In mathematics, the Poisson summation formula is an equation that relates the Fourier series coefficients of the periodic summation of a function to values of the function's continuous Fourier transform. Consequently, the periodic summation of a function is completely defined by discrete samples of the original function's Fourier transform. And conversely, the periodic summation of a function's Fourier transform is completely defined by discrete samples of the original function. The Poisson summation formula was discovered by Siméon Denis Poisson and is sometimes called Poisson resummation.
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In mathematics, the Poissonsummationformula is an equation that relates the Fourier series coefficients of the periodic summation of a function to values...
mathematics, the Poissonformula, named after Siméon Denis Poisson, may refer to: Poisson distribution in probability Poissonsummationformula in Fourier analysis...
abelian groups. The Poissonsummationformula (PSF) is an equation that relates the Fourier series coefficients of the periodic summation of a function to...
more broadly. For instance, it is used in the statement of the Poissonsummationformula, transference theorems provide connections between the geometry...
n = − ∞ ∞ s [ n ] ⋅ e − i 2 π f n T ⏞ Fourier series (DTFT) ⏟ Poissonsummationformula = F { ∑ n = − ∞ ∞ s [ n ] δ ( t − n T ) } , {\displaystyle S_{\frac...
subgroup Z of the real numbers G = R, the Selberg trace formula is essentially the Poissonsummationformula. The case when Γ\G is not compact is harder, because...
matrix-exponential functions in Matlab Inverse Fourier transform Poissonsummationformula Cohen, A. M. (2007). "Inversion Formulae and Practical Results"...
either side. It can be regarded as a Poissonsummationformula for non-abelian groups. The Voronoi (summation) formula for GL(2) has long been a standard...
1P{\displaystyle {\tfrac {1}{P}}}. That identity is a form of the Poissonsummationformula. Similarly, a Fourier series whose coefficients are samples of...
statistics, Poisson regression is a generalized linear model form of regression analysis used to model count data and contingency tables. Poisson regression...
following interesting[clarification needed] identity from the Poissonsummationformula: ∑ k ∈ Z exp ( − π ⋅ ( k c ) 2 ) = c ⋅ ∑ k ∈ Z exp ( − π ⋅...
Convolution Theorem on tempered distributions which turns out to be the Poissonsummationformula, in signal processing, the Dirac comb allows modelling sampling...
{f}}\operatorname {\text{Ш}} } is precisely the Poissonsummationformula. More generally, this formula remains to be true if f is a tempered distribution...
\operatorname {\text{Ш}} } is the Dirac comb both equations yield the Poissonsummationformula and if, furthermore, u ≡ δ {\displaystyle u\equiv \delta } is...
integral multiples of 2π. This is a version of the one-dimensional Poissonsummationformula. The constant π is connected in a deep way with the theory of...
2})}\int _{0}^{\infty }x^{{1 \over 2}{s}-1}\psi (x)\,dx.} By the Poissonsummationformula we have ∑ n = − ∞ ∞ e − n 2 π x = 1 x ∑ n = − ∞ ∞ e − n 2 π x...
the central sphere of the packing and f̂ positive. Then, the Poissonsummationformula for f is used to compare the density of the optimal lattice with...
theory) Signal (information theory) Data conversion Interpolation Poissonsummationformula Realizable low-pass filters have a transition band where the response...
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