# 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 $$M-1$$

• this answer has more relations and formulas but here $N=M-1$ is the filter order, one less than the number of nonzero taps. Jul 19 '20 at 0:05
• Does this answer your question? Filter order vs number of taps vs number of coefficients Jul 19 '20 at 8:01
• "one less than the number of nonzero taps." I don't think that's correct. The $y[n] = ax[n] + bx[n-50]$ is a 50-order filter, while having just 2 nonzero taps. Jul 23 '20 at 21:46

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