convolution
Noun
Meaning
The act of rolling anything upon itself, or one thing upon another; a winding motion.
The state of being rolled upon itself, or rolled or doubled together; a tortuous or sinuous winding or fold, as of something rolled or folded upon itself.
An irregular, tortuous folding of an organ or part; as, the convolutions of the intestines; the cerebral convolutions. See Brain.
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Alternative statements of the theorem Density functions The density of the sum of two or more independent variables is the convolution of their densities (if these densities exist).
Definition The convolution of f and g is written f∗g, using an asterisk or star.
Also, convolution in the time domain corresponds to ordinary multiplication in the frequency domain.
Circular convolution arises most often in the context of fast convolution with an FFT algorithm.
;Convolution of a test function with a distribution If f ∈ D(R n ) is a compactly supported smooth test function, then convolution with f, : defines a linear operator which is continuous with respect to the LF space topology on D(R n ).
Convolutions on groups If G is a suitable group endowed with a measure λ, and if f and g are real or complex valued integrable functions on G, then we can define their convolution by : It is not commutative in general.