Wolfram Research

Function Repository Resource:

NFourierCosTransform

Source Notebook

Find a numerical approximation for a Fourier cosine transform

Contributed by: Wolfram Research

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

gives a numerical approximation to the Fourier cosine 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 cosine 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["NFourierCosTransform"] is .
The parameter b in the setting FourierParameters{a,b} must be numeric.
In addition to the option FourierParameters, ResourceFunction["NFourierCosTransform"] can also accept the options available to NIntegrate. These options are passed directly to NIntegrate.

Examples

Basic Examples

Numerical approximation for a Fourier cosine transform:

In[1]:=
ResourceFunction["NFourierCosTransform"][E^(-7 t), t, 0.4]
Out[1]=

Compare with the answer from symbolic evaluation:

In[2]:=
FourierCosTransform[E^(-7 t), t, \[Omega]]
Out[2]=
In[3]:=
% /. {\[Omega] -> 0.4}
Out[3]=

Requirements

Wolfram Language 11.3 (March 2018) or above

Resource History

See Also

License Information