BUILT-IN MATHEMATICA SYMBOL

FourierSequenceTransform

gives the Fourier sequence transform of expr.

gives the multidimensional Fourier sequence transform.

MORE INFORMATION

FourierSequenceTransform 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:

			default settings
	{1, -2Pi}		period 1
			general setting

EXAMPLES

CLOSE ALL

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:

In[1]:=

Out[1]=

In[2]:=

Out[2]=

Find a bivariate discrete-time Fourier transform:

In[1]:=

Out[1]=

In[2]:=

Out[2]=

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

-analog generating function: