Generate an impulse train containing 207 samples. In between impulses there should be 22 zeros. The height of each impulse should be constant. Call this signal p(n).

Compute the 207-point DFT of p(n). Observe that in the DFT domain, P(k) also takes on only values of zero and a constant. Determine the spacing between impulses in the k domain. Plot the transform pair in one figure using subplot and save as *D2.fig.

The period of the input signal, Mo, is a divisor of the length of the DFT. Use this fact to explain the mathematical form of P(k). Generalize this result. In particular, predict the DFT if p(n) contained 23 impulses separated by 9; then verify with MATLAB. Plot the transform pair in one figure using subplot and save as *D3.fig.

Change the DFT length slightly and compute a 200-point DFT. Since the last 22 points of p(n) are zero, we only need to drop off the zeros at the end. Explain why the transform values are so different but notice that the DFT still has a number of large regularly spaced peaks. Plot the transform pair in one figure using subplot and save as *D4.fig.

Compute the 1024-point DFT of p(n) , with zero-padding prior to the fft() . Note that the transform has many peaks, and they seem to be at a rectangular spacing, at least approximately. Measure the spacing and count the peaks. State the general relationship between the period of the input signal, p(n) , the length of the DFT, and the rectangular spacing of the peaks. Plot the transform pair in one figure using subplot and save as *D5.fig.