estimating spectral optimization I'm relatively new to DSP so excuse my simplified words, and my detailed explanation.

if the signal have non-coherent sinusiod, it will induce energy spreading into the frequency domain.




One of the solutions is :


how to estimate the signal component correctly?

And I'm stuck here, I don't really know how to optimize such problem and setting a stopping criterion in Matlab,R..etc 

How to optimize such objective function?

What are you thoughts about the drawbacks about such solution to separate signal components?

Thanks in advance :) ,
If you know the number of sinusoidal components, parametric estimators such as MUSIC may be suitable. ESPRIT might be another.  Both seem similar to you proposed optimization/minimization search.  

But parametric estimators are reported to produce bogus decompositions if given the wrong number of components.  Possible reason: For a decomposition into an arbitrary number of arbitrary frequency sinusoids, there can be a near infinite number of solutions that might be arbitrarily close (e.g. you can get a bunch of cosines to converge to one sine wave of yet another frequency.)