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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Multidimensional transform ： ウィキペディア英語版 Multidimensional transform In mathematical analysis and applications, multidimensional transforms are used to analyze the frequency content of signals in a domain of two or more dimensions. == Multidimensional Fourier transform == One of the more popular multidimensional transforms is the Fourier transform, which converts a signal from a time/space domain representation to a frequency domain representation.〔Smith,W. Handbook of Real-Time Fast Fourier Transforms:Algorithms to Product Testing, Wiley_IEEE Press, edition 1, pages 73–80, 1995〕 The discrete-domain multidimensional Fourier transform (FT) can be computed as follows: :$F(w\_1,w\_2,\backslash dots,w\_m)\; =\; \backslash sum\_^\backslash infty\; \backslash sum\_^\backslash infty\; \backslash cdots\; \backslash sum\_^\backslash infty\; f(n\_1,n\_2,\backslash dots,n\_m)\; e^$ where ''F'' stands for the multidimensional Fourier transform, ''m'' stands for multidimensional dimension. Define ''f'' as a multidimensional discrete-domain signal. The inverse multidimensional Fourier transform is given by :$f(n\_1,n\_2,\backslash dots,n\_m)\; =\; \backslash left(\backslash frac\backslash right)^m\; \backslash int\_^\; \backslash cdots\; \backslash int\_^\; F(w\_1,w\_2,\backslash ldots,w\_m)\; e^\; \backslash ,\; dw\_1\; \backslash cdots\; \backslash ,dw\_m$ The multidimensional Fourier transform for continuous-domain signals is defined as follows:〔 :$F(\backslash Omega\_1,\backslash Omega\_2,\backslash ldots,\backslash Omega\_m)\; =\; \backslash int\_^\; \backslash cdots\; \backslash int\_^$ f(t_1,t_2,\ldots,t_m) e^ \, dt_1 \cdots \,dt_m A fast Fourier transform (FFT) is an algorithm to compute the discrete Fourier transform (DFT) and its inverse. An FFT computes the DFT and produces exactly the same result as evaluating the DFT definition directly; the only difference is that an FFT is much faster. (In the presence of round-off error, many FFT algorithms are also much more accurate than evaluating the DFT definition directly).There are many different FFT algorithms involving a wide range of mathematics, from simple complex-number arithmetic to group theory and number theory. See more in FFT. The multidimensional discrete Fourier transform (DFT) is a sampled version of the discrete-domain FT by evaluating it at sample frequencies that are uniformly spaced.〔Dudgeon and Mersereau, Multidimensional Digital Signal Processing,2nd edition,1995〕 The DFT is given by: :$Fx(K\_1,K\_2,\backslash ldots,K\_n)=\; \backslash sum\_^\; \backslash cdots\; \backslash sum\_^\; fx(n\_1,n\_2,\backslash ldots,n\_N)\; e^\; n\_1\; K\_1\; -j\; \backslash frac\; n\_2\; K\_2\; \backslash cdots\; -j\; \backslash frac\; n\_m\; K\_m\}$ for , . The inverse multidimensional DFT equation is :$fx(n\_1,n\_2,\backslash ldots,n\_m)=\; \backslash frac\; \backslash sum\_^\; \backslash cdots\; \backslash sum\_^\; Fx(K\_1,K\_2,\; \backslash ldots\; ,K\_m)\; e^\; n\_1\; K\_1\; +j\; \backslash frac\; n\_2\; K\_2\backslash cdots+j\; \backslash frac\; n\_m\; K\_m\}$ for . 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「Multidimensional transform」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.