In mathematics, the Poisson summation formula is an equation that relates the Fourier series coefficients of the periodic summation of a function to values...

more broadly. For instance, it is used in the statement of the Poisson summation formula, transference theorems provide connections between the geometry...

mathematics, the Poisson formula, named after Siméon Denis Poisson, may refer to: Poisson distribution in probability Poisson summation formula in Fourier analysis...

n = − ∞ ∞ s [ n ] ⋅ e − i 2 π f n T ⏞ Fourier series (DTFT) ⏟ Poisson summation formula = F { ∑ n = − ∞ ∞ s [ n ]   δ ( t − n T ) } , {\displaystyle S_{\tfrac...

subgroup Z of the real numbers G = R, the Selberg trace formula is essentially the Poisson summation formula. The case when Γ\G is not compact is harder, because...

computational chemistry. Ewald summation is a special case of the Poisson summation formula, replacing the summation of interaction energies in real...

n/P.} The identity is also a form of the Poisson summation formula. This implies that the periodic summation of any band-limited function, such as the...

either side. It can be regarded as a Poisson summation formula for non-abelian groups. The Voronoi (summation) formula for GL(2) has long been a standard...

Convolution Theorem on tempered distributions which turns out to be the Poisson summation formula, in signal processing, the Dirac comb allows modelling sampling...

matrix-exponential functions in Matlab Inverse Fourier transform Poisson summation formula Cohen, A. M. (2007). "Inversion Formulae and Practical Results"...

{f}}\operatorname {\text{Ш}} } is precisely the Poisson summation formula. More generally, this formula remains to be true if f is a tempered distribution...

Riemann.) When Re(s) = σ > 1, the function can be written as a converging summation or as an integral: ζ ( s ) = ∑ n = 1 ∞ 1 n s = 1 Γ ( s ) ∫ 0 ∞ x s − 1...

Fourier series coefficients proportional to those samples by the Poisson summation formula: f P ( x ) ≜ ∑ n = − ∞ ∞ f ( x + n P ) = 1 P ∑ k = − ∞ ∞ f ^ (...

interpretation of the Fourier transform, the Plancherel theorem and the Poisson summation formula. The image of Gaussian functions under the Weil–Brezin map are...

statistics, Poisson regression is a generalized linear model form of regression analysis used to model count data and contingency tables. Poisson regression...

function related to Weierstrass elliptic functions. Applying the Poisson summation formula to the characteristic function of the polygon leads to another...

rooted in the Poisson summation formula, which tells us that the periodic function represented by the Fourier series is a periodic summation of the continuous...

Fourier series Gibbs phenomenon Sigma approximation Dini test Poisson summation formula Spectrum continuation analysis Convergence of Fourier series List...

formula Poisson–Jensen formula Fourier analysis Poisson summation formula (Poisson resummation) Wavelet theory Poisson wavelet Poisson disk Poisson image...

theorem Convolution Convolution theorem Positive-definite function Poisson summation formula Paley-Wiener theorem Sobolev space Time–frequency representation...

integral multiples of 2π. This is a version of the one-dimensional Poisson summation formula. The constant π is connected in a deep way with the theory of...

following interesting[clarification needed] identity from the Poisson summation formula: ∑ k ∈ Z exp ⁡ ( − π ⋅ ( k c ) 2 ) = c ⋅ ∑ k ∈ Z exp ⁡ ( − π ⋅...

study its properties. Using harmonic analysis, more precisely the Poisson summation formula, he proved the functional equation and meromorphic continuation...

{\displaystyle g(x)=f(ye^{x})e^{ax}} for some positive a turns the Poisson summation formula into a formula involving the Mellin transform. Here y is a real parameter...

\operatorname {\text{Ш}} } is the Dirac comb both equations yield the Poisson summation formula and if, furthermore, u ≡ δ {\displaystyle u\equiv \delta } is...

In mathematics and classical mechanics, the Poisson bracket is an important binary operation in Hamiltonian mechanics, playing a central role in Hamilton's...

of integers, then the trace formula becomes the Poisson summation formula. In most cases of the Arthur–Selberg trace formula, the quotient G(F)\G(A) is...

theory) Signal (information theory) Data conversion Interpolation Poisson summation formula Realizable low-pass filters have a transition band where the response...

p {\displaystyle \mu /p} , with the distribution becoming identical to Poisson in the limit p → 1 {\displaystyle p\to 1} for a given mean μ {\displaystyle...

the central sphere of the packing and f̂ positive. Then, the Poisson summation formula for f  is used to compare the density of the optimal lattice with...