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Function Repository Resource:

NInverseFourierSequenceTransform

Source Notebook

Find a numerical approximation to the inverse Fourier sequence transform of a periodic function

Contributed by: Wolfram Research

ResourceFunction["NInverseFourierSequenceTransform"][expr,ω,n]

gives a numerical approximation to the inverse Fourier sequence transform of expr, evaluated at the integer n.

Details and Options

Fourier sequence transform is also known as discrete-time Fourier transform (DTFT).
The numerical approximation to the inverse Fourier sequence transform of expr is by default defined to be .
Different choices for the definition of the inverse Fourier sequence transform can be specified using the option FourierParameters.
With the setting FourierParameters{a,b}, expr is assumed to have a period of , and the inverse Fourier sequence transform computed by ResourceFunction["NInverseFourierSequenceTransform"] is .
The parameter b in the setting FourierParameters{a,b} must be numeric.
In addition to the option FourierParameters, ResourceFunction["NInverseFourierSequenceTransform"] can also accept the options available to NIntegrate. These options are passed directly to NIntegrate.

Examples

Basic Examples

Numerical value for a sequence with a given Fourier sequence transform:

In[1]:=
ResourceFunction["NInverseFourierSequenceTransform"][
 Exp[-\[Omega]^2 + \[Omega]], \[Omega], 4]
Out[1]=

Compare with the answer from symbolic evaluation:

In[2]:=
InverseFourierSequenceTransform[
 Exp[-\[Omega]^2 + \[Omega]], \[Omega], n]
Out[2]=
In[3]:=
% /. {n -> 4.}
Out[3]=

Requirements

Wolfram Language 11.3 (March 2018) or above

Resource History

See Also

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