This problem illustrates the basis for an FFT-based procedure for interpolating the samp...

This problem illustrates the basis for an FFT-based procedure for interpolating the samples (obtained at a rate satisfying the Nyquist theorem) of a periodic continuous-time signal. Let

be a periodic signal that is processed by the system in Figure P10.48.

(a) Sketch the 16-point sequence G[k].

(b) Specify how you would change G[k] into a 32-point sequence Q[k] so that the 32-point inverse DFT of Q[k] is a sequence

for some nonzero constant α. You need not specify the value of α.