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Mathematica > Mathematics and Algorithms > Calculus > Integral Transforms > Fourier Analysis >

InverseFourierSequenceTransform

InverseFourierSequenceTransform[expr, Omega, n]
gives the inverse discrete-time Fourier transform of expr.
InverseFourierSequenceTransform[expr, {Omega1, Omega2, ...}, {n1, n2, ...}]
gives the multidimensional inverse Fourier sequence transform.
  • The inverse Fourier sequence transform of f(omega) is by default defined to be .
  • The m-dimensional inverse transform is given by .
  • The following options can be given:
Assumptions$Assumptionsassumptions on parameters
FourierParameters{1,1}parameters to define transform
GenerateConditionsFalsewhether to generate results that involve conditions on parameters
{1, 1}default settings
{1, -2Pi}period 1
{a, b}general setting
Find the discrete-time inverse Fourier transform of |omega|:
Find a bivariate discrete-time inverse Fourier transform:
Find the discrete-time inverse Fourier transform of |omega|:
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Find a bivariate discrete-time inverse Fourier transform:
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Inverse transform of rational exponential function:
Gaussian function:
A constant frequency gives an impulse and vice versa:
Rational function in exp(ⅈ omega):
Specify assumptions on a parameter:
Use a non-default setting for FourierParameters:
InverseFourierSequenceTransform is defined by an integral:
Just as InverseFourierTransform is closely related to InverseLaplaceTransform:
Inverse discrete-time Fourier transform for basis exponentials:
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