scale convolution of two functions s ( t ) {\displaystyle s(t)} and r ( t ) {\displaystyle r(t)} , also known as their logarithmic convolution or log-volution...

convolution Logarithmic convolution Vandermonde convolution Convolution, in digital image processing, with a Kernel (image processing) Convolutional code...

distribution Logarithmic algorithm Logarithmic convolution Logarithmic decrement Logarithmic derivative Logarithmic differential Logarithmic differentiation...

density is a logarithmically concave function. Thus, any Gaussian measure is log-concave. The Prékopa–Leindler inequality shows that a convolution of log-concave...

In convex analysis, a non-negative function f : Rn → R+ is logarithmically concave (or log-concave for short) if its domain is a convex set, and if it...

input cannot take logarithmic time, as the time taken for reading an input of size n is of the order of n. An example of logarithmic time is given by dictionary...

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...

] {\displaystyle \operatorname {E} \left[X^{-n}\right]} and the n-th logarithmic moment about zero is E ⁡ [ ln n ⁡ ( X ) ] . {\displaystyle \operatorname...

before the first success (i.e. one less). The Hermite distribution The logarithmic (series) distribution The mixed Poisson distribution The negative binomial...

_{a}^{b}x(\tau )h(t-\tau )\,d\tau } That is the convolution integral and is used to find the convolution of a signal and a system; typically a = -∞ and...

(s-a-b)}{\zeta (2s-a-b)}},} which is a special case of the Rankin–Selberg convolution. A Lambert series involving the divisor function is: ∑ n = 1 ∞ q n σ...

is the particle velocity, ∗ {\displaystyle *} is the convolution operator, z−1 is the convolution inverse of the specific acoustic impedance, hence the...

f(q)b ... While the Dirichlet convolution of two multiplicative functions is multiplicative, the Dirichlet convolution of two completely multiplicative...

S2CID 30368541 Chan, Timothy M. (2020), "More logarithmic-factor speedups for 3SUM, (median,+)-convolution, and some geometric 3SUM-hard problems", ACM...

Hence, y ( n ) = x ( n ) ∗ h ( n ) {\displaystyle y(n)=x(n)*h(n)} (convolution) As speech is not stationary signal, it is divided into overlapped frames...

between s(t) and a Dirac comb function. The spectrum of a product is the convolution between S(f) and another function, which inevitably creates the new frequency...

transforms, list of Fourier-related transforms Kernel (integral operator) Convolution Radon transform Buffon's needle Hadwiger's theorem mean width intrinsic...

{\displaystyle F} , the convolution of F {\displaystyle F} with itself, written F ∗ 2 {\displaystyle F^{*2}} and called the convolution square, is defined...

intervals are 20 Hz wide. Note that spectra are often plotted with a logarithmic frequency axis rather than a linear one, in which case equal physical...

f\star g} is the pdf of X + Y {\displaystyle X+Y} , we also have that the convolution of two log-concave functions is log-concave. Suppose that H(x,y) is a...

encountered when the usual arithmetic computations are performed on a logarithmic scale, as in log probability. Similar to multiplication operations in...

n + 1 {\displaystyle 2^{n}+1} ) can be calculated by evaluating the convolution of A , B {\displaystyle A,B} . Also, with g = 2 2 M ′ {\displaystyle...

interpolated at an arbitrary real argument x is obtained by the discrete convolution of those samples with the Lanczos kernel: S ( x ) = ∑ i = ⌊ x ⌋ − a +...

figure. The product of two Gaussian functions is a Gaussian, and the convolution of two Gaussian functions is also a Gaussian, with variance being the...

Iwaniec generalized the Elliott-Halberstam conjecture, using Dirichlet convolution of arithmetic functions related to the von Mangoldt function. The Elliott–Halberstam...

integral equations into algebraic polynomial equations, and by simplifying convolution into multiplication. For example, through the Laplace transform, the...

Logarithmic identities Several important formulas, sometimes called logarithmic identities or log laws, relate logarithms to one another. Logarithmic...

either linear or logarithmic, depending on what the graph is being used for. Audio would usually be represented with a logarithmic amplitude axis (probably...

called the Dirichlet convolution of a and b, and is denoted by a ∗ b {\displaystyle a*b} . A particularly important case is convolution with the constant...

technical school in Paris. In 1791, Prony embarked on the task of producing logarithmic and trigonometric tables for the French Cadastre (geographic survey)...