Fourier coefficients from FFT regarding

Hi all,

   i understand that the fourier series coefficients is defined for the limt -pi to pi, for continuous fourier transform it is -inf to +inf and for discrete fourier transform it is -pi to pi.
   While using FFT in Matlab, for a periodic signal length 2pi, am able to verify its complex valued fourier coefficients. Suppose the signal is periodic but of length multiples of 2pi, say 4pi or 6pi (as in the case of a windowed periodic signal chosen for fft) ; am unable to get the same fourier coefficients (complex value). As FFT is definitely for large number of samples, i think i am missing upon something. Can anyone suggest me ?

Thanks and Regards, Nani.

Answer 1

[Azzi Abdelmalek]

if T=2pi is a period of your signal, then your are looking for coefficient that respect

 x(t)=a0+a1 cos(w0.t)+b1sin(w0.t)+a2cos(2w0.t)+..      with w0=2pi/T

when you consider a period T=2*2pi that means new_w0=2*w0 which means your looking for coefficint new_ak new_bk that veify

 x(t)=new_a0+ new_a1 cos(new_w0.t)+....

which explain the difference between your coefficients

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