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Is it possible to design an LPF that has an output identical to the input at specific points in time domain (the rest of the input waveform can get filtered/distorted)? Is there a general name/technique for this kind of thing (assuming it is possible), so that I can search for more information on this topic?

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  • $\begingroup$ yea, use FIR and not apply it to that point in time. $\endgroup$ – thang Feb 27 '15 at 5:26
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What you probably are looking for are Nyquist/$M$th-band filters. The impulse response of these have the following property (assuming a non-causal impulse response centered around tap 0 for ease of exposition)

$h_n = \left\{ \begin{matrix} \frac{1}{M} & n=0\\ 0 & n = kM, k=\pm 1, \pm 2, \dots\end{matrix} \right.$

This means that every $M$th sample is untouched (the $1/M$ term is for scaling purposes). Often it is said that these filters have zero inter symbol interference, assuming that a symbol arrived every $M$th sample.

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  • $\begingroup$ The response is unspecified for $n$ not being a multiple of $M$. So, how does this filter make the output be the same as the input at specific instants of time? $\endgroup$ – Dilip Sarwate May 28 '15 at 12:56

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