Sampling Signals for Digital Use

Sampling signals for digital use turns a continuous-time signal, x(t), into a discrete-time signal. This step is essential when a real-world signal must be stored or processed by a digital system. A train of impulses sets the sampling interval, and the sampling frequency describes how often the signal is measured.

Consider the continuous-time signal x(t), and a train of impulses where T_s,  is the sampling interval, and f_s, is the sampling frequency.

Multiplying both signals results in a series of discrete impulses.

The Fourier transform shows that the spectrum of the sampled signal is...