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- Overlap–save_method abstract "Overlap–save is the traditional name for an efficient way to evaluate the discrete convolution between a very long signal and a finite impulse response (FIR) filter :</dl>where h[m]=0 for m outside the region [1, M].The concept is to compute short segments of y[n] of an arbitrary length L, and concatenate the segments together. Consider a segment that begins at n = kL + M, for any integer k, and define:Then, for kL + M ≤ n ≤ kL + L + M − 1, and equivalently M ≤ n − kL ≤ L + M − 1, we can write:The task is thereby reduced to computing yk[n], for M ≤ n ≤ L + M − 1.Now note that if we periodically extend xk[n] with period N ≥ L + M − 1, according to:the convolutions and are equivalent in the region M ≤ n ≤ L + M − 1. So it is sufficient to compute the N-point circular (or cyclic) convolution of with in the region [1, N]. The subregion [M, L + M − 1] is appended to the output stream, and the other values are discarded.The advantage is that the circular convolution can be computed very efficiently as follows, according to the circular convolution theorem:where:DFT and DFT−1 refer to the Discrete Fourier transform and inverse Discrete Fourier transform, respectively, evaluated over N discrete points, andN is customarily chosen to be an integer power-of-2, which enables use of the FFT algorithm.Optimal N is in the range [4M, 8M].".
- Overlap–save_method abstract "Overlap–save is the traditional name for an efficient way to evaluate the discrete convolution between a very long signal and a finite impulse response (FIR) filter :where h[m]=0 for m outside the region [1, M].The concept is to compute short segments of y[n] of an arbitrary length L, and concatenate the segments together. Consider a segment that begins at n = kL + M, for any integer k, and define:Then, for kL + M ≤ n ≤ kL + L + M − 1, and equivalently M ≤ n − kL ≤ L + M − 1, we can write:The task is thereby reduced to computing yk[n], for M ≤ n ≤ L + M − 1.Now note that if we periodically extend xk[n] with period N ≥ L + M − 1, according to:the convolutions and are equivalent in the region M ≤ n ≤ L + M − 1. So it is sufficient to compute the N-point circular (or cyclic) convolution of with in the region [1, N]. The subregion [M, L + M − 1] is appended to the output stream, and the other values are discarded.The advantage is that the circular convolution can be computed very efficiently as follows, according to the circular convolution theorem:where:DFT and DFT−1 refer to the Discrete Fourier transform and inverse Discrete Fourier transform, respectively, evaluated over N discrete points, andN is customarily chosen to be an integer power-of-2, which enables use of the FFT algorithm.Optimal N is in the range [4M, 8M].".
- Overlap–save_method thumbnail Overlap-save_algorithm.png?width=300.
- Overlap–save_method wikiPageID "17160278".
- Overlap–save_method wikiPageRevisionID "598301121".
- Overlap–save_method subject Category:Fourier_analysis.
- Overlap–save_method subject Category:Numerical_analysis.
- Overlap–save_method subject Category:Signal_processing.
- Overlap–save_method subject Category:Transforms.
- Overlap–save_method comment "Overlap–save is the traditional name for an efficient way to evaluate the discrete convolution between a very long signal and a finite impulse response (FIR) filter :</dl>where h[m]=0 for m outside the region [1, M].The concept is to compute short segments of y[n] of an arbitrary length L, and concatenate the segments together.".
- Overlap–save_method comment "Overlap–save is the traditional name for an efficient way to evaluate the discrete convolution between a very long signal and a finite impulse response (FIR) filter :where h[m]=0 for m outside the region [1, M].The concept is to compute short segments of y[n] of an arbitrary length L, and concatenate the segments together.".
- Overlap–save_method label "Overlap-Save-Verfahren".
- Overlap–save_method label "Overlap–save method".
- Overlap–save_method label "重疊-儲存之摺積法".
- Overlap–save_method sameAs Overlap%E2%80%93save_method.
- Overlap–save_method sameAs Overlap-Save-Verfahren.
- Overlap–save_method sameAs Q1791834.
- Overlap–save_method sameAs Q1791834.
- Overlap–save_method wasDerivedFrom Overlap–save_method?oldid=598301121.
- Overlap–save_method depiction Overlap-save_algorithm.png.