% Function:	
%		fhp - calculate the first Fourier harmonic projection of a give data set.
% Input:	
%		data - m x n numerical matrix
% Output:	
%		out - m x 2 matrix containing the real and imaginary parts
%			of the first Fourier harmonic projection
% Usage:
%		proj = fhp(inputdata);
%
% Date: 2/27/2006



function out = fhp(data)

	[m n] = size(data);	% calculate the input data dimension
	outR = zeros(m, 1);	% real part
	outI = zeros(m, 1);	% imaginary part

	theta = (-2 * pi) / n;	% incremental angel

	
	% for every data point, do the projection
	for i=1:m
		rowdata = data(i, :);
		x = 0.0;
		y = 0.0;
		
		% take the first Fourier harmonic projection
		for j=1:n
			x = x + data(i,j) * cos(theta * (j-1));
			y = y + data(i,j) * sin(theta * (j-1));
		end
		outR(i) = x;	% real part
		outI(i) = y;	% imaginary part
	end

	% combine real and imaginary parts into one matrix
	out = [outR outI];