A_SN wrote:It's good to not be the most qualified person in the thread to explain things anymore, so now I can ask questions instead of speculating . Do you think what people like about this EQ's sound just has to do with the unusual curves
Yes. And the truncated IRs. I'm fairly sure there's something to that. We'll find out over the next few years. Besides phase, there's literally nothing more to it.
and that you can get the same results with any other EQ that can reproduce those curves
Obviously. That said, reproducing those curves very accurately might well require very short IR lengths. As an EQ designer, it's unlikely to occur to you that that could be something anyone could want. Can you set SplineEQ into ultra lo-fi mode? Like, maybe, 256 samples?
(or what about the phase response?) ?
I reckon it's linear phase most of the time, but anyone with the plugin analyser could take a look.
A simple rule of thumb is this: if you can hear a glaring, obvious difference, then it's the curve shape. If you hear a subtle, delicate difference, relative to other tracks/parts of the mix it's the phase.
And if so do you have any idea what's so great about those types of curves?
Well, they do display a spectacular naïveté.
I could (and might) go into horrible technical depth about the decomposition of meromorphic functions, and why that gives us the shapes we use, and an understanding of the uncertainty principle (sharp in one domain means ringy in the other) is fairly essential, but these just aren't audio shapes. They're engineering shapes.
These have been designed as "design a filter with N dB of attenuation in the stopband, and M dB of ripple". I won't expect anyone to see by eye that there's a discontinuity in the derivative, but there is, and that's going to cause serious ringing. Without resonance, none of our usual EQ shapes will do that.
What's missing is smoothness (in the technical sense). In your SplineEQ (and here I must confess I don't know what constraints you place on your knots), a single spline is guaranteed smoothness because derivatives above three are zero! (Almost everywhere. DC and nyquist are always exceptions).
Well, there's no consideration of smoothness in these designs. These are wacky shapes. They don't transition in a smooth way, they have some unusual ringing discontinuities. And that ringing gets truncated. You see that little ripple as the graph hits flatness? That's a tell-tale sign of a truncated IR. It's only because the edge is so sharp that we can see it at all. Rare to have an example of ripple so visible.
To OP. I'd strongly urge you to avoid further investment in patents on this. DSP as a field is founded on telecoms, and I reckon I can find prior art for this kind of strategy from the 60s. Using PMC like this for audio, from the 70s definitely. I don't have the books to hand, but I'd definitely check the later chapters of Rabiner&Gold and Oppenheim&Schafer. 50years of prior art could leave you with a hideously expensive and completely indefensible patent, if it were to be awarded.