DTFT problem provides a nice precursor to the several ideas encountered in FIR filter design.
Let h[n] be the signal
h[n] =
{2, -2, -4, 8, -4, -2, 2}, -3 ≤ n ≤ 3
0, otherwise
(a) What is the phase response for {h[n]}? That is, what is the phase versus ω of H(e^jω)?
(b) Write H(e^jω) as a sum of cosines. We'll use this result in designing equiripple filters