FourierSequenceTransform

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

FourierSequenceTransform[expr, {n1, n2, ...}, {1, 2, ...}]
gives the multidimensional Fourier sequence transform.

Details and OptionsDetails and Options

  • FourierSequenceTransform is also known as discrete-time Fourier transform (DTFT).
  • FourierSequenceTransform[expr, n, ] takes a sequence whose n^(th) 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$Assumptionsassumptions on parameters
    FourierParameters{1,1}parameters to definite discrete-time Fourier transform
    GenerateConditionsFalsewhether 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:

In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=

Find a bivariate discrete-time Fourier transform:

In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=
New in 7
New to Mathematica? Find your learning path »
Have a question? Ask support »