Sine wave least squares curve fitting possible (using GSL)?

Question

Is it possible to fit an A*sin(B*t+C) function with GSL or a similar library?

i want to get the A and C parameter of a sine wave present in 4096 samples (8bit) and can provide an good approximation of B.

A think that should be possible with GSLs non-linear multifit but I don’t understand the mathematical background with all that Jacobian matrix stuff...

Answer 1

Yes,

You have probably read this: http://www.gnu.org/software/gsl/manual/html_node/Overview-of-Nonlinear-Least_002dSquares-Fitting.html#Overview-of-Nonlinear-Least_002dSquares-Fitting

What is required from you is to provide two functions

the objective:

`

int sine_f (const gsl_vector * x, void *data, 
        gsl_vector * f){
    ...
    for(...){
    ...
      double Yi = A * sin(B*t +C);
      gsl_vector_set (f, i, (Yi - y[i])/sigma[i]);
    }
    ...
    }

and then the derivative of the objective with respect to the parameters

int
sine_df (const gsl_vector * x, void *data, 
         gsl_matrix * J)
//the derivatives of Asin(Bt +C) wrt A,B,C for each t

This is straight from http://www.gnu.org/software/gsl/manual/html_node/Example-programs-for-Nonlinear-Least_002dSquares-Fitting.html#Example-programs-for-Nonlinear-Least_002dSquares-Fitting

So the Jacobian is just a 3xN matrix, where N is the number of data points For example J(0,3) = sin(B*t_3 + C)

if A,B,C correspond to x[0],x[1],x[2]

And J(1,5) = A*t_5*cos(B*t_5 + C) This is the derivative wrt. B