Wolfram Research

Function Repository Resource:

NFourierTrigSeries

Source Notebook

Find a numerical approximation for a trigonometric Fourier series expansion of a function

Contributed by: Wolfram Research

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

gives a numerical approximation to the nth-order Fourier trigonometric series expansion of expr in t.

Details and Options

The numerical approximation to the order n Fourier exponential series expansion of expr is by default defined to be .
The coefficient ck is defined to be and the coefficient dk is defined to be .
With the setting FourierParameters{a,b}, the order n Fourier exponential series expansion computed by ResourceFunction["NFourierTrigSeries"] is . Here, the coefficient ck is defined to be and the coefficient dk is defined to be .
The parameter b in the setting FourierParameters{a,b} must be numeric.
In addition to the option FourierParameters, ResourceFunction["NFourierTrigSeries"] can also accept the options available to NIntegrate. These options are passed directly to NIntegrate.

Examples

Basic Examples

Numerical approximation for a trigonometric Fourier series:

In[1]:=
ResourceFunction["NFourierTrigSeries"][t^2 + t, t, 3]
Out[1]=
In[2]:=
Plot[%, {t, -2, 2}]
Out[2]=

Compare with a plot of the original function:

In[3]:=
Plot[t^2 + t, {t, -2, 2}]
Out[3]=

Requirements

Wolfram Language 11.3 (March 2018) or above

Resource History

License Information