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The term convolution refers to both the resulting function and to the process of computing it. It is defined as the integral of the product of the two functions after one is reflected about the y-axis and shifted. The integral is evaluated for all values of shift, producing the convolution function.
The probability distribution of the sum of two or more independent random variables is the convolution of their individual distributions. The term is motivated by the fact that the probability mass function or probability density function of a sum of independent random variables is the convolution of their corresponding probability mass functions or probability density functions respectively.
In probability theory, the probability distribution of the sum of two or more independent random variables is the convolution of their individual distributions. The term is motivated by the fact that the probability mass function or probability density function of a sum of independent random variables is the convolution of their corresponding ...
The pseudo-Voigt profile (or pseudo-Voigt function) is an approximation of the Voigt profile V(x) using a linear combination of a Gaussian curve G(x) and a Lorentzian curve L(x) instead of their convolution. The pseudo-Voigt function is often used for calculations of experimental spectral line shapes.
Visual comparison of convolution, cross-correlation and autocorrelation.For the operations involving function f, and assuming the height of f is 1.0, the value of the result at 5 different points is indicated by the shaded area below each point.
In telecommunication, a convolutional code is a type of error-correcting code that generates parity symbols via the sliding application of a boolean polynomial function to a data stream. The sliding application represents the 'convolution' of the encoder over the data, which gives rise to the term 'convolutional coding'.
This terminology is because the space L 1 (R) of absolutely integrable functions is closed under the operation of convolution of functions: f ∗ g ∈ L 1 (R) whenever f and g are in L 1 (R). However, there is no identity in L 1 (R) for the convolution product: no element h such that f ∗ h = f for all f.
If x is the distribution function of a random variable on the real line, then the n th convolution power of x gives the distribution function of the sum of n independent random variables with identical distribution x. The central limit theorem states that if x is in L 1 and L 2 with mean zero and variance σ 2, then
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