What is a Fourier series?
A way to build any repeating signal by adding simple sine (and cosine) waves of different frequencies and sizes.
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Fourier Series
A square wave built one harmonic at a time, showing how any signal can be made by stacking simple sine waves.
building a square wave from sine waves
A mind behind this: Joseph Fourier 1768–1830
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Frequently asked questions
Why only odd harmonics for a square wave?
A square wave's symmetry cancels the even ones, leaving the 1st, 3rd, 5th... harmonics with amplitudes 4/(πk).
Where is this used every day?
MP3 audio, JPEG images, MRI scans and noise-cancelling headphones all rely on breaking signals into their frequencies.
Why doesn't it become a perfect square?
With finite terms a small overshoot remains near the edges (the Gibbs phenomenon); infinitely many terms would be needed for a perfect square.
What is a harmonic?
A wave whose frequency is a whole-number multiple of the base frequency - the same idea as overtones in music.