Module's Phase offset in modular

[Faxi Nadu]

Hey

I was reading filter tutorials by Rob Hardijk. He mentions that in the nord modular every module in the patch shifts the phase of the incoming signal by about 1/8 of a full phase cycle.

I'm wondering if Creamware's Modular, and for that matter all digital modulars, works the same way (1/8 shift between each modules) and if every single module induces this shift. (For instance Rob used a multiplier module in his nord modular filter patch and didn't take that module into account when doing phase calculations).

Thanks for any insight,
Faxi

[at0m]

The only delays/buffers that exist on our DSp's is caused by the dsp memory, a buffer which is amongst others used for chips to talk to each other. This can introduce 3-4 samples latency. In practice that should be way faster than the phase shifting you mention!

[Faxi Nadu]

hey

I don't think it is a latency or buffer issue.
I think what Rob means is that in the Nord Modular this 1/8 phase delay is done on purpose. When he talks about making 4 pole filters, this phase offseting feature of the nord mod is the key to correctly designing the filter.

I quote from his totorial:
"In a resonant four-pole filter the poles are cascaded in series and the output signal at the end of the cascade is fed back to the input of the first pole to create a feedback loop. Feedback is very important as feedback is always necessary to create resonance. Each of the four poles will cause a very short delay on the signal. This delay is only 1/8th of the length of a single cycle of a waveform tuned to the pitch that is equal to the cutoff frequency of the filter pole. The four poles together will cause a total shift of four times 1/8th, so one half of this waveform cycle. If this delayed signal is additionally reversed in phase this ‘inversion’ will create an additional ‘phaseshift’ of another 180 degrees. This causes the delayed and inverted waveform at the output of the four poles to appear to have a delay of exactly a full cycle of the waveform, and so lag one cycle of the waveform behind in respect to the input signal."
taken from: http://www.xs4all.nl/~rhordijk/G2Pages/ResFilters.htm

[at0m]

That specific phase shift is inherent to some filter types, not to all modules, as you mentioned in the original post. I've mentioned this before, here.

[doof]

This brings up a good question- is designing your own resonant filters even possible within mod3/FleXor?

Feedback in the mixer modules triggers a recursion error message preventing the necessary connection.

[at0m]

You could calculate the offset in the design, but the problem is that between modules we cannot guarantee phase coherence.

The parts used in filter modules we have available, we have no option to have them all loaded on the same chip. So there's a variable in the feedback that will make the filter instable. Working in some cases, but mostly unpredictable. In DP, the problem is solved by forcing the whole module on a single chip, hence the limitation of voices per module.

[Faxi Nadu]

ahhhhh so thats why those flexor filters are polyphony limited...
But this brings up a number of questions.

First off, lets say you are using 2/3 of a dsp chip and then load a flexor filter. How does the filter module distribute itself on the dsp in such a case? Start up on a new chip or?

Now in light of what has been said in this thread so far let me rephrase my original question:
I don't have the SDK yet, but my Scope Pro card is on the way (on a Scope Home setup now). Let's say we are dealing with 1 note monophonic filter for simplisity sake, and we force the entire 24db filter module (4x6db) onto a single dsp chip in the SDK. In this case, would each module have the exact phase relationship with the other and is this relationship 1/8 of a cycle as Rob states on his Nord Mod tutorial?

Hoping for some more insight,
Faxi

<font size=-1>[ This Message was edited by: Faxi Nadu on 2005-02-06 19:51 ]</font>

[Faxi Nadu]

@doof:
if i understand correctly your problem, you need to use a Xmod&Feedback Connector found in the Modifier section anytime you are doing anything with feeback in modular - like in the filter instance. connect the output of the final filter in your ladder to the Xmod module input and the Xmod output to the 2nd mixer input.
Hope this helps,
Faxi

[Faxi Nadu]

another point, in the crossover thread here people discuss standard techniques involving filtering, invertion and mixing for making crossovers.
Wouldn't you need to take into account the phase ofset (1/8 or whatever) we are talking about for these modular patch crossovers? Does the dsp forcing issue (ie the instable phase element) make crossover patches in modular rather useless as crossovers are based soley on the principles of phase invertion?
Again thanks for any insight,
Faxi

[symbiote]

Yeah, you will get the same effect on the CW Modular (or any other filter, digital or analog) for a similar filter design, but what he says (about the 1/8th cycle shift) only applies at the cutoff/resonance frequency.

The phase shift induced by a 1st order filter at the cutoff frequency will be 45 degrees, i.e. 1/8th of a cycle, but that shift won't be the same at other frequencies. For example, for a low pass filter, the lower (non-attenuated) frequencies will get much less of a phase shift, while the higher frequencies will have a phase shift that approaches 90 degrees (1/4th of a cycle.)

Since in this case, there are 4 cascaded 1st odrder filters, you'll get 4x45 or 180 degrees of phase shift at the cutoff/resonance frequency, but not at the other frequencies.

[Faxi Nadu]

thanks

so what is done in practise during filter design in terms of phase?
I mean if we are to get proper inverted signals for making the feebackloop(resonance) and for making various multimodes out of the 4pole ladder?

<font size=-1>[ This Message was edited by: Faxi Nadu on 2005-02-06 20:26 ]</font>

[symbiote]

The crossover stuff is mostly to compensate for the duplicate frequency content you will get in the different signal. Instead of using 2 different filters to extract the correct frequency content for each path, you filter one, invert its phase, and sum it with the original signal. So when the 2 speakers spew their noises out, you'll get a pretty near-perfect reconstruction. If you use 2 filters instead, your reconstruction will probably have uneven frequency reconstruction near the crossover frequency, for which you could compensate by adding more filters/gimmicks. The phase inversion stuff simply makes this alot simpler than building fairly complex filters that evenly distributes some the frequencies near the crossover.

What isn't clear in that tutorial (at least, the part I read, didn't go thru the whole thing =P) is that phase shift induced by a filter isn't constant, it varies with the frequency. It also varies with the filter type, as poles will induce a negative phase shift, while zeros will induce a positive phase shift.

Also, remember that, for frequencies that are in the hearing range, you'll need more than a single cycle to hear anything that you would qualify as a frequency. The reason for the 180 degrees phase inversion is that the output gets feeded back with the output, and because of the 4 phase shift, the output signal would cancel out the frequency-content at the cutoff/resonance frequency, which wouldn't resonate very hard. By inverting the phase, you prevent this cancellation and instead get a nice amplification (i.e. resonance.)

For a crossover application, you don't use a resonant type of filter (well, you could, but ...), so your design won't contain any feedback. Thus you don't really need to compensate for the phase shift. Both crossover "paths" will get phase-shifted by about the same amount in similar regions, so you will get (almost) no cancellation when both speakers reconstruct the sound.

[Faxi Nadu]

I understand all this, the reason for inversion and mostly everything you mentioned.
My question has exactly to do with this inversion -
we took 4 filter, so like you said 4x45 = 180, and after an inversion thats 360.
So at the citoff freq everything is fine and the phasing works out like it should.
But what about those other frequences?
You mentioned the high can have as much as 1/4. So 4x90 and we get 360. So when inverted thats another 360 and everything is still fine?
And what about lower freqs? As we are dealing with lowpass filters it is most important the filter be phase linear in the lowpband right? Anyways so lets take say 1/10 phase drift on a lowpass signal. 4x36 =144. Inverted it is 288. Now we are out of phase in a pretty nasty manner aren't we?
Please correct me if I am wrong on anything.
Thanks,
Faxi

[symbiote]

To add a bit more on the subject, the phase stuff with filters will depend on the application and wether it involves feedback. If you have some feedback, you have to make sure both signals (the original input, and the output that gets fed back, or say a processed signal and unprocessed signal that get mixed back together) have the same phase, otherwise they will cancel. Of course, this is something you might want (I guess you'd get a notch filter in that case.)

For stuff that doesn't involve feedback, phase is a bit less of an issue. With non-audio application, it's mostly a matter of stability and phase/amplitude margin, i.e. having a filter that doesn't start to self-oscillate when say processing a signal that controls a motor or a production line, as that tends to, like, break stuff. With audio, self-oscillation is a bit less of an issue if you are careful, i.e in the analog domain you'll just get saturation (which might or might not damage the circuit,) while in the digital world you'll just get a clipping signal that slowly moves toward a perfect square wave, etc.

With audio, if it's not a resonant filter involving feedback, the phase-shift effect will be almost unperceivable (unless you stack both processed and unprocessed signal together.) The effect on the frequency will be much more drastic/perceivable at this point.

[symbiote]

On 2005-02-06 20:46, Faxi Nadu wrote:
we took 4 filter, so like you said 4x45 = 180, and after an inversion thats 360.
So at the citoff freq everything is fine and the phasing works out like it should.
But what about those other frequences?

The idea in this case is that the resonant frequency will be several dBs over all the other frequencies, so that's probably where you want to concentrate. You can concentrate your phase-coherence somewhere else, but you won't have a resonant filter anymore.

Also for audio, it's not really important to have phase-linear processing, UNLESS processed and unprocessed signal get put back together. Otherwise, it won't matter much, except in a few odd situations, like a mastering EQ where you process a full mix, then, yeah, you will want to have much more of a linear/constant phase. You can get pretty close to a flat phase-response, it won't be perfectly flat, but more than enough given the way your hear is built =P.

But for like filter banks and synths, it doesn't matter, listen to the 1000 filtered-housey stuff and all the noises coming out of synths, those don't get phase-compensated and still sound pretty fun.

[Faxi Nadu]

symbiote, I am not talking about precieved sonic phasing.
I'm talking about the mathematical aspect
of what needs to be done for a filter to be phase linear(or close to it to retain some analog feel or whatnot).
Yes, I am talking about making a resonant filter, and also mixing cobinations of diffrently phased and inverted signals from the filters (ie the 6db output, 12db, 18db, 24db with subtractions and additions) to get a wide range of filter types out of a ladder.

Acctualy , you can in this manner make a filter that lets you choose from dif types like the modu3 poly filter with those same types including the eliptic "phaser" type curves. (or at least this is what im after).

Again, note that I have Mod3 now but my question is for SDK/DP also as i have SDK+Flexor on the way.

[symbiote]

On 2005-02-06 20:55, Faxi Nadu wrote:
symbiote, I am not talking about precieved sonic phasing.
I'm talking about the mathematical aspect
of what needs to be done for a filter to be phase linear(or close to it to retain some analog feel or whatnot).

Analog filters aren't any more phase-linear that other filters, unless you design/stack them up to make them so.

If you want a detailed analysis of what happens to the frequency and phase response if you stack different things together, I suggest you pickup MATLAB or something similar (GNU Octave and Scilab should have all the necessary stuff) and do some more detailed analysis with proper filter models. I could try and whip up some equations in ASCII, but you're probably better off with a good book on the subject =P. It's not too hard tho, you can deconstruct filters of any complexity/order into a cascade of simple first order filters fairly easily.

Getting a flatter phase response usually involves a filter with some zeros, since those have a positive phase advance. This can compensate for the negative phase induced by a 1-pole filter. Filters that affect the phase but not the frequency are called "all-pass filters" so that's probably what you want to Google for. If you stack one of those with say a low-pass filter, you can get something pretty linear.

Remember, also, that the most phase-shifted frequencies will also be the most frequency-attenuated. So for a resonant filter, it won't matter too much that the frequencies sitting at -20dB get a 90 degree shift, especially since your peak frequencies can sit a few dB higher than unity gain.

[Faxi Nadu]

About Flexor vs Mod2/3 filters...
I am assuming part of the key to the flexor filter sound is the polyphony limit to limit the filter to a single dsp chip?
If so, what does that say about the standard cw modular filters? Do they in essence have a sort of minor phasing "flaw" induced by the structure of the dsp environment (and corrected by flexor?)
Cheers,
Faxi

[alfonso]

For what I know, FleXor filters are a design from scratch starting from basic math atoms, without any use of the CW pre-built filter stuff. I think that a lot of their sonic quality is defined by their own design. This is true also for oscillators, if you hook them to an oscilloscope you will notice different shapes from the CW ones.

This is not a prejudicial element of superior quality, the great thing is that they are different flavors. I love FleXor and I love CW stuff and there are sonic territories where each of them excels.

[at0m]

What's different on Flexor, is most parameters in the package are updated at samplerate. All of them except Pattern Change in sequencers which triggers presets and a couple of other functions. The rest can be modulated by an audible oscillator if you wish.

CW modules, like Reaktor and most software, usually use a much slower update rate for their parameters, let's say 400Hz (one of Reaktor's settings) instead of 44.100Hz. This saves lots of dsp power, and is in most cases not noticeable.

To modulate cutoff frequency by a sub-oscillator to make formants for example has to be done at audio rate, Flexor can do that.

As a result of the update rate, it's a difference to weither something should be forced on the same chip or not.
For something (slow) like 400Hz, sample-accuracy is not essential. It can be processed on another chip, no problem. This allows SFP to balance DSP load better amongst the chips, to load more instances of the same module with the audio core on a single chip and modulation and other calculations on another chip for example.