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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.
Convolution has applications that include probability, statistics, acoustics, spectroscopy, signal processing and image processing, geophysics, engineering, physics, computer vision and differential equations. [1] The convolution can be defined for functions on Euclidean space and other groups (as algebraic structures).
2D convolution with an M × N kernel requires M × N multiplications for each sample (pixel). If the kernel is separable, then the computation can be reduced to M + N multiplications. Using separable convolutions can significantly decrease the computation by doing 1D convolution twice instead of one 2D convolution. [2]
By virtue of the linearity property of optical non-coherent imaging systems, i.e., . Image(Object 1 + Object 2) = Image(Object 1) + Image(Object 2). the image of an object in a microscope or telescope as a non-coherent imaging system can be computed by expressing the object-plane field as a weighted sum of 2D impulse functions, and then expressing the image plane field as a weighted sum of the ...
A set of convolution coefficients may then be derived as = (). Alternatively the coefficients, C, could be calculated in a spreadsheet, employing a built-in matrix inversion routine to obtain the inverse of the normal equations matrix. This set of coefficients, once calculated and stored, can be used with all calculations in which the same ...
By Raphael Satter. WASHINGTON (Reuters) -A large number of Americans' metadata has been stolen in the sweeping cyberespionage campaign carried out by a Chinese hacking group dubbed "Salt Typhoon ...
The Hilbert transform of u can be thought of as the convolution of u(t) with the function h(t) = 1 / π t , known as the Cauchy kernel.Because 1/ t is not integrable across t = 0, the integral defining the convolution does not always converge.
Corrections & clarifications: A previous version of this report gave an incorrect full name for The Amazing Kreskin. George Kresge Jr., better known by his stage name The Amazing Kreskin, has died ...