Learn Fourier Analysis
A four-lesson learning path that takes you from "What is a signal?" to designing your own digital filters — with interactive tools at every step.
No textbook required. Each lesson builds on the last, with clear explanations, real formulas, and hands-on practice.
Prerequisites
These lessons are designed to be approachable. Here's what will help:
- ✓ Basic trigonometry — you should be comfortable with sine, cosine, amplitude, and frequency. If you know what sin(x) looks like, you're ready.
- ✓ Algebra fundamentals — summation notation (Σ) appears in Lesson 2, but we'll walk through it step by step.
- ○ Complex numbers (optional) — Euler's formula shows up in the DFT. We explain it when it appears, so prior experience is helpful but not required.
- ○ Calculus (optional) — not needed for these lessons, but useful if you continue into continuous-time Fourier transforms later.
Learning Path
Signals & Sinusoids
What is a signal? Learn about continuous and discrete signals, and the sinusoidal building blocks that make Fourier analysis possible. Build intuition for amplitude, frequency, and phase.
Start Lesson →DFT & FFT Basics
Discover what the Discrete Fourier Transform actually computes, decode the DFT formula, and learn why the FFT algorithm changed the world. Interpret magnitude, phase, and frequency bins.
Start Lesson →Sampling & Aliasing
Understand the Nyquist–Shannon sampling theorem, why aliasing happens, and how to prevent it. See and hear aliasing artifacts with our interactive tools.
Start Lesson →Filtering
Learn how filters shape signals in the frequency domain. Explore low-pass, high-pass, band-pass, and notch filters, understand convolution, and compare FIR vs IIR designs.
Start Lesson →Hands-On Practice
Each lesson links to relevant interactive tools. You can also explore them all directly — no sign-up, no download, everything runs in your browser.
View All Tools →