Fourier fit

function [Yp, Parm] = fourier_fit(Ye,X,N)
% written by Trent E. Balius
% modified by Lingling Jiang
% Robert C. Rizzo Research Group
% Stony Brook University
% syntax: [Yp,Parm] = fourier_fit(Ye,X,N)
% Yp is the predicted Y values
% Parm is the parameter set = 2*N + 1
% Parm = {V,A1,B1,A2,B2}
% f(x) = V(1) + sum(i=1:N){A1(i)*cos(i*x)+B1(i)*sin(i*x)}
% f(x) = P(1) + sum(i=1:N){P(2*i)*cos(i*x)+P(2*i+1)*sin(i*x)}

% f(x) = P(1) + sum(j=2:2:2*N){P(j)*cos((j/2)*x)}
%             +sum(j=3:2:2*N+1){P(j)*sin(((j-1)/2)*x)}

% Ye is the Y value from the data
% X is the X value from the data
% N is the number over which sum is calculated
% uses fmincon

 input = rand( (2*N + 1),1); %intial guess
 lb    =  -1000*ones(2*N + 1,1); % lower bound
 ub    =  1000*ones(2*N + 1,1); % upper bound
 [Parm,f] = fmincon(@objective_function,input,[],[],[],[],lb,ub,[],[],Ye,X);
 Yp = fourier_series(Parm,X);


function [val] = objective_function(Parm,Y,X)
 Yp = fourier_series(Parm,X);
 %[Y,Yp]
 val = sum((Y-Yp).^2);
return


function [Yp] = fourier_series(Parm,X)
 %whos
 % f(x) = V(1) + sum(i=1:N){A1(i)*cos(i*x)+B1(i)*sin(i*x)}
 % f(x) = P(1) + sum(i=1:N){P(2*i)*cos(i*x)+P(2*i+1)*sin(i*x)}

 % f(x) = P(1) + sum(j=2:2:2*N){P(j)*cos((j/2)*x)}
 %             +sum(j=3:2:2*N+1){P(j)*sin(((j-1)/2)*x)}

 Yp = Parm(1)*ones(size(X));

 for i = 2:length(Parm)
     if (mod(i,2) == 0) % i is even
        Yp = Yp + Parm(i)*cos((i/2)*X);
     else % i is odd
        Yp = Yp + Parm(i)*sin((i-1)/2*X);
     end
 end
return