Typically, polynomials can be used to model nonlinear distortion in microwave passive/active devices. However, polynomial models are analytical functions.
I would like to know if there is any empirical evidence supporting that nonlinear distortion can be explained using non-analytical functions.
Volterra representation demands analytical functions. A piecewise characteristic like I/V flat-linear-flat does not have defined the derivatives at two positions, but can be considered as analytical with two singularity points.
Thanks Carlos for the reply.
I have found some papers were they use swicthed models, that is, piecewise polynomial or piecewise Volterra models. These models are motivated empirically, showing good error performance, even better than their counterparts as polynomial or Volterra models.
I wonder what is the reason for this behavior?. Is it that these devices have some non-analiticity?
The reason why a piecewise Volterra model could have a better output errors with respect to simple Volterra model is the "locality" of the Volterra model.
Ideally, if you have an infinite series you can identify a analitical system with an ideal gaussian noise (with any variance) as the input of the system to be identified.
But when you identify a nonlinear system with a truncated Volterra series with finite memory and by using a discrete time pseudo-random input, what do you get?
You get that your model will depend on the variance of the input you have used to identify it. This is what I have called "locality" of the model.
Some researchers used different Volterra models, identified with different input and realized what you called "piecewise Volterra models", but switching beetwen a model and another is a drawback not an advantage.
As research material on this matter and for a possible solution of the "locality" of Volterra series I suggest you the linked paper.
Article Improving the approximation ability of Volterra series ident...
Now we come to the topic of "empirical evidence" of non-"analyticity".
You kown that the old principal "Natura non facit saltus" was rebutted only by quantum mechanics or in biology by the discrete nature of DNA.
But our "empirical evidence", unless we are making the Double-slit experiment, will be the result of a very huge number of "discrete" events, so why there should be a reason for non-analytical models?
Let us take a simple counterexample of my previous statement: any mechanical system that has a limit, for example an electrodynamic loudspeaker. The coil displacement have an physical hard limit so its movement can meet hard stops.
It may be convenient to model such nonlinearity with a step function but a sigmoid function with the right slope can have the same physical evidence.
Going back to Volterra series, are the polynomial the best functions to model all physical systems? I don't think so.
Can be non analytical function a better alternative? Hard.
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