12.1: Introduction

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Learning Objectives

Learn methods to do convolution by FFT more efficiently.

One of the main applications of the FFT is to do convolution more efficiently than the direct calculation from the definition which is:

\[y(n)=\sum h(m)x(n-m) \nonumber \]

which, with a change of variables, can also be written as:

\[y(n)=\sum x(m)h(n-m) \nonumber \]

This is often used to filter a signal $x (n) " role="presentation" style="position:relative;" tabindex="0">$