Convolve vs. convolute

Solution 1:

The mathematical procedure is called convolution or deconvolution, and you convolve or deconvolve two functions; you do not convolute or deconvolute two functions.

Outside of math convolve and convolute mean pretty much the same thing:

to coil up; form into a twisted shape.

Although deconvolute and deconvolve are not in the dictionary, I imagine you could use them colloquially as a verb to mean:

to uncoil

Solution 2:

Setting aside the fact that "convolve" is the usual mathematical term defined for this process, there is something else that tips the scales clearly in favor of "convolve" over "convolute":

Convoluted is an adjective.

Convolved is a verb (both transitive and intransitive).

As such, while you might say that "signal A is convolved with signal B", to say that "signal A is convoluted with signal B" would be butchery of the English language. (And using convoluted as an adjective isn't terribly useful, unless you wanted to complain about the convoluted process.) So convolve and its associated forms appear to fit the process of convolution, and signal processing and math in general, better.