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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 Rectangular mask short-time Fourier transform ： ウィキペディア英語版 Rectangular mask short-time Fourier transform In mathematics, a rectangular mask short-time Fourier transform has the simple form of short-time Fourier transform. Other types of the STFT may require more computation time than the rec-STFT. Define its mask function : $w(t)\; =\backslash begin$ \ 1; & |t|\leq B \\ \ 0; & |t|>B \end We can change ''B'' for different signal. Rec-STFT : $X(t,f)=\backslash int\_^\; x(\backslash tau)\; e^\; \backslash ,\; d\backslash tau$ Inverse form : ==Property== Rec-STFT has similar properties with Fourier transform * Integration (a) : $\backslash int\_^\backslash infty\; X(t,\; f)\backslash ,\; df\; =\; \backslash int\_^\; x(\backslash tau)\backslash int\_^\backslash infty\; e^\backslash ,\; df\; \backslash ,\; d\backslash tau\; =\; \backslash int\_^\; x(\backslash tau)\backslash delta(\backslash tau)\; \backslash ,\; d\backslash tau=\backslash begin$ \ x(0); & |t|< B \\ \ 0; & \text \end (b) : $\backslash int\_^\backslash infty\; X(t,\; f)e^\; \backslash ,df\; =\backslash begin$ \ x(v); & v-B\ 0; & \text \end *Shifting property(shift along x-axis) :: $\backslash int\_^\; x(\backslash tau+\backslash tau\_0)\; e^\backslash ,\; d\backslash tau\; =\; X(t+\backslash tau\_0,f)e^$ *Modulation property (shift along ''y''-axis) :$\backslash int\_^\; (e^)\; d\backslash tau\; =\; X(t,f-f\_0)$ *special input #When $x(t)=\backslash delta(t),\; X(t,f)=\backslash begin$ \ 1; & |t|< B \\ \ 0; & \text \end #When $x(t)=1,X(t,f)=2B\backslash operatorname(2Bf)e^$ *Linearity property If $h(t)=\backslash alpha\; x(t)+\backslash beta\; y(t)\; \backslash ,$,$H(t,f),\; X(t,f),$and $Y(t,f)\; \backslash ,$are their rec-STFTs, then : $H(t,f)=\backslash alpha\; X(t,f)+\backslash beta\; Y(t,f)\; .$ * Power integration property :: $\backslash int\_^\backslash infty\; |X(t,\; f)|^2\backslash ,\; df\; =\; \backslash int\_^\; |x(\backslash tau)|^2\backslash ,d\backslash tau$ :: $\backslash int\_^\backslash infty\; \backslash int\_^\backslash infty\; |X(t,\; f)|^2\backslash ,df\backslash ,dt\; =\; 2B\; \backslash int\_^\backslash infty\; |x(\backslash tau)|^2\backslash ,d\backslash tau$ * Energy sum property(Parseval's theorem) :: $\backslash int\_^\backslash infty\; X(t,f)Y^$ *(t,f)\,df = \int_^ x(\tau)y^ *(\tau)\,d\tau :: $\backslash int\_^\backslash infty\; \backslash int\_^X(t,f)Y^$ *(t,f)\,df\,dt =2B \int_^\infty x(\tau)y^ *(\tau)\,d\tau 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「Rectangular mask short-time Fourier 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.