Problem 3. Consider a filter h[n].

a) Find the Fourier transform of its autocorrelation sequence

a[n] =Σ h[k]h* [k — n] .

b) Show that if (h[k – n], h[k]) = δ[n], then

c) Show that if |H(jw)| = 1, then

|H(e^jw)| = 1, Vw.

(h[k — n], h[k]) = 8[n].

d) Show that if |H(e^jw)| = 1, Vw, then {h[k – n], n € Z} is an orthonormal basis for l² (Z).