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

be a periodic signal that is processed by the system in Figure P10.42-1.

(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 

q[n] = αx_c (n2π/32) ,                0 ≤ n ≤ 31,

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

, x. (1) eiki 16 k=-4 Part B 16-point DFT C/D g[n} G(k] 2 u{n] u[n - 16] 16