function f = dfft(y)
 
% First use standard Matlab routine to find Fourier transform of y.
% z contains the complex coefficeints of the Fourier exponential series.
 z=fft(y); 

 n = length(y);
 half=n/2;


% This section takes the exponential series coefficients and gives the     
% coefficients of the Fourier Sine and Cosine series.
% f(1) = constant term = average value of the function over period sampled
% f(2) = 

 for i = 1:2:n
  j=(i+1)/2;
  f(i)=real(z(j))/half;
  f(i+1)=-imag(z(j))/half;
 end  

 j=n/2 +1;
 f(2)=real(z(j))/half;