| Author |
Comment/Response |
Peter Pein
|
 10/09/06 4:31pm
Hi Kris,
UnitStep[Sin[3x]] is not defined for Complex x. Neither are most of the following working examples. Maybe not a bug, but an inconsistency.
In[1]:=
<< "Calculus`FourierTransform`"
In[2]:=
FourierTrigSeries[UnitStep[Sin[3*Re[x]]] - 1/2, x, 5]
Out[2]=
(2*Sin[2*Pi*x])/Pi + (2*Sin[6*Pi*x])/(3*Pi) + (2*Sin[10*Pi*x])/(5*Pi)
In[3]:=
FourierTrigSeries[UnitStep[Sin[3*x]] - 1/2, x, 5, Assumptions -> Im[x] == 0]
Out[3]=
(2*Sin[2*Pi*x])/Pi + (2*Sin[6*Pi*x])/(3*Pi) + (2*Sin[10*Pi*x])/(5*Pi)
In[4]:=
FourierTrigSeries[Sign[Sin[3*x]]/2, x, 5]
Out[4]=
(2*Sin[2*Pi*x])/Pi + (2*Sin[6*Pi*x])/(3*Pi) + (2*Sin[10*Pi*x])/(5*Pi)
In[5]:=
FourierTrigSeries[Boole[Sin[3*x] > 0] - 1/2, x, 5]
Out[5]=
(2*Sin[2*Pi*x])/Pi + (2*Sin[6*Pi*x])/(3*Pi) + (2*Sin[10*Pi*x])/(5*Pi)
In[6]:=
FourierTrigSeries[Piecewise[{{1/2, Sin[3*x] > 0}}, -2^(-1)], x, 5]
Out[6]=
(2*Sin[2*Pi*x])/Pi + (2*Sin[6*Pi*x])/(3*Pi) + (2*Sin[10*Pi*x])/(5*Pi)
In[7]:=
FourierTrigSeries[Mod[Ceiling[3*(x/Pi)], 2] - 1/2, x, 5]
Out[7]=
(2*Sin[2*Pi*x])/Pi + (2*Sin[6*Pi*x])/(3*Pi) + (2*Sin[10*Pi*x])/(5*Pi)
And quite sure there are more possibilities.
Peter
P.S.: have a look at the option Fourierparameters too.
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