Fourier Series
An expansion of a periodic function f(x) into an infinite sum of orthogonal sine and cosine harmonic functions.
Governing formula
f(x) = a₀/2 + ∑_(n=1)^(∞) [a_n cos(n x) + b_n sin(n x)]
SI unit
Harmonic Series Expansion
In depth
Formulated by Joseph Fourier in 1807. Demonstrates that any piecewise smooth periodic function can be represented as a sum of fundamental and harmonic frequency sines and cosines.
Examples in the real world
Analyzing harmonic overtones of vibrating guitar strings and square wave electronic signals.