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- W3553059 abstract "One approach to the calculation of Fourier trigonometric coefficients f(r) of a given function f(x) is to apply the trapezoidal quadrature rule to the integral representation f(r) = {line_integral}{sub 0}{sup 1} f(x)e{sup -2{pi}irx}dx. Some of the difficulties in this approach are discussed. A possible way of overcoming many of these is by means of a subtraction function. Thus, one sets f(x) = h{sub p-1}(x) + g{sub p}(x), where h{sub -1}(x) is an algebraic polynomial of degree p-1, specified in such a way that the Fourier series of g{sub p}(x) converges more rapidly than that of f(x). To obtain the Fourier coefficients of f(x), one uses an analytic expression for those of h{sub p-1}(x) and numerical quadrature to approximately those of g{sub p}(x)." @default.
- W3553059 created "2016-06-24" @default.
- W3553059 creator A5003093498 @default.
- W3553059 date "2001-10-10" @default.
- W3553059 modified "2023-09-24" @default.
- W3553059 title "Sets of Fourier coefficients using numerical quadrature" @default.
- W3553059 hasPublicationYear "2001" @default.
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