NFourierTrigSeries


gives a numerical approximation to the order n Fourier trigonometric series expansion of expr, where expr is a periodic function of t with period .

DetailsDetails

  • To use , you first need to load the Fourier Series Package using Needs["FourierSeries`"].
  • The numerical approximation to the order n Fourier exponential series expansion of expr is by default defined to be c0+ckCos[k t]+dk Sin[k t].
  • The coefficient is defined to be NIntegrate[expr Cos[k t],{t,-π,π}] and the coefficient is defined to be NIntegrate[expr Sin[k t],{t,-π,π}].
  • Different choices for the period of expr can be specified using the option FourierParameters.
  • With the setting FourierParameters->{a,b}, expr is assumed to have a period of , and the order n Fourier exponential series expansion computed by is (+ck Cos[2π b k t]+dk Sin[2π b k t]). Here, the coefficient is defined to be NIntegrate[expr Cos[b k t],{t,-,}] and the coefficient is defined to be NIntegrate[expr Sin[b k t],{t,-,}].
  • The parameter b in the setting FourierParameters->{a,b} must be numeric.
  • In addition to the option FourierParameters, can also accept the options available to NIntegrate. These options are passed directly to NIntegrate.

ExamplesExamplesopen allclose all

Basic Examples  (1)Basic Examples  (1)

In[1]:=
Click for copyable input

Numerical approximation for a trigonometric Fourier series:

In[2]:=
Click for copyable input
Out[2]=
In[3]:=
Click for copyable input
Out[3]=

Compare with a plot of the original function:

In[4]:=
Click for copyable input
Out[4]=