Non-linearity

So right now I am battling with the linearity of nonlinear equations.
In the Hawksford paper I linked in the last post, there are a number of nonlinear equations.

This includes half-wave rectifiers, full wave, SQRT, Clippers (the obvious one), Fuzz exponentials and other bits and pieces.

The difficulty I am currently facing is that, by extension, some of these nonlinear equations are behaving constantly, regardless of the amplitude offset I give the normalised signal I feed them.

This may seem dead obvious, but I think I am about to start venturing into unknown (to me) territory. For example: applying the absolute square root of a signal to itself seems at the moment to be causing a constant 138.5332% total harmonic distortion to the signal, regardless of the amplitude offset I have given it. I think the problem is not in the equations, but my approach to signal modification. At the stage of distortion, the signal has already be normalized and split into mono channels for processing. I am sure the behavior of some of these nonlinearities is very particular in terms of a bandwidth of amplitudes, and even though everything is normalized to one, there should be a bit more variation in THD%. A fundamental problem with what I am doing is comparing the THD caused to a sine wave, with the effect the NLD is having on some music. How can I change things and expect the results to be constant?

More paper reading to be done this afternoon for some literature review. Maybe I will realise the cripplingly obvious thing I am missing. Either way, I am on schedule at the moment.


My aim is the apply a definite and controllable % of THD to a signal, by increasing and decreasing the amplitude of the signal. I need to come up with a way of pre-determining for each nonlinear equation, what ratio of the signal sits above a given threshold (in amplitude), and modify said threshold to give how much a signals total level needs to be modified by to achieve the given % THD.

Looking forward to the listening test, I think I will have to make it loud enough to force everyone into the acoustic reflex (middle ear compression), while still sitting in CONAW levels. Its a point of compression that fundamentally happens at different points for everyone. I might have to start thinking about more ear based factors too, like masking.