SinCosFit.m

function [a,yy] = SinCosFit(x,y,n,xx)
% SinCosFit : Trigonometric function fitting and interpolating
%   [a,yy] = SinCosFit(x,y,n,xx)
%     use least-squares method to calculate the A B and C
%     A B should be vectors, and the formula is like this
%     y = C + Σ[A(i)*sin(i*x) + B(i)*cos(i*x)],i = 1,2...n
%     n is given by the user
% input:
%   x = independent variable
%   y = dependent variable
%   xx = value of independent variable at which the
%        interpolation is calculated
%   n = the order of trigonometric function
% output:
%   yy = interpolated value of dependent variable
% Record of revisions
%     Date           Programmer        Description of change
%  ++++++++++++     +++++++++++++     +++++++++++++++++++++++
%   2011/10/08    Vencent.Young@XJTU       Original code
if nargin<3
    error('at least 3 input arguments required')
end
m = length(x);
if length(y)~=m；
    error('x and y should be the same length')
end
z = ones(m,2*n+1);
a = zeros(2*n+1,1);
p = [1:1:n];
for i = 1:m
    z(i,2:2:2*n)   = sin(p*x(i));
    z(i,3:2:2*n+1) = cos(p*x(i));
end
a = (z'*z)\(z'*y');
a = a';
l = length(xx);
for j = 1:l
    yy(j) = a(1)+sum(a(2:2:2*n).*sin(p*xx(j)))+sum(a(3:2:2*n+1).*cos(p*xx(j)));
end