On Sat, May 16, 1998 at 09:45:06PM -0400, Heber Farnsworth wrote:

> This may not be an octave question so much as a question about how the FFT

> library works. I've never used it before but when I try it on simple

> functions for which I know the fourier transform (heaviside, gaussian,

> triangle, etc) I don't get anything like what I get analytically. For

> instance try a gaussian

>

> exp(-t.^2)/sqrt(2*pi)

>

> Since this function is even you should get a real transform and, in fact,

> it should be another gaussian. Instead you get something who's real and

> imaginary parts both oscillate very fast and which look a lot different at

> the ends than in the middle. What do I not understand here?

well the fft is an algorithm for performing the discrete fourier

transform (DFT). (why it's not called dft in the program, i don't

know.) anyhow the fft is a mapping from complex valued functions of

the group Z_n to itself (where n is the length of the vector). this

isn't what is generally meant by fourier transform in most textsbooks.

for one, the function is even if it is even over Z_n,

i.e. f(i) = f(-i) = f(n-i) for all i in Z_n.

the discrete time fourier transform DTFT maps complex valued functions

of the integers to complex valued function an the interval usually

[-0.5,0.5], [-pi,pi], [0,1] or [0,2pi] depending on the particular

definition of the intregral.

by padding a vector with zeros, you can enlist the DFT to give you a

sampled DTFT for a finite length sequence which is generally what you

want.

hope this helps.

--

Johan Kullstam [

[hidden email]]