In mathematics, the convolution power is the n-fold iteration of the convolution with itself. Thus if x {\displaystyle x} is a function on Euclidean space...

In mathematics (in particular, functional analysis), convolution is a mathematical operation on two functions ( f {\displaystyle f} and g {\displaystyle...

A convolutional neural network (CNN) is a regularized type of feed-forward neural network that learns features by itself via filter (or kernel) optimization...

limit. (The operation of repeatedly taking a convolution of something with itself is called the convolution power.) Pascal's triangle has many properties and...

In mathematics, the Dirichlet convolution (or divisor convolution) is a binary operation defined for arithmetic functions; it is important in number theory...

distorting the signal tendency. This is achieved, in a process known as convolution, by fitting successive sub-sets of adjacent data points with a low-degree...

additive and reproductive convolution as well as under scale transformation. Consequently, these models all express a power-law relationship between the...

{x}}_{T}(f)|^{2}\,df} Then the power spectral density is simply defined as the integrand above. From here, due to the convolution theorem, we can also view...

partial differential equations, and to perform other operations such as convolutions or multiplying large integers. Since it deals with a finite amount of...

section of the beam. However, convolution can be used in certain cases to improve computational efficiency. In order for convolution to be used to calculate...

rate is 128.6 kbit/s, while its most robust is 21.4 kbit/s. It uses a convolutional code for error detection and correction. The upper layer is usually...

that has been encoded using a convolutional code or trellis code. There are other algorithms for decoding a convolutionally encoded stream (for example...

product of the two sequences of coefficients, and is a sort of discrete convolution. With these operations, R N {\displaystyle R^{\mathbb {N} }} becomes...

Inception is a family of convolutional neural network (CNN) for computer vision, introduced by researchers at Google in 2014 as GoogLeNet (later renamed...

the overlap–add method is an efficient way to evaluate the discrete convolution of a very long signal x [ n ] {\displaystyle x[n]} with a finite impulse...

LeNet is a series of convolutional neural network structure proposed by LeCun et al.. The earliest version, LeNet-1, was trained in 1989. In general,...

specifically in mathematical analysis, the Cauchy product is the discrete convolution of two infinite series. It is named after the French mathematician Augustin-Louis...

A.; Allauzen, A. (2023), "Efficient Bound of Lipschitz Constant for Convolutional Layers by Gram Iteration", Proceedings of the 40th International Conference...

{\displaystyle u_{1}^{*n}} denotes the n {\displaystyle n} -fold convolution power. Moreover, explicit asymptotes for w n {\displaystyle w_{n}} are known...

a cyclic convolution (the other algorithm for FFTs of prime sizes, Bluestein's algorithm, also works by rewriting the DFT as a convolution). Since Rader's...

AlexNet is the name of a convolutional neural network (CNN) architecture, designed by Alex Krizhevsky in collaboration with Ilya Sutskever and Geoffrey...

obtain the convolution of a and b, according to the usual convolution theorem. Let us also be more precise about what type of convolution is required...

In mathematics, deconvolution is the inverse of convolution. Both operations are used in signal processing and image processing. For example, it may be...

function F with a power series expansion such that F(0) = 1. We say that a family of polynomials, f0, f1, f2, ..., forms a convolution family if deg fn...

The sparse nature of velvet noise allows for efficient time-domain convolution, making velvet noise particularly useful for applications where computational...

the diagonal of a matrix Kernel density estimation, the width of the convolution kernel used in statistics Graph bandwidth, in graph theory Coherence...

may involve infinite sums which need not converge (one cannot take the convolution of integer sequences). Geometrically, the two Laurent series may have...

signals combined by convolution (such as a source and filter) into sums of their cepstra, for linear separation. In particular, the power cepstrum is often...

+f_{m}^{*}.} The infimal convolution of two functions has a geometric interpretation: The (strict) epigraph of the infimal convolution of two functions is...

refinement equation, dilation equation or two-scale equation. Using the convolution (denoted by a star, *) of a function with a discrete mask and the dilation...