Hi,
I am trying to find a closed form expresion for the
discrete fourier transform of a chirp signal.
The summation I am trying to simplify:
expr:exp(-%i*n*w/N)*exp(%i*b*n^2);
sum(expr, n, 0, N-1), simpsum;
GosperSum or nosum can also not simplify it.
(BTW GosperSum with Maxima 5.9.3 gave a wrong result, but
with more recent version it says it is not hypergeometric.)
My question is if anybody has an idea how to find
a closed form expression for the above stated summation.
I was wondering if there is a way to bring 'expr' in
another form which maybe could be simplified.
Also I am interested in understanding the functions in
the "fourie" package. Somehow I could not really understand how
those are supposed to be used.
Another thing I thought about, is if it is possible to
use an integration instead of the summation (evaluate a
continous fourier transform) and somehow relate that
to the needed discrete version. I just thought because it
is possible to get approximate results for integrals by
summations (like in numerical methods), it might be also
possible to do the opposite.
I know that I cannot simply "sample" the result of
the integration, but maybe there is some technique to do this
correctly.
I hope somebody can make sense of my question, otherwise
I try to explain myself better...
gr.
Anton