Wolfram alpha says:
fourier transorm(dirac delta function(x-1)) ~ exp(i*w)
http://mathworld.wolfram.com/DeltaFunction.html says:
fourier transorm(dirac delta function(x-1)) ~ exp(-i*w)
Is it a bug in wolfram alpha?
I think this is just an convention issue. see: http://mathworld.wolfram.com/FourierTransform.html. You can use the FourierParameter option to get different versions of result.
FourierParameter
