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InverseFourierSequenceTransform

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:

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