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FourierCoefficient

FourierCoefficient
gives the n^(th) coefficient in the Fourier series expansion of expr.
FourierCoefficient
gives a multidimensional Fourier coefficient.
  • The ^(th) coefficient in the Fourier series expansion of is by default given by .
  • The -dimensional Fourier coefficient is given by .
  • The following options can be given:
Assumptions$Assumptionsassumptions on parameters
FourierParameters{1,1}parameters to define Fourier series
GenerateConditionsFalsewhether to generate results that involve conditions on parameters
  • The function expr is assumed to be periodic in t with period , except when otherwise specified by FourierParameters.
{1,1}f(t) e-i n tdtdefault settings
{1,-2Pi}f(t) ei 2 n tdtperiod 1
{a,b}general setting
Find the 5^(th) Fourier coefficient:
Find the coefficient of the general term in a Fourier series:
Plot the sequence:
Find the Fourier coefficient:
Find the coefficient of the general term:
Plot the absolute value of coefficients:
Find the 5^(th) Fourier coefficient:
In[1]:=
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Out[1]=
Find the coefficient of the general term in a Fourier series:
In[2]:=
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Out[2]=
Plot the sequence:
In[3]:=
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Out[3]=
 
Find the Fourier coefficient:
In[1]:=
Click for copyable input
Out[1]=
Find the coefficient of the general term:
In[2]:=
Click for copyable input
Out[2]=
Plot the absolute value of coefficients:
In[3]:=
Click for copyable input
Out[3]=
Find the 3^(rd) Fourier coefficient for an exponential function:
General Fourier coefficient for a Gaussian function:
General Fourier coefficients for Abs:
Fourier coefficient for a basis exponential function:
Specify assumptions on a parameter:
Use a nondefault setting for FourierParameters:
FourierCoefficient is defined by an integral:
Compute the exponential Fourier series using the individual coefficients:
Fourier coefficients for basis exponentials:
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