Discrete Systems and Digital Signal Processing with MATLAB, 2nd Edition

3

Fourier Series and the Fourier Transform of Discrete Signals

3.1    Introduction

According to Joseph Fourier, a discrete periodic signal can be represented as a sum of complex exponentials or sinusoids. Also, a nonperiodic discrete signal and a finite-duration discrete signal can be represented as a finite sum of complex exponentials. This last representation for finite-duration discrete signals is called the Fourier transform of discrete signals. There are many advantages for this representation. The most important one is that if the discrete signal is put in the frequency domain, every single frequency in the signal will be clearly identified. Consider the plot of the discrete signal

$y(n)=cos(2\text{π}n)+200cos(4\text{π}n)+0.1cos(10\text{π}n)$

as shown ...