Function Repository Resource:

# NFourierCoefficient

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]:=
 Out[1]=

Compare with the answer from symbolic evaluation:

 In[2]:=
 Out[2]=
 In[3]:=
 Out[3]=

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

 In[4]:=
 Out[4]=

## Requirements

Wolfram Language 11.3 (March 2018) or above

## Version History

• 1.0.0 – 26 April 2019