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

7

Discrete Fourier Transform and Discrete Systems

7.1    Introduction

We have two types of linear systems: the continuous linear system and the discrete linear system. The Fourier transform of the continuous signal x(t) is

$X\left(w\right)={\displaystyle \underset{-\infty }{\overset{+\infty }{\int }}x\left(t\right){\text{e}}^{-jwt}dt}$

(7.1)

By observing the signal x(t) in the frequency domain, we are able to see all the frequencies that x(t) contains, and based on that we can further process the signal x(t) and alter its frequency components in any way we wish.

But the Fourier transform equation (7.1) is not suitable for computer evaluation since the bounds on the integral are infinite. By discretizing the signal x(t) and obtaining the discrete signal x(n), we can Fourier transform the signal x(n) into the frequency domain ...