vlt.math.fouriercoeffs

   vlt.math.fouriercoeffs - find Fourier coefficients for data

   Uses FFT to compute the Fourier coefficients for a vector of data.

   [FC,FREQS]=vlt.math.fouriercoeffs(DATA,SI)

   where DATA is a vector of data and SI is the sampling interval (in seconds),
   returns FC the Fourier coefficients and FREQS, the frequency of
   each coefficient.

   The Fourier coefficients are defined [1] to be:
     B0   = (1/T) * sum(data)   (returned in FC(1))
     Bn   = (2/T) * integral(0,T,data.*cos(2*pi*n/T))  (returned in real(FC(n+1)))
     An   = (2/T) * integral(0,T,data.*sin(2*pi*n/T))  (returned in imag(FC(n+1)))

   Each entry of FC is the sum of Bn+An*sqrt(-1) so that
   Bn = real(FC(n+1)) and An = imag(FC(n+1))

   Note that these Fourier cofficients are normalized differently than those returned
   by the Matlab function FFT.

   [1]: _Waves_, Berkeley Physics Course Volume 3, Crawford, 1968

   See also:  FFT

   Example:
     t = 0:0.001:3;
     f = 4; % 4 Hz
     phase = pi/3;
     s = 2+0.5*sin(2*pi*f*t+phase); % sinusoidal function with amplitude 0.5
     [fc,freqs] = fouriercoeffs(s,0.001);
     figure;
     subplot(2,1,1); 
     plot(t,s);
     xlabel('Time(s)');
     ylabel('Signal(a.u.)');
     box off;
     subplot(2,1,2);
     plot(freqs,abs(fc),'o');
     A=axis;
     axis([0 10 0 3]);
     xlabel('Frequency (Hz)');
     ylabel('Magnitude of Fourier coefficient');
     box off;