% USAGE [alpha,c,rms] = expfit( deg, x1, h, y ) % % Prony's method for non-linear exponential fitting % % Fit function: \sum_1^{deg} c(i)*exp(alpha(i)*x) % % Elements of data vector y must correspond to % equidistant x-values starting at x1 with stepsize h % % The method is fully compatible with complex linear % coefficients c, complex nonlinear coefficients alpha % and complex input arguments y, x1, non-zero h . % Fit-order deg must be a real positive integer. % % Returns linear coefficients c, nonlinear coefficients % alpha and root mean square error rms. This method is % known to be more stable than 'brute-force' non-linear % least squares fitting. % % Example % x0 = 0; step = 0.05; xend = 5; x = x0:step:xend; % y = 2*exp(1.3*x)-0.5*exp(2*x); % error = (rand(1,length(y))-0.5)*1e-4; % [alpha,c,rms] = expfit(2,x0,step,y+error) % % alpha = % 2.0000 % 1.3000 % c = % -0.50000 % 2.00000 % rms = 0.00028461 % % The fit is very sensitive to the number of data points. % It doesn't perform very well for small data sets. % Theoretically, you need at least 2*deg data points, but % if there are errors on the data, you certainly need more. % % Be aware that this is a very (very,very) ill-posed problem. % By the way, this algorithm relies heavily on computing the % roots of a polynomial. I used 'roots.m', if there is % something better please use that code. %

- expdemo % An example of expfit in action

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