# Relation between filter order and window length for FIR filter

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 $$M-1$$

## 1 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.

• calling a single delay tap (plus an undelayed tap) a "reverb" is a bit of a stretch. – robert bristow-johnson Jul 18 '20 at 23:54
• Yeah, you’re right. I hope the “naive” makes it a bit more appropriate. – Michael Gruner Jul 19 '20 at 0:56
• Is a zero coefficient a "tap"? – Cedron Dawg Jul 19 '20 at 23:03