1. Equations (6.158) summarize the theory behind the sampling of a signal r(t) with a frequency fs. (The full calculation is on the preceding page, it doesn't hurt to read through it) In this equation, X(f) is the Fourier transform of r(t); X, (f) is the Fourier transform of the sampled signal, which includes the original signal plus all its images to the left and right, as shown in figure 6-72 (b).

Consider that x(t) is a pure sine wave with frequency fo. The sampling is done at exactly the Nyquist rate.

Calculate Xs, (f) for a few terms, say n = 0, ±1, ±2 and show that Xs (f) = 0 and hence xs(t) = 0, too.

Click here for a nice example of this calculation.