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Convolution is a weighted moving average with one signal flipped back to front.
Convolving a signal with a smooth weighting function can be used to smooth a signal:
The diagram shows how a noisy sine wave can be smoothed by convolving with a rectangular smoothing function - this is just a moving average.
The smoothing property leads to the use of convolution for digital filtering.
Last updated: 10th December 1997 | http://www.bores.com/courses/intro/time/2_smooth.htm