# Wolfram Language & System 10.3 (2015)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# FourierSequenceTransform

FourierSequenceTransform[expr,n,ω]
gives the Fourier sequence transform of expr.

FourierSequenceTransform[expr,{n1,n2,},{ω1,ω2,}]
gives the multidimensional Fourier sequence transform.

## Details and OptionsDetails and Options

• FourierSequenceTransform is also known as discrete-time Fourier transform (DTFT).
• FourierSequenceTransform[expr,n,ω] takes a sequence whose n term is given by expr, and yields a function of the continuous parameter ω.
• 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

## ExamplesExamplesopen allclose all

### Basic Examples  (2)Basic Examples  (2)

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

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Find a bivariate discrete-time Fourier transform:

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 Out[2]=