How to find minimum length of a FIR symmetric filter if I am given DTFT I am practising for upcoming exams and came across this question.
Let $h[n]$ be an FIR filter such that $h[n] = 0$ when $|n| &gt; M$ and $h[n] = h[−n]$. A plot of $H(e^{j\omega})$ (DTFT of $h[n]$) is shown below.
The eventual goal is to implement this filter digitally. Then, with the given information, is it possible to determine the minimum
value of $M$? Yes or no, with a suitable technical explanation.
What I though was that if I knew the order of this filter I could have found the length of the FIR filter as well. However order cannot be extracted from this graph.
HINT: How many zeros of $H(e^{j\omega})$ do you count? Does that say anything about the (minimum) order of the corresponding polynomial?