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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 Gabor transform ： ウィキペディア英語版 Gabor transform The Gabor transform, named after Dennis Gabor, is a special case of the short-time Fourier transform. It is used to determine the sinusoidal frequency and phase content of local sections of a signal as it changes over time. The function to be transformed is first multiplied by a Gaussian function, which can be regarded as a window function, and the resulting function is then transformed with a Fourier transform to derive the time-frequency analysis.〔E. Sejdić, I. Djurović, J. Jiang, “Time-frequency feature representation using energy concentration: An overview of recent advances,” ''Digital Signal Processing'', vol. 19, no. 1, pp. 153-183, January 2009.〕 The window function means that the signal near the time being analyzed will have higher weight. The Gabor transform of a signal x(t) is defined by this formula: :$G\_x(t,f)\; =\; \backslash int\_^\backslash infty\; e^e^x(\backslash tau)\backslash ,d\backslash tau$ The Gaussian function has infinite range and it is impractical for implementation. However, a level of significance can be chosen (for instance 0.00001) for the distribution of the Gaussian function. :$\backslash begin$ e^ \ge 0.00001; & \left| a \right| \le 1.9143 \\ e^ < 0.00001; & \left| a \right| > 1.9143 \end Outside these limits of integration ($\backslash left|\; a\; \backslash right|\; >\; 1.9143$) the Gaussian function is small enough to be ignored. Thus the Gabor transform can be satisfactorily approximated as :$G\_x(t,f)\; =\; \backslash int\_^\; e^\; e^\; x(\backslash tau)\; \backslash ,\; d\backslash tau$ This simplification makes the Gabor transform practical and realizable. The window function width can also be varied to optimize the time-frequency resolution tradeoff for a particular application by replacing the $$ with $$ for some chosen alpha. == Inverse Gabor transform == The Gabor transform is invertible. The original signal can be recovered by the following equation :$x(t)\; =\; \backslash int\_^\backslash infty\; \backslash int\_^\backslash infty\; G\_x(\backslash tau,f)\; e^\backslash ,df\; \backslash ,d\backslash tau$ Compare this inversion formula with property No. 5 below. 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「Gabor 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.