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§1.16(vii) Fourier Transforms of Tempered Distributions… ►Then its Fourier transform is … ►The Fourier transform of a tempered distribution is again a tempered distribution, and … ►
§1.16(viii) Fourier Transforms of Special Distributions… ►Since , we have …
§1.14(i) Fourier Transform… ►
Inversion… ►In this subsection we let , , , and . … ►
Fourier Transform… ►where is given by (1.14.1). …
§27.17 Other Applications►Reed et al. (1990, pp. 458–470) describes a number-theoretic approach to Fourier analysis (called the arithmetic Fourier transform) that uses the Möbius inversion (27.5.7) to increase efficiency in computing coefficients of Fourier series. …
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§30.15(iii) Fourier Transform… ►Equations (30.15.4) and (30.15.6) show that the functions are -bandlimited, that is, their Fourier transform vanishes outside the interval . …
There have been extensive changes in the notation used for the integral transforms defined in §1.14. These changes are applied throughout the DLMF. The following table summarizes the changes.
Previously, for the Fourier, Fourier cosine and Fourier sine transforms, either temporary local notations were used or the Fourier integrals were written out explicitly.
Several changes have been made to
An entire new Subsection 1.16(viii) Fourier Transforms of Special Distributions, was contributed by Roderick Wong.