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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 Discrete Hartley transform ： ウィキペディア英語版 Discrete Hartley transform A discrete Hartley transform (DHT) is a Fourier-related transform of discrete, periodic data similar to the discrete Fourier transform (DFT), with analogous applications in signal processing and related fields. Its main distinction from the DFT is that it transforms real inputs to real outputs, with no intrinsic involvement of complex numbers. Just as the DFT is the discrete analogue of the continuous Fourier transform, the DHT is the discrete analogue of the continuous Hartley transform, introduced by R. V. L. Hartley in 1942. Because there are fast algorithms for the DHT analogous to the fast Fourier transform (FFT), the DHT was originally proposed by R. N. Bracewell in 1983 as a more efficient computational tool in the common case where the data are purely real. It was subsequently argued, however, that specialized FFT algorithms for real inputs or outputs can ordinarily be found with slightly fewer operations than any corresponding algorithm for the DHT (see below). == Definition == Formally, the discrete Hartley transform is a linear, invertible function ''H'' : R''n'' -> R''n'' (where R denotes the set of real numbers). The ''N'' real numbers ''x''0, ...., ''x''''N''-1 are transformed into the ''N'' real numbers ''H''0, ..., ''H''''N''-1 according to the formula :$H\_k\; =\; \backslash sum\_^\; x\_n\; \backslash left(\backslash cos\; \backslash left(\; \backslash frac\; n\; k\; \backslash right)\; +\; \backslash sin\; \backslash left(\; \backslash frac\; n\; k\; \backslash right)\; \backslash right)$ \quad \quad k = 0, \dots, N-1 . The combination $\backslash cos(z)\; +\; \backslash sin(z)\; \backslash !$ $=\; \backslash sqrt\; \backslash cos(z-\backslash frac)$ is sometimes denoted $\backslash mathrm(z)\; \backslash !$, and should be contrasted with the $e^\; =\; \backslash cos(z)\; -\; i\; \backslash sin(z)\; \backslash !$ that appears in the DFT definition (where ''i'' is the imaginary unit). As with the DFT, the overall scale factor in front of the transform and the sign of the sine term are a matter of convention. Although these conventions occasionally vary between authors, they do not affect the essential properties of the transform. 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「Discrete Hartley 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.