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## Re: fft

**From**: |
johan19 |

**Subject**: |
Re: fft |

**Date**: |
Sun, 17 May 1998 18:05:03 -0400 |

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 address@hidden

**fft**, *Heber Farnsworth*, `1998/05/16`