Let x[n] and y[n] denote complex sequences and X (ejω) and Y (ejω) their respective Four...

Let x[n] and y[n] denote complex sequences and X (e^jω) and Y (e^jω) their respective Fourier transforms.

(a) By using the convolution theorem (Theorem 6 in Table 2.2) and appropriate properties from Table 2.2, determine, in terms of x[n] and y[n], the sequence whose Fourier transform is X (e^jω)Y ^∗ (e^jω).

(b) Using the result in part (a), show that

Equation (P2.84-1) is a more general form of Parseval’s theorem, as given in Section 2.9.5.

(c) Using Eq. (P2.84-1), determine the numerical value of the sum