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Convolution and related operations are found in many applications in science, engineering and mathematics. Convolutional neural networks apply multiple cascaded convolution kernels with applications in machine vision and artificial intelligence. [36] [37] Though these are actually cross-correlations rather than convolutions in most cases. [38]
In mathematics, the convolution theorem states that under suitable conditions the Fourier transform of a convolution of two functions (or signals) is the product of their Fourier transforms. More generally, convolution in one domain (e.g., time domain ) equals point-wise multiplication in the other domain (e.g., frequency domain ).
Many applications of the convolution power rely on being able to define the analog of analytic functions as formal power series with powers replaced instead by the convolution power. Thus if F ( z ) = ∑ n = 0 ∞ a n z n {\displaystyle \textstyle {F(z)=\sum _{n=0}^{\infty }a_{n}z^{n}}} is an analytic function, then one would like to be able ...
In artificial neural networks, a convolutional layer is a type of network layer that applies a convolution operation to the input. Convolutional layers are some of the primary building blocks of convolutional neural networks (CNNs), a class of neural network most commonly applied to images, video, audio, and other data that have the property of uniform translational symmetry.
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 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 signal processing, multidimensional discrete convolution refers to the mathematical operation between two functions f and g on an n-dimensional lattice that produces a third function, also of n-dimensions. Multidimensional discrete convolution is the discrete analog of the multidimensional convolution of functions on Euclidean space.
In mathematics, symmetric convolution is a special subset of convolution operations in which the convolution kernel is symmetric across its zero point. Many common convolution-based processes such as Gaussian blur and taking the derivative of a signal in frequency-space are symmetric and this property can be exploited to make these convolutions easier to evaluate.