4. Let x[n] and y[n] denote complex sequences and X(ej) and Y(ej) 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(ej)Y(ej). (b) Using the result in part (a), show that n=x[n]y[n]=21X(ej)Y(ej)d. 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 n=2nsin(n/4)5nsin(n/6) 4. Let x[n] and y[n] denote complex sequences and X(ej) and Y(ej) 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(ej)Y(ej). (b) Using the result in part (a), show that n=x[n]y[n]=21X(ej)Y(ej)d. 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 n=2nsin(n/4)5nsin(n/6)