio effects like chorus, flanger, or phaser are time-varying filters.

Of course there are also non-linear filters, the most well-known of which is probably the median filter, which is very useful for removing impulsive noise. Many different types of non-linear filters are used in image processing.

Note that none of the above mentioned filters can be characterized by their impulse response or, equivalently, by their frequency response. This is only possible for LTI systems.

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  • $\begingroup$ this isn't the answer I was expecting, but it has none the less helped me very much and does technically answer my question and serves to teach me that I know very little about this subject :-) $\endgroup$ – keith Jan 25 '16 at 22:22
  • $\begingroup$ Note that time varying coefficients prohibits the notion of z parameters. So they only make sense in time domain $\endgroup$ – percusse Jan 27 '16 at 20:26

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