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A mathematical operation producing a function from a certain kind of summation or integration of two other functions. For audio, convolution is a mathematical process that takes one signal and modifies it using another signal. If you are interested in the mathematics, it is equivalent to a multiplication of two signals in the frequency domain. What this allows one to do is to use one signal as a kind of “filter” for another signal. Essentially you use one waveform to “model” the sound of another. Select a waveform, create an “impulse file” from it, then apply it to any other waveform. Alternatively, you could cull a particular reverb profile from one sample and apply it to other samples.

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