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## convolution

convolution Mathematically, the operation of combining two functions, w and f, to produce a third function, g, such that

(or the corresponding continuous operation). This is envisaged as a transformation of an input function f to an output function g, by viewing f through a fixed window w.

In coding theory, f is considered as a signal and w as the response of a linear channel; g is then the effect upon that signal (regarded as a sequence of successive elements) brought about by the time response of the linear channel. The channel time response is the sequence of successive elements output by the channel in response to a signal that has one element of unit amplitude and all other elements zero. The input signal sequence and the channel time response are said to be convolved.

The inverse process is deconvolution: the convolved output sequence can be deconvolved with the channel time response sequence to restore the original input signal sequence.

It is important, both mathematically and practically, that the convolution of discrete-time signals corresponds to the conventional multiplication of polynomials.

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## convolution

con·vo·lu·tion / ˌkänvəˈloōshən/ • n. 1. (often convolutions) a coil or twist, esp. one of many. ∎  a thing that is complex and difficult to follow: the convolutions of farm policy. ∎  a sinuous fold in the surface of the brain. ∎  the state of being coiled or twisted, or the process of becoming so. 2. (also convolution integral) Math. a function derived from two given functions by integration that expresses how the shape of one is modified by the other. ∎  a method of determination of the sum of two random variables by integration or summation. DERIVATIVES: con·vo·lu·tion·al / -shənl/ adj.

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## convolution

convolution A mathematical operation (symbol*) to define the change in the shape of a wave-form caused by its passage through a filter. If an impulse response function f is convolved with an input g, then the output, h, is given by: h = g*f = Σjxg(tj) × f(j).

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## convolution

convolution (kon-vŏ-loo-shŏn) n. a folding or twisting, such as one of the many that cause the fissures, sulci, and gyri of the surface of the cerebrum.

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## convolution

convolution XVI. — medL. convolūtiō, -ōn-, f. pp. stem of convolvere, f. CON- + volvere roll; see -TION.
So convolvulus XVI.

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## convolution

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