FFT is not accurate?

I have a question about FFT. I thought the FFT should converge to the continious fourier transform for a large number of samples. Is that true? Performing an FFT of a rectangular pulse with Matlab leads to a function that resembles a sinc function but is not identical to it, no matter how many samples I use.

Here is how I have implemented it:

k=[0:2048,-2047:-1];
r=[ones(1,64),zeros(1,3969),ones(1,63)];
sitrafo=real(fft(r,4096,2));
sireal=127*sinc(k*127/4096);

figure(1);
plot(k,sitrafo);grid;
hold on;
plot(k,sireal,'g');

Any hints are very much appreciated!

Answer 1

[Azzi Abdelmalek]

i have posted a function get_harmoniques on file exchange, it will appear, maby tomorow, or after the week-end. try it and tell me about it.

[Azzi Abdelmalek]

http://www.mathworks.com/matlabcentral/fileexchange/37654-get-harmoniques-of-a-real-signal