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Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

 NFourierCoefficient

Source Notebook

Find a numerical approximation for a Fourier exponential series coefficient of a function

Contributed by: Wolfram Research

ResourceFunction["NFourierCoefficient"][expr,t,n]

gives a numerical approximation to the nth coefficient in the Fourier exponential series expansion of expr.

Details and Options

The numerical approximation to the nth coefficient in the Fourier exponential series expansion of expr is by default defined to be , where n must be an integer.
Different choices for the definition of the Fourier exponential series expansion can be specified using the option FourierParameters.
With the setting FourierParameters→{a,b}, the nth coefficient computed by ResourceFunction["NFourierCoefficient"] is .
The parameter b in the setting FourierParameters→{a,b} must be numeric.
In addition to the option FourierParameters, ResourceFunction["NFourierCoefficient"] can also accept the options available to NIntegrate. These options are passed directly to NIntegrate.

Examples

Basic Examples (3) 

Calculate numerical approximation for a Fourier coefficient:

In[1]:=
ResourceFunction["NFourierCoefficient"][t^2 + 3 t, t, 5]
Out[1]=

Compare with the answer from symbolic evaluation:

In[2]:=
FourierCoefficient[t^2 + 3 t, t, n]
Out[2]=
In[3]:=
% /. {n -> 5.}
Out[3]=

Repeat the computation, using a different definition of the Fourier transform:

In[4]:=
ResourceFunction["NFourierCoefficient"][t^2 + 3 t, t, 5, FourierParameters -> {1, -2 \[Pi]}]
Out[4]=

Requirements

Wolfram Language 11.3 (March 2018) or above

Version History

  • 1.0.0 – 26 April 2019

Related Resources

License Information