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Fast Numerical Creation of the List of Fourier Coefficients

Anry Nersessian
Organization: National Academy of Sciences of Armenia
Department: Institute of Mathematics
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The package NFourierListCoefficients is intended for calculation of list of Fourier coefficients for a given function. It is necessary in many applications when a decomposition of Fourier series is used. The current Mathematica package NFourierCoefficient gives each Fourier coefficient separately and demands a lot of time for calculation the all coefficients for requested trancation of Fourier series. Besides the package NFourierCoefficient works by default settings with significant errors for the far coefficients as integrals from oscillating functions are calculated. The package NFourierListCoefficients is based on a wavelet-like algorithm that allows to avoid above mentioned difficulties to some extent. Note that this package intended only for calculation all coefficients in requested range {-N,N}, N>1, but not for one or few of them.

*Mathematics > Calculus and Analysis

fourier series, NFourierListCoefficients
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NFLC.nb (158.1 KB) - Mathematica notebook