Proposed fixes for the biquad filter and Leveller device about wavesabre

[yupferris]

While not directly related to the issues above, another thing we've discussed previously is that the current param <-> freq mapping is too coarse at low frequencies. Admittedly, the currently-used curve is something I just threw together as a "nonlinear mapping" and is basically x^2 mapped to the desired cutoff range. It seems the desired curve is typically logarithmic (eg exp(ln(20) + x * (ln(20000) - ln(20))), proposed here). I graphed the two to compare:

Clearly, the logarithmic curve offers significantly better resolution in the lowend (as well as other crucial parts of the spectrum), just like we want. Further, the curve is the same regardless of the base used, which is convenient for us, as we already have an implementation of exp2 in Helpers. This implies that we'd likely need to add log2 as well, but this may not be the case - if we can get away with only ever doing the forward mapping, then because the inputs to log2 are only ever constants, constant folding removes the calls altogether.

Thus, I propose the new mapping be exp2(log2(low) + x * (log2(high) - log2(low))) where low=10 (judging from the -3dB point in your graph above) and high=22000, with no inverse; if an inverse is desired, it should be (log2(y) - log2(low)) * (1 / (log2(high) - log2(low))) and the log2 shim, if required, is then trivial to write using fyl2x.

Admittedly, though, I have yet to actually try such a mapping (nor the extended range) in an actual plugin; these are just some notes as I happened to think about it. It should be tested, preferably against another plug like Pro-Q 3.

EDIT: Just to make the logarithmic mapping a bit clearer, I generated a log-linear plot as well:

Even though I've been a bit lazy with the labels, I still find it more intuitive to imagine scaling the parameter linearly and using this plot to determine what the frequencies would be. I'm guessing this would feel a lot better. In fact, even just comparing against a screenshot of Pro-Q 2:

Just to pick a point of reference, in both pictures, 1kHz appears to be mapped to ~0.6, which is a good sign.

[yupferris]

Also, to clarify: the peaking behavior of the LPF with default settings currently, is that only due to the current “neutral” Q mapping, and/or is it also related to the trig tables like the HPF?