# 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:

Wolfram Research (2008), InverseFourierSequenceTransform, Wolfram Language function, https://reference.wolfram.com/language/ref/InverseFourierSequenceTransform.html.

#### Text

Wolfram Research (2008), InverseFourierSequenceTransform, Wolfram Language function, https://reference.wolfram.com/language/ref/InverseFourierSequenceTransform.html.

#### CMS

Wolfram Language. 2008. "InverseFourierSequenceTransform." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/InverseFourierSequenceTransform.html.

#### APA

Wolfram Language. (2008). InverseFourierSequenceTransform. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/InverseFourierSequenceTransform.html

#### BibTeX

@misc{reference.wolfram_2024_inversefouriersequencetransform, author="Wolfram Research", title="{InverseFourierSequenceTransform}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/InverseFourierSequenceTransform.html}", note=[Accessed: 22-May-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_inversefouriersequencetransform, organization={Wolfram Research}, title={InverseFourierSequenceTransform}, year={2008}, url={https://reference.wolfram.com/language/ref/InverseFourierSequenceTransform.html}, note=[Accessed: 22-May-2024 ]}