In case of FIR filter design, is the following relation always applicable or there are other relations/formulas also?

If window length is denoted by $M$ ,then filter order will be $M-1$


Yes. The number of taps or coefficients in a FIR filter (or window length as you call it) tell the order of the filter. A more general way to see it, to avoid confusions, is to think of the order as the largest delay in the filter. For example, consider the following naive reverb:

$$y[n] = a x[n] + (1 - a) x[n-D]$$

Even though there are only two (visible) coefficients, the order of the filter is $D$ because it’s the largest delay. The window length is $D+1$ but all the middle coefficients are $0$, hence not visible.

  • 1
    $\begingroup$ calling a single delay tap (plus an undelayed tap) a "reverb" is a bit of a stretch. $\endgroup$ Jul 18 '20 at 23:54
  • $\begingroup$ Yeah, you’re right. I hope the “naive” makes it a bit more appropriate. $\endgroup$ Jul 19 '20 at 0:56
  • $\begingroup$ Is a zero coefficient a "tap"? $\endgroup$ Jul 19 '20 at 23:03

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