Zero Delay Feedback Filter

[tester]

It goes down at around 18kHz at SR/2=22k.

[KG_is_back]

It goes down at around 18kHz at SR/2=22k.

You may put stream min just before the actual ZDF code block with the cutoff connected and value close to 1 in the other (like 0.9999) to prevent the cutoff from exceeding that point.

JUST BEFORE the CODE block. that is inside the filter module.

[tester]

I did so. Just before the code module. After multiplications. Yes, cutoff node. Yes, resonance node is not zero.

I don't know, if it works on your machinery, then maybe I left something else in the schematic, that hangs the whole audio part.

[KG_is_back]

try lower values (like 0.9 instead of 0.999). Maybe near the nyquist the filter still becomes unstable. If that doesn't help, then I do not know what's wrong... Still filters seem like black magic to me...

[tester]

Hmm... Now it seems to work... At max=1. Must been some sily module somewhere blocking the whole stuff. Thanks for help KG.

[KG_is_back]

Sorry for bringing up the old topic, but what's the Z-transform of a ZDF filter given frequency, Q and gain factors for HPF, BPF and LPF bands?
My problem: I have an automated (cutoffs are controlled by pitch form midi or audio) EQ made of series of ZDF filters (each has gain for each of 3 bands, to achieve peaking, shelving curves etc.). I need to dynamically display the EQ curve. FFT doesn't cut it (either I need very large windows to display low end smoothly, but then I get like 3FPS because of pointless high-end data).
Flowstone has a prim called "biquad frequency response" which supposedly uses Z-transform to calculate log-scaled frequency graph form the coefficients. I either need similar module to work for ZDF or a module that calculates biquad coefficients from f,q and gains for high/band/low pass.

[martinvicanek]

The transfer function is that of an ordinary biquad

Code: Select all

       b0 + b1*z^-1 + b2*z^-2
H(z) = -----------------------
        1 + a1*z^-1 + a2*z^-2


with the coefficients given by RBJ formulas.

[noisenerd]

First off, many thanks for this filter! I quite like it.

There are various options for introducing nonlinearities to saturate self-oscillation. The simplest would be to make 1/Q increase with |BP|, I think. Haven't actually done it, but tanh or tanh^-1 isn't cheap. Note that you have an implicit equation to solve, it's a bit harder than just calculate tanh for some given argument. Vadim also suggests simpler functions but the expressions are still awkward.

Sorry to dredge up an old post, but could you please elaborate on this a bit for a noob? If it sounds good, I'll pay the CPU cost.

[tulamide]

I would also like to ask questions about the filter, especially the value ranges.

1) Frequency goes from 0 - 1, am I right that 1 refers to Nyquist?

2) Resonance is labeled ">0". I would love to have a fix point here. When other synths have resonance = 0 (no resonance), what would be the equivalent here? I do remember something like 0.7, but I'm not sure, if I remember correctly.

3) Attenuation: What exactly is it used for? What is the difference of using attenuation opposed to gain after the filter?

[stw]

I would also like to ask questions about the filter, especially the value ranges.

1) Frequency goes from 0 - 1, am I right that 1 refers to Nyquist?

Yes

2) Resonance is labeled ">0". I would love to have a fix point here. When other synths have resonance = 0 (no resonance), what would be the equivalent here? I do remember something like 0.7, but I'm not sure, if I remember correctly.

This is a quote from martins post earlier in this thread:

For even order N we have i = 1, 2, ..., N/2 biquads with
Q_i = 0.5/cos(alpha_i)
where the alpha_i are spread uniformly over (0,Pi/2):
alpha_i = (i - 0.5)*Pi/N

You can obtain the Q values from this, e.g :

1 biquad: i=1; N=2; Qi = 0.707
2 biquads: First: i=1; N=4; Qi = 0.541 Second: i=2; N=4; Qi = 1.307
...

or take it directly from the various filter examples martin already posted!