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The representation of functions (or objects which are in some generalize the notion of function) as constant linear combinations of sines and cosines at integer multiples of a given frequency, as Fourier transforms or as Fourier integrals.
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votes
complex fourier coefficients, introduced by?
An "engineer" playing with Fourier series around 1900 sounds to me like Oliver Heaviside. In Electromagnetic Theory volume 2, chapter 279, equation 112 (dating from 1895) there is a complex representa …