# InverseFourierSequenceTransform

InverseFourierSequenceTransform[expr,ω,n]

gives the inverse discrete-time Fourier transform of expr.

InverseFourierSequenceTransform[expr,{ω1,ω2,},{n1,n2,}]

gives the multidimensional inverse Fourier sequence transform.

# Details and Options • The inverse Fourier sequence transform of is by default defined to be .
• The dimensional inverse transform is given by .
• In the form InverseFourierSequenceTransform[expr,t,n], n can be symbolic or an integer.
• The following options can be given:
•  Assumptions \$Assumptions assumptions on parameters FourierParameters {1,1} parameters to define transform GenerateConditions False whether to generate results that involve conditions on parameters
• Common settings for FourierParameters include:
•  {1, 1} default settings {1,-2Pi} period 1 {a,b} general setting

# Examples

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## Basic Examples(2)

Find the discrete-time inverse Fourier transform of :

Find a bivariate discrete-time inverse Fourier transform:

## Scope(3)

Inverse transform of rational exponential function:

Gaussian function:

A constant frequency gives an impulse and vice versa:

Rational function in :

## Options(2)

### Assumptions(1)

Specify assumptions on a parameter:

### FourierParameters(1)

Use a nondefault setting for FourierParameters:

## Properties & Relations(6)

InverseFourierSequenceTransform is defined by an integral:

InverseFourierSequenceTransform and FourierSequenceTransform are inverses:

InverseFourierSequenceTransform is closely related to InverseZTransform:

Just as InverseFourierTransform is closely related to InverseLaplaceTransform:

InverseFourierSequenceTransform is the same as FourierCoefficient:

Inverse discrete-time Fourier transform for basis exponentials:

InverseFourierSequenceTransform is closely related to InverseBilateralZTransform: