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FourierCosTransform and FourierTransform don't agree for even functions.


The Wolfram-Language specification states:

Results from FourierCosTransform and FourierTransform agree for even functions

In this respect, Mathematica does not conform to the Wolfram-Language specification:

In[1]:= x = E^(+I s)/2 + E^(-I s)/2;

In[2]:= FourierTransform[x, s, t]

Out[2]= Sqrt[\[Pi]/2] DiracDelta[-1 + t] + 
 Sqrt[\[Pi]/2] DiracDelta[1 + t]

In[3]:= FourierCosTransform[x, s, t]

Out[3]= 0

Moreover, Mathematica gives inconsistent results on arguments claimed equal by Mathematica:

In[4]:= x == ExpToTrig[x] // Simplify

Out[4]= True

In[5]:= x = ExpToTrig[x]

Out[5]= Cos[s]

In[6]:= FourierCosTransform[x, s, t]

Out[6]= Sqrt[\[Pi]/2] (DiracDelta[-1 + t] + DiracDelta[1 + t])
POSTED BY: Joe Donaldson
3 months ago

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