FInding the breakpoint of a frequency spectra and its associated error

Hi all,

I was wondering whether somebody could help me in finding the first breakpoint of a frequency spectra and its associated error. The spectra is as shown in the attached figure (spectrum.jpg). The spectrum should be fitted as shown in spectrum_fitted.jpg inorder to find the first breakpoint (labelled as A) so as to get the corresponding frequency which is about 1.2Hz (in figure spectrum_fitted.jpg). The fit might not be accurate and hence there would be an associated error in the value obtained for the frequency at A. So I would need both the value for frequency at A( first breakpoint) as well as its associated error. Wondering if that is possible.

The data used to get the frequency plot has been attached as data.mat

Thank you.

Answer 1

[Mathieu NOE]

hello

I combinde this

Piecewise linear least square fit - File Exchange - MATLAB Central (mathworks.com)

and fminsearch to create that code - seems to work finding the optimal values for break points

% load x and y data
load('data.mat');
xdata = xdata(:);
ydata = ydata(:);

% Init of fminsearch 
a = max(xdata)/4;
b = max(xdata)*3/4;
global xdata ydata

x0 = [a,b];
x = fminsearch(@obj_fun, x0);
a_sol = x(1);
b_sol = x(2);

XI = [min(xdata),a_sol,b_sol,max(xdata)]; % vector of 1-D look-up table "x" points
YI = lsq_lut_piecewise( xdata, ydata, XI ); % obtain vector of 1-D look-up table "y" points
% plot fit
plot(xdata,ydata,'.',XI,YI,'+-')
legend('experimental data (x,y(x))','LUT points (XI,YI)')
title('Piecewise 1-D look-up table least square estimation')

function err = obj_fun(x)
global xdata ydata
    XI = [min(xdata),x(1),x(2),max(xdata)];  % vector of 1-D look-up table "x" points
    YI = lsq_lut_piecewise( xdata, ydata, XI ); % obtain vector of 1-D look-up table "y" points
    Yint = interp1(XI,YI,xdata);
    err = sum((Yint-ydata).^2);
end

Answer 2

[Mahith Madhana Kumar]

Thank you Mathieu. That was helfpul.

I was wondering what the error associated with the a_sol value is (the first breakpoint). How should I find the error associated with a_sol?

Thanks.

[Mathieu NOE]

hello again

well, there is no "reference" value for a , so I cannot say the error is the norm of a_ref-a_sol , because a_ref cannot be defined (or ?)

the only error we can define is : err = sum((Yint-ydata).^2); used in the function

but that is not specific to a but to the entire fit model

[Mahith Madhana Kumar]

Thank you for the clarification, Mathieu