Abstract
AbstractWe provide a basic overview of Fourier expansion: a method for representing a function as an infinite sum of sine waves with different amplitudes and frequencies. We develop the Fourier expansion of a function using either real or complex Fourier modes and discuss some issues of convergence and approximation by truncated Fourier series. We briefly mention the theoretical connection with the continuous Fourier transform and discuss generalizations to other types of orthogonal function expansion. Lastly, we point out some applications of Fourier expansion in statistics and other disciplines.
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2. Osgood B.G.(2019)Lectures on the Fourier Transform and Its Applications vol. 33 American Mathematical Soc.
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