Sampling Theorem

In signal processing, the analysis of continuous-time signals, denoted as x(t), often involves sampling techniques to convert these signals into discrete-time signals. This process is essential for digital representation and manipulation. A critical component in sampling is the train of impulses, characterized by the sampling i...

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...