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Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

 NFourierSinTransform

Source Notebook

Find a numerical approximation for a Fourier sine transform

Contributed by: Wolfram Research

ResourceFunction["NFourierSinTransform"][expr,t,ω]

gives a numerical approximation to the Fourier sine transform of expr evaluated at the numerical value ω, where expr is a function of t.

Details and Options

The numerical approximation to the Fourier sine transform of expr is by default defined to be .
Different choices for the definition of the Fourier cosine transform can be specified using the option FourierParameters.
With the setting FourierParameters→{a,b}, the Fourier cosine transform computed by ResourceFunction["NFourierSinTransform"] is .
The parameter b in the setting FourierParameters→{a,b} must be numeric.
In addition to the option FourierParameters, ResourceFunction["NFourierSinTransform"] can also accept the options available to NIntegrate. These options are passed directly to NIntegrate.

Examples

Basic Examples (2) 

Numerical approximation for a Fourier sine transform:

In[1]:=
ResourceFunction["NFourierSinTransform"][(t + 3) E^(-t), t, 0.9]
Out[1]=

Compare with the answer from symbolic evaluation:

In[2]:=
FourierSinTransform[(t + 3) E^(-t), t, \[Omega]]
Out[2]=
In[3]:=
% /. {\[Omega] -> 0.9}
Out[3]=

Requirements

Wolfram Language 11.3 (March 2018) or above

Version History

  • 1.0.0 – 03 April 2019

Related Resources

License Information