Creating a Fourier Transform Function in C: A Step-by-Step Guide

Introduction

Fourier transforms are a fundamental tool in signal processing, allowing you to transform a time-domain signal into its frequency-domain representation. This capability is essential for analysing the frequency content of signals, filtering, and many other applications. In this article, we will walk through how to implement a Discrete Fourier Transform (DFT) function in C, one of the most popular programming languages for system-level programming.

Understanding the Basics of Fourier Transform

Before diving into the code, it’s essential to understand what the Fourier Transform does. The DFT converts a sequence of complex numbers, usually samples of a real-world signal, into another sequence of complex numbers representing the signal’s frequency spectrum.

The mathematical formula for the DFT is given by:

Implementing the DFT in C

Let’s implement the DFT in C. We will write a function that takes an array of samples and outputs the frequency spectrum.