# LPF - signal values unaffected at specific times

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?

• yea, use FIR and not apply it to that point in time. – thang Feb 27 '15 at 5:26

## 1 Answer

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.

• 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? – Dilip Sarwate May 28 '15 at 12:56