A mathematical operation that combines two signals to generate a third signal. Convolution often arises in audio processing (e.g., filtering, reverb) and image processing (e.g., blurring, edge detection).
Convolution takes two signals and combines them to generate a third signal. For 1-D signals, the operation can be thought of as sliding the time-reverse of one signal along the other, and at each time step, taking the integral of the product of the signals (see wikipedia). The convolution operation describes the response of linear time-invariant systems to common input signals. Therefore, it commonly occurs in digital signal processing (DSP) contexts. Audio and image processing are two very common application areas for convolution.
A simple implementation for convolving two discrete time signals requires M*N multiply-add operations, where M and N are the lengths of the two signals. However, by taking advantage of the fact that convolution in the time domain is equivalent to multiplication in the frequency domain, and that transforming between domains can be implemented with O(N*log N) operations, convolution can be sped up. See here for more details.
