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Mathematical & Computational Physics

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.