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Results tagged with fourier-transform
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user 213984
A unitary linear operator which resolves a function on $\mathbb{R}^N$ into a linear superposition of "plane wave functions". Most often used in physics for calculating the response of a time shift invariant linear system as the sum of its response to time harmonic excitation or for transforming a quantum state in position co-ordinates into one in momentum co-ordinates and contrawise. There is also a discrete, fast Fourier transform for discretised data.
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Why use Fourier series instead of Taylor?
One of the deepest reasons to use the Fourier expansion is the idea of Harmonic Analysis induced by symmetries. The main topic is called Representation Theory and it forms the foundation to large part …
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