Function lsqlin smooth results

Question

Tobias Grempels 2022-11-7

编辑： Matt J 2022-11-10

Hi, I used lsqlin to create a linear model. The results are like this:

There are hard peaks and i want to smoot them. In first try i used A and b lsqlin(C,d,A,b) to limit the gradients. The results are like these

Have anyone an idea how to round the spikes?

Thank you very much!

Answer 1

Matt J 2022-11-10

编辑：Matt J 2022-11-10

You could add smoothing penalties on first differences to your lsqlin data. Assuming your signal is of length n, this would look like,

D=beta*diff(eye(n)); %differencing operator, in matrix form, with penatly weight beta
z=zeros(n-1,1);
C=[C;D];
d=[d;z];
signal = lsqlin(C,d,A,b);

Answer 2

Youssef Noureddine 2022-11-10

Hi Tobias,

I have 2 primary suggestions that would help you smooth this data,

I would try using the 'smooth' function and selecting low span numbers and varying the smoothing method to and select the pair that produce the most ideal result.

https://www.mathworks.com/help/curvefit/smooth.html

If that doesn't work, you can use the interp1 function to interpolate points between each sample to artifically smoothen the data. You can select the interpolation method to things such as 'cubic' or 'spline' here (although linear might work depending on if your sampling frequency is high enough). I would first start by interpolating mid way points to see if that is enough. If it is still rough, I would find every quarter jump and keep shrinking the jump size until your data is smooth enough.

https://www.mathworks.com/help/matlab/ref/interp1.html

Sincerely,

Youssef