do we have better way to do Fourier Transform now?

Hi,

I am thinking about using Maxima to do Fourier Transform since I am tried on
many formula deduction...

I found a very old email in the mailing list:
http://www.math.utexas.edu/pipermail/maxima/2002/002945.html

So I copied that example to define the Fourier Transform function and tried
to compute the FT of exponential function. (I used the definition of Fourier
Transform generally used in Signal Processing, G(w)=\int_{-\infty}^{\infty}
g(t) exp(-i w t) dt  )

(%i1) ft(expr,t,w):=integrate(expr*exp(-%i*w*t),t,-inf,inf);
(%o1)  ft(expr, t, w) := integrate(expr exp((- %i) w t), t, - inf, inf)
(%i2) ft(exp(-1*a*t),t,w);
Is  a  positive, negative, or zero?

positive;
Is  w  positive, negative, or zero?

positive;
                           inf
                          /
                          [        - %i t w - a t
(%o2)                     I      %e               dt
                          ]
                          /
                           - inf

Sadly, I was wondering why Maxima asked me the sign of w. I think Maxima
should be able to handle one-variable integral of multi-variable expressions
- at least my calculus professor said "just consider the other variable as a
constant".

Do we have a better way to do Fourier transform in Maxima now?

PS: I think, Maxima can handle Laplapce Transform well. Then it should not
be very had to deal Fourier Transform. The Laplace Transform just replaced
%i*w by s.

Cheers,
Forrest

-- 
Forrest Sheng Bao, B.S. EE
Ph.D. student/Teaching Assistant, Dept. of Computer Science
M.Sc. student/Research Assistant, Dept. of Electrical & Computer Engineering
Rm 115, Experimental Sciences Building
Texas Tech University, Lubbock, Texas, USA
http://narnia.cs.ttu.edu