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FourierSequenceTransform

FourierSequenceTransform
gives the Fourier sequence transform of expr.
FourierSequenceTransform
gives the multidimensional Fourier sequence transform.
  • FourierSequenceTransform 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
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:
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]=
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:
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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