Overlap–add method: Difference between revisions

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{{Short description|Method in signal processing}}
{{about|the convolution method|the "Weight, OverLap, Add" channelization method|Discrete-time Fourier transform#Sampling the DTFT{{!}}Sampling the DTFT}}
 
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:<math>N_x\cdot (\log_2(N) + 1)\cdot \frac{N}{N-M+1}.</math>
 
Hence the ''cost'' of the overlap–add method scales almost as <math>O\left(N_x\log_2 N\right)</math> while the cost of a single, large circular convolution is almost <math>O\left(N_x\log_2 N_x \right)</math>. The two methods are also compared in Figure 3, created by [[MATLAB|Matlab]] simulation. The contours are lines of constant ratio of the times it takes to perform both methods. When the overlap-add method is faster, the ratio exceeds 1, and ratios as high as 3 are seen.
 
[[Image:gain oa method.png|frame|none|Fig 3: Gain of the overlap-add method compared to a single, large circular convolution. The axes show values of signal length N<sub>x</sub> and filter length N<sub>h</sub>.]]