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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 Overlap add ： ウィキペディア英語版 Overlap–add method In signal processing, the overlap–add method (OA, OLA) is an efficient way to evaluate the discrete convolution of a very long signal $x()$ with a finite impulse response (FIR) filter $h()$: :$$ \begin y() = x() * h() \ \stackrel \ \sum_^ h() \cdot x() = \sum_^ h() \cdot x(), \end where ''h''() = 0 for ''m'' outside the region (''M'' ). The concept is to divide the problem into multiple convolutions of ''h''() with short segments of $x()$: :$x\_k()\; \backslash \; \backslash stackrel$ \begin x() & n=1,2,\ldots,L\\ 0 & \textrm, \end where ''L'' is an arbitrary segment length. Then: :$x()\; =\; \backslash sum\_\; x\_k(),\backslash ,$ and ''y''() can be written as a sum of short convolutions: :$$ \begin y() = \left(\sum_ x_k()\right) * h() &= \sum_ \left(x_k() * h()\right)\\ &= \sum_ y_k(), \end where  $y\_k()\; \backslash \; \backslash stackrel\; \backslash \; x\_k()$ *h()\,  is zero outside the region ().  And for any parameter  $N\backslash ge\; L+M-1,\backslash ,$  it is equivalent to the $N\backslash ,$-point circular convolution of $x\_k()\backslash ,$ with $h()\backslash ,$  in the region (). The advantage is that the circular convolution can be computed very efficiently as follows, according to the circular convolution theorem: where FFT and IFFT refer to the fast Fourier transform and inverse fast Fourier transform, respectively, evaluated over $N$ discrete points. == The algorithm == Fig. 1 sketches the idea of the overlap–add method. The signal $x()$ is first partitioned into non-overlapping sequences, then the discrete Fourier transforms of the sequences $y\_k()$ are evaluated by multiplying the FFT of $x\_k()$ with the FFT of $h()$. After recovering of $y\_k()$ by inverse FFT, the resulting output signal is reconstructed by overlapping and adding the $y\_k()$ as shown in the figure. The overlap arises from the fact that a linear convolution is always longer than the original sequences. In the early days of development of the fast Fourier transform, $L$ was often chosen to be a power of 2 for efficiency, but further development has revealed efficient transforms for larger prime factorizations of L, reducing computational sensitivity to this parameter. A pseudocode of the algorithm is the following: Algorithm 1 (''OA for linear convolution'') Evaluate the best value of N and L (L>0, N = M+L-1 nearest to power of 2). Nx = length(x); H = FFT(h,N) (''zero-padded FFT'') i = 1 y = zeros(1, M+Nx-1) while i <= Nx (''Nx: the last index of x()'') il = min(i+L-1,Nx) yt = IFFT( FFT(x(i:il),N) * H, N) k = min(i+N-1,M+Nx-1) y(i:k) = y(i:k) + yt(1:k-i+1) (''add the overlapped output blocks'') i = i+L end 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「Overlap–add method」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.