Linear Combination Analysis help

I have a spectrum (Stot) that's a linear combination of two known spectra (Sa and Sb). I would like to fit Stot , Stot = kSa + (1-k)Sb, and extract k and 1-k for Sa and Sb respectively from this fit. I have the Stot spectrum at a series of times, can I fit multiple spectra at one time?

Answer 1

[Star Strider]

One possibility:

k = 4.2;                                                % Define ‘k’
t = linspace(1, 4*pi);
Sa = sin(t);                                            % Create ‘spectra’
Sb = cos(t);                                            % Create ‘spectra’
Stot = k*Sa + (1 - k)*Sb;

f = @(k) norm(Stot - (k*Sa + (1-k)*Sb));                % Cost Function: Nonlinear Approach
K = fminsearch(f, 2)                                    % Estimate ‘k’: Nonlinear Approach

K = [Sa(:) Sb(:)]\Stot(:)                               % Estimate ‘k’: Linear Approach

However without your data I cannot claim that either of these will work reliably with it. Experiment to get the result you want.