DISCUSSION

Will it work? I do not know. What I do know is that it will fail for a well-defined class of model traces, those with the so-called Bussgang Property, which was defined and discussed by Rocca &al (1979). The class includes all stationary sequences (of any color) that have a Gaussian distribution of amplitudes, so it seems reasonable to expect that the method will work increasingly well as the traces depart from Gaussian. A trace consisting of a few, well-defined compact wavelets is a good example of a far-from-Gaussian model.

How do they fail? Simply put, the Bussgang property is that if two sequences have zero correlation, then any memoryless non-linear transformation of either of them leaves them uncorrelated. In the present case, the HF and LF partitions are uncorrelated, and the amplitude cubing is a memoryless, non-linear mapping. Thus there is no prediction of the high frequencies from the low.

I have found Thomas' textbook (1969) to be a useful introduction to non-linear filtering.