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This is a list of linear transformations of functions related to Fourier analysis. Such transformations map a function to a set of coefficients of basis functions, where the basis functions are sinusoidal and are therefore strongly localized in the frequency spectrum. (These transforms are generally designed to be invertible.) In the case of the Fourier transform, each basis function corresponds to a single frequency component. == Continuous transforms == Applied to functions of continuous arguments, Fourier-related transforms include: * Two-sided Laplace transform * Mellin transform, another closely related integral transform * Laplace transform * Fourier transform, with special cases: * * Fourier series * * * When the input function/waveform is periodic, the Fourier transform output is a Dirac comb function, modulated by a discrete sequence of finite-valued coefficients that are complex-valued in general. These are called Fourier series coefficients. The term Fourier series actually refers to the inverse Fourier transform, which is a sum of sinusoids at discrete frequencies, weighted by the Fourier series coefficients. * * * When the non-zero portion of the input function has finite duration, the Fourier transform is continuous and finite-valued. But a discrete subset of its values is sufficient to reconstruct/represent the portion that was analyzed. The same discrete set is obtained by treating the duration of the segment as one period of a periodic function and computing the Fourier series coefficients. * * Sine and cosine transforms: When the input function has odd or even symmetry around the origin, the Fourier transform reduces to a sine or cosine transform. * Hartley transform * Short-time Fourier transform (or short-term Fourier transform) (STFT) * * Rectangular mask short-time Fourier transform * Chirplet transform * Fractional Fourier transform (FRFT) * Hankel transform: related to the Fourier Transform of radial functions. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「List of Fourier-related transforms」の詳細全文を読む スポンサード リンク
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