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Relation between filter order and window length for FIR filter

Signal Processing Asked on October 24, 2021

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 $M-1$

One Answer

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.

Answered by Michael Gruner on October 24, 2021

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