Where do I search for mathematical modeling of data exhibiting trends arising from a general function of sinusoidal equations? I am not referring to the Fourier analysis. In the Fourier analysis, we consider the addition of sinusoidal functions. This data is where the data is a function of multiplicative sinusoidal functions such as
f(t) = A1*sin(W1*t) * A2*sin(W2*t)* A3Sin(W3*t)….
Or
f(t) = A(t)*sin(W(t)*t) ,
where A(t) and W(t) can take any other functional form.
Is there any literature that describes a method for identifying such terms?
Why don't you try the EMD?
I can send you 2 routines and theoretical information.
Anyway, let me do some reasoning. Any product of sinusoids can be brought to a sum. Using a discretization you can obtain a discrete-time formulation from where you can obatin an AR model, if you have some noise. If this does not happen, you can use a nonlinear method like, Pisarenko, MUSIC or min-Norm. This lead always to a model that is a sum of sinusoids.
Thanks for the response. The AR models work well for the exponential relationship. However, for a sinusoidal one, it will not give exact results.
My question is more general than the multiplication of two sinusoids. Yes, for a simple case of two sinusoids, it is the same as addition. However, what happens when one has 3 or more? Or worse yet if there are an exponential function and 3 or sinusoids combined together?
At this stage, my objective is to generate synthetic data without noise and then reverse the process to find out if there is an algorithm I can develop that will give me the exact ground truth. Once this is done, it can be applied to real data with noise.
By the way, I am not familiar with the EMD. Please explain.
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