Intrigued by the air of mystery, I also investigated this plugin and came to the same conclusion as others before me; it's a waveshaper.
That doesn't make it bad or not worth the asking price. The controls and curves are very well tuned for the purpose of increasing perceived loudness. However I have to say the vague way Sonnox describes the plugin feels a little disingenuous. For example the manual seems to imply it is some kind of probabilistic statistical process:
If that is how it is implemented, then the effect appears to be identical to a conventional waveshaper. Perhaps a good plugin dressed as secret sauce sells better than just a good plugin.
I figured out the waveshaping function it uses (or at least something close), and was able to create pretty good nulls using Melda MWaveShaper. Here's a video demonstrating that:
The waveshaping curves:
(Math warning)
The waveshaping function of Inflator is:
Code:
f(x) = A⋅x + B⋅x² + C⋅x³ - D⋅(x² - 2⋅x³ + x⁴)
where the coefficients A, B, C and D are given by the Curve parameter:
A(curve) = 1 + (curve + 50)/100
B(curve) = - curve/50
C(curve) = (curve - 50)/100
D(curve) = ¹⁄₁₆ - curve/400 + curve²/(4⋅10⁴)
This gives us the following resulting curves:
At +50:
2⋅x - x²
at 0:
³⁄2⋅x - ¹⁄₁₆⋅x² - ³⁄₈⋅x³ - ¹⁄₁₆⋅x⁴
at -50:
x + ³⁄₄⋅x² - ¹⁄₂⋅x³ - ¹⁄₄⋅x⁴
The Clip 0 dB off mode:
In this mode Inflator takes overshooting samples and maps them back under 0 dB. It uses the curve according to the shape parameter for levels up to 0 dB. The overshooting samples are mapped back down below 0 dB according to a curve similar to the +50 curve, ie. 2⋅x - x², regardless of what curve is set to.
I didn't investigate the multiband mode. According to the manual it splits the signal into three bands, which are processed independently.
Curve presets for MWaveShaper attached: