Built-in Mathematica Symbol

FourierSequenceTransform

FourierSequenceTransform[expr, n,

]
gives the Fourier sequence transform of expr.

FourierSequenceTransform[expr, {n₁, n₂, ...}, {

₁,

₂, ...}]
gives the multdimensional Fourier sequence transform.

MORE INFORMATION

FourierSequenceTransform[expr, n, ] takes a sequence whose n term is given by expr, and yields a function of the continuous parameter .

The Fourier sequence transform of is by default defined to be .

The multidimensional transform of is defined to be .

The following options can be given:

Assumptions	$Assumptions	assumptions on parameters
FourierParameters	{1,1}	parameters to definite discrete-time Fourier 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 Fourier transform of a simple signal:

Find a bivariate discrete-time Fourier transform:

Find the discrete-time Fourier transform of a simple signal:

Find a bivariate discrete-time Fourier transform:

Scope (3)

Compute the transform for each frequency

:

Plot the spectrum:

The phase:

Plot both spectrum and phase using color:

Constant:

Periodic:

Impulse:

Exponential:

Exponential polynomial:

Rational sequence:

Rational-trigonometric:

Hypergeometric terms:

Options (2)

Use a non-default setting for FourierParameters:

Obtain conditions on parameters:

Properties & Relations (4)

FourierSequenceTransform is defined by a doubly infinite sum:

FourierSequenceTransform is closely related to ZTransform:

A discrete analog of FourierTransform being closely related to LaplaceTransform:

FourierSequenceTransform is the periodic inverse to FourierCoefficient:

The result is periodic, which is assumed in the definition for FourierCoefficient:

FourierSequenceTransform provides a q-analog for generating function: