Periodic Functions

Fourier Analysis · Axiom Academy

What makes a function periodic, and why does it matter for Fourier analysis? Click on each example to see if it represents a periodic pattern. Drag the slider to change the period of the wave and observe how it affects the function. Frequency and period are two ways to describe the same thing. Adjust the frequency slider to explore. Fourier's key insight: periodic functions can be broken into simple waves. A function f(x) that satisfies f(x + T) = f(x) for some period T > 0. Period T (seconds per cycle) and frequency f (cycles per second) are inverses: f = 1/T. Every periodic function can be decomposed into a sum of simple sine and cosine waves. We'll learn exactly how to find these component waves using Fourier coefficients.

This is the written version of the interactive lesson above. See the full Fourier Analysis course.