Verification of Nyquist Sampling Theorem for a given Continuous-Time (CT) Signal and a given frequency in the Signal Processing Environment

Abstract

In this paper, the verification of the sampling theorem for a signal of a given frequency using MATLAB is presented. In the area of digital signal processing, the Nyquist-Shannon sampling theorem is a theorem that serves as a fundamental bridge between continuous-time and discrete-time signals. Sampling is carried out using a device called a sampler, which is nothing but a switch. The sampler is a switch that is continuously opened & closed at regular intervals of time, the time intervals between the successive samples are called the sampling period and the reciprocal of the sampling period is called the sampling frequency. The sampling rate has to be very very high to preserve the contents of the original image, i.e., the switch has to open & close at a very faster rate. The sampling theorem forms the basis of all communication electronics and can use for various applications. Here, the theorem is verified using a code developed in Matlab & the simulation results show the effectiveness of the programming approach developed.