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).

Fig: 1