This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# FourierSequenceTransform

 FourierSequenceTransform gives the Fourier sequence transform of expr. FourierSequenceTransformgives the multidimensional Fourier sequence transform.
• 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
 default settings {1, -2Pi} period 1 general setting
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:
 Out[1]=
 Out[2]=

Find a bivariate discrete-time Fourier transform:
 Out[1]=
 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:
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:
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