@spoidy23 You mean something like a variable kernel density estimation (with adaptive bandwidth)? I guess, that would be difficult ...

@spoidy23 Interesting ... I didn't know about KDE, but it seems to be more or less the same thing. The iterative approach I proposed could be seen as a way to find the "right" bandwidth (whatever that is). To illustrate this, I added a plot for the corresponding kernel, which is just the impulse response of the filter: filtered-histogram-kernel.pd

@jameslo said:

It even looks like what I was proposing, a moving RMS window, might be another instance of a zero-phase lowpass filter

Yes, indeed! Or to be exact, that's only true as long as there are data points available for the whole RMS window. At the beginning and end of your dataset, you still have a phase shift (of half the effective window size). But that's always a problem, and I don't have a solution for that ...

BTW you could also try using a weighted average. I did that indirectly by repeating the process many times (which has the effect of approaching a Gaussian filter).

@jameslo What's wrong with low-pass filtering? Not being a data-scientist I would have thought that this is what they are doing all the time.

But yes, of course, there's a problem with low-pass filtering that you have to be aware of (and that you are maybe refering to): If the output of your filter only depends on the current input and previous input or output values, then you will always have some phase shift, which is certainly not what you want when dealing with a histogram! So you have to use a zero-phase filter.

Here's how I would do it ... filtered-histogram.pd

@Element-S I can't help you with the Pultec EQP-1 implementation, but since you're talking about being late to the party it might be worth pointing out that at least some of [bob~]'s weaknesses, mentioned in this thread, may have been the result of a bug, that was fixed around three years ago. If I remember correctly, the output wasn't taken after the fourth stage of the filter but before the first (= input + feedback). So no surprise, that this was considered a bad implementation of the Moog ladder filter.

Edit: Had to look it up ... It was actually a bit different from what I remembered: The incorrect output was the first instead of the fourth state variable. So the output was taken AFTER the first stage.

@trummerschlunk Here's my implementation of the 2nd (more accurate) version: dynamic-smoothing.pd
Not tested yet, so I'm not sure that it actually works ...

@trummerschlunk I made a little test patch for the different options that you described, hope it's helpful in some way ... crossover-filter-test.pd

The version with shelving filters shouldn't be more cpu-expensive (it might even be cheaper), and the math for the gains is quite simple. Or am I missing something?

But I don't think any of these approaches is suitable for as much as 32 bands! Wouldn't you need much steeper filter slopes for that? Of course, you could use higher order Butterworth shelving filters, but that's gonna be really expensive! So maybe, as @jameslo suggested, you should go for frequency domain techniques in that case.

@melter If I understand correctly what your abstraction is doing, you would have to apply its output (the desired rms value) to the analyzed signal after you have divided it by the actual rms value ....

BUT: That's much too complicated! You don't even have to analyze the signal with [env~]. Under the link that you posted there's a table from which you can see, that doubling the distance corresponds to a decrease of sound pressure by 6dB, which is 1/4 power or 1/2 amplitude. So I guess all you have to do is to multiply the signal with d1/d2.

@jameslo said:

Teach a man to fish: you know this because you looked at source code, or some other way?

I just compared the output of both filters, and it turned out to be exactly the same.

Oh look, and they take the cube root for vcf_hp6~ when they chain 3 filters. I wasn't aware that Q worked that way. Do you know what they are doing with the cutoff freq signal, [iem_cot4~]?

Not sure if you can say in general that Q works this way. It might depend on how the filter is normalized. [vcf~], for example, has unit gain at the resonant frequency, but other filters produce higher gains at the resonant frequency. So if you put them in series the gains potentiate, and there has to be some compensation for that. What the [iem_cot4~] does, I don't know. Unfortunately I can't read C code.

@jameslo With just vanilla objects that's gonna be difficult, because you'd have to use the raw filters like [cpole~]. Since the iemlib filter is a series of two 2nd order filters, my first guess would be to do the same with ELSE's [highpass~], which is also 2nd order. Its exact formula might be different though.

Edit: It actually seems to be the same, but you also have to take the square root of the Q factor!