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Applications of the Fourier Series

The Fourier Series, the founding principle behind the field of Fourier Analysis, is an infinite expansion of a function in terms of sines and cosines. In physics and engineering, expanding functions in terms of sines and cosines is useful because it allows one to more easily manipulate functions that are, for example, discontinuous or simply difficult to represent analytically. In particular, the fields of electronics, quantum mechanics, and electrodynamics all make heavy use of the Fourier Series. Additionally, other methods based on the Fourier Series, such as the FFT (Fast Fourier Transform – a form of a Discrete Fourier Transform [DFT]), are particularly useful for the fields of Digital Signal Processing (DSP) and Spectral Analysis.