Overlap–add method: Difference between revisions

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{{hatnote|This article uses common abstract notations, such as <math display="inline">y(t) = x(t) * h(t),</math> or <math display="inline">y(t) = \mathcal{H}\{x(t)\},</math> in which it is understood that the functions should be thought of in their totality, rather than at specific instants <math display="inline">t.</math> (see [[Convolution#Notation]])}}

In [[signal processing]], the '''Overlap–addoverlap–add method''' is an efficient way to evaluate the discrete [[convolution]] of a very long signal <math>x[n]</math> with a [[finite impulse response]] (FIR) filter <math>h[n]</math>''':'''

[[Image:Overlap-add algorithm.svg|thumb|500px|Fig 1: A sequence of 5 plots depicts one cycle of the Overlap-add convolution algorithm. The first plot is a long sequence of data to be processed with a lowpass FIR filter. The 2nd plot is one segment of the data to be processed in piecewise fashion. The 3rd plot is the filtered segment, including the filter rise and fall transients. The 4th plot indicates where the new data will be added with the result of previous segments. The 5th plot is the updated output stream. The FIR filter is a boxcar lowpass with M=16 samples, the length of the segments is L=100 samples and the overlap is 15 samples.]]