# Table of Contents

- Page ID
- 11977

This book focuses on the discrete Fourier transform (DFT), discrete convolution, and, particularly, the fast algorithms to calculate them. These topics have been at the center of digital signal processing since its beginning, and new results in hardware, theory and applications continue to keep them important and exciting.

## 4: The DFT as Convolution or Filtering

A major application of the FFT is fast convolution or fast filtering where the DFT of the signal is multiplied term-by-term by the DFT of the impulse (helps to be doing finite impulse response (FIR) filtering) and the time-domain output is obtained by taking the inverse DFT of that product. What is less well-known is the DFT can be calculated by convolution. There are several different approaches to this, each with different application.