Consider a complex signal composed of a dc term and two complex exponentials

Plot each N-point DFT as a function of frequency fk = k/N.

(a) Compute and plot the DFT of x[n] using 20 samples (0 ≤ n ≤ 19). From the plot, can the two non-dc exponentials be identified? Given the amplitude relation between the two, the lower-frequency peak should be twice as large as the higher-frequency peak. Is this the case? Explain.

(b) Zero pad the signal from (a) to a total length of 500. Does this improve locating the two non-dc exponential components? Is the lower-frequency peak twice as large as the higherfrequency peak? Explain.

(c) Generate a length-20 Hann window (see Table 8.5) and apply it to x[n]. Using this windowed function, repeat parts (a) and

(b). Comment on whether the window function helps or hinders the analysis.