waves

Fourier Synthesis

Build complex waveforms from harmonics — stack sine waves to construct square, sawtooth, and triangle waves in 3D. See how Fourier series works in real time with animated waveforms.

Fourier Synthesis

A-Level

Any periodic waveform can be expressed as a sum of sine and cosine waves (harmonics). A square wave contains only odd harmonics with amplitudes 1/n. Fourier analysis decomposes complex signals into their frequency components.

Harmonics5

Base Frequency1.0Hz

📐 Formulas

f(t) = a_0 + \sum a_n\cos(n\omega t) + b_n\sin(n\omega t)General Fourier series

f(t) = \frac{4}{\pi}\sum_{n=1,3,5,\ldots}\frac{\sin(n\omega t)}{n}Odd harmonics only

📋 Syllabus

AQA3.13.1

OCR5.3.2