[sdiy] More on Xpander modes was Re: HP from LP ?
Andrew Simper
andy at cytomic.com
Wed Nov 15 06:23:03 CET 2017
Hi David,
I've been a bit busy moving house, so sorry for the late reply.
If you label the voltages as follows for a 4 pole low pass cascade
structure:
voltages : {v0 - res*v4, v1, v2, v3, v4}
then generate the transfer function by summing these voltages with the
weighting terms: {m0, m1, m2, m3, m4}
You get the following transfer function:
(g^4 (m0 + m1 + m2 + m3 + m4) + g^3 (4 m0 + 3 m1 + 2 m2 + m3) s +
g^2 (6 m0 + 3 m1 + m2) s^2 + g (4 m0 + m1) s^3 +
m0 s^4)/(g^4 (1 + k) + 4 g^3 s + 6 g^2 s^2 + 4 g s^3 + s^4)
where g is the cutoff, k is the resonance and s is the regular frequency
domain laplace variable.
Now just solve for your mix terms to place the zeros where you want them.
The resonance path was always the same, and interestingly enough you can
turn any filter type into any other, so you could have a high pass core
turned into a low pass filter if you really wanted to.
The T was my way of saying "twin", basically saying a zero is happening at
1/2 or x2 the cutoff, instead of just dc, infinity, or at the cutoff.
For example, to form a two pole notch you want a numerator of (g + s)^2
(g^2 + s^2), which solves to:
v0-res*v4 - 2*v1 + 2*v2
Here are all the coefficients {m0, m1, m2, m3, m4} for various responses:
low2 : {0, 0, 1, 0, 0}
low4 : {0, 0, 0, 0, 1}
band2 : {0, -1, 1, 0, 0}
band4 : {0, 0, 1, -2, 1}
notch2 : {1, -2, 2}
notch4 : {1, -4, 8, -8, 4}
high2 : {1, -2, 1}
high4 : {1, -4, 6, -4, 1}
To generate further shapes just crossfade between the responses above, or
try out any old combinations you want. You may notice that some of the
coefficients are FIR edge detection type filters, for example {-1, 1}, and
this convolved with itself gives you {1, -2, 1} etc.
Have fun!
Cheers,
Andrew
On 9 August 2017 at 15:02, David Moylan <dave at westphila.net> wrote:
> Andy, do you have any coefficients for these shapes? The double notches
> seem interesting. Was your resonance path always from a 4th LP pole? Can
> you breakdown the abbreviations used for the responses? For instance,
> what's the T suffix?
>
> Thanks.
>
> Dave
>
> On 08/08/2017 09:45 PM, Andrew Simper wrote:
>
>> In digital you get pretty spot on shapes since your tolerances are around
>> 0.0001% ;)
>>
>> I worked on all this stuff over 10 years ago and came up with my
>> favourite list of responses:
>> https://cytomic.com/files/dsp/cascade-tapped-filter-responses.pdf
>>
>> I implemented these in a software synth plugin called Strobe over 8 years
>> ago. A while later the guys at Motu liked them so much they copied the
>> shapes and the names and used them in their software sampler plugin Mach 5.
>>
>> Cheers,
>>
>> Andy
>>
>>
>>
>> On 1 August 2017 at 07:48, David Moylan <dave at westphila.net <mailto:
>> dave at westphila.net>> wrote:
>>
>> I'm just finishing up an add on to a Roland IR3109 to do the pole
>> mixing, same basic method as the Xpander. From my early listening
>> tests I will say that the high pass modes still seem to have some
>> low pass in them. Can any Xpander users comment?
>>
>> This is due to the fact that achieving HP responses relies on
>> nulling out terms in the transfer function via mixing the different
>> poles. If you're not exact you don't get a full null and the
>> attenuation of low frequencies suffers (looks more like a shelf
>> instead of continuing roll off of low frequencies and usually has a
>> little dip in the middle). I'm using 1% tolerance resistors, but am
>> about to sub in some 33.2k for 33k to get even closer to the
>> theoretically perfect values.
>>
>> Even if you had perfect resistors I would imagine any mismatching
>> between the OTA stages would also cause the attenuation to suffer,
>> but I haven't modeled that.
>>
>> Still, each mode sounds sufficiently different and I particularly
>> like the modes with notches in them like 1 pole LP + notch. I
>> wouldn't expect to like a less "dramatic" filter but I love the
>> sound of that one.
>>
>> FYI, one of the Xpander modes is All Pass / 1P LP or "Phaser" with
>> first pole switched out. The shape has a notch off center and its
>> pole weights are 1 3 6 4. If you change the weights to 1 3 4 2 the
>> notch becomes centered and it looks like a 2P band pass with a notch
>> at the center and with the first pole switched out it's like a 1P HP
>> + notch, mirroring the 1P LP + notch that is already available.
>> Something different to try... The PDF mentioned in the last post
>> has good drawings of the filter shapes which might help make sense
>> of this.
>>
>> I'm working on this in a Roland GR-300 but the boards could
>> theoretically work in any synth that uses the IR3109, like the
>> SH-101 and MC-202. Not sure how much room is available inside
>> those, the boards are 1.3" x 2.6" using 3 SOIC chips, a small number
>> of 1206 SMT resistors and the rest through hole. Not very difficult
>> to solder. The filter selection is via a pot into a 3 bit ADC, and
>> the first filter pole is switched manually. (Haven't had any problem
>> with pops when switching that pole.) That gives the 16
>> combinations, of which, there's one duplicate so you get 15 modes.
>>
>> If you're interested in a board let me know. I should have a video
>> on YouTube later this week showing it's operation in the GR300.
>> Will post here.
>>
>> On 07/31/2017 02:28 PM, Tom Wiltshire wrote:
>>
>> I’m getting the feeling here that just a simple subtraction of
>> the lowpass response from the input isn’t enough (ahem). If you
>> want better than -6dB/oct, you need to do some more
>> sophisticated summing of the input and the various outputs, and
>> you’d better make sure you’ve got accurate resistor values and
>> signal levels too, since that provides a limit to how m such
>> attenuation you can expect in the stop band off you high pass
>> filter. How good is your signal cancellation? -40db? -60dB?
>> Unlikely to be better than that.
>>
>> That’s not to say that it’s not worth it.. As Paula said, the
>> Xpander service manual is the original source, and Oliver
>> Gillet’s documents on the Four Pole Mission board for the
>> Shruthi expand on that:
>>
>> https://mutable-instruments.net/archive/documents/pole_mixing.pdf
>> <https://mutable-instruments.net/archive/documents/pole_mixing.pdf>
>>
>> Basically, generating a multi-pole highpass from a multipole
>> lowpass response isn't as simple as just taking one off the
>> other. These are both great filters and worth doing.
>>
>> HTH,
>> Tom
>>
>>
>> ==================
>> Electric Druid
>> Synth & Stompbox DIY
>> ==================
>>
>> On 31 Jul 2017, at 20:50, Julian Schmidt <elfenjunge at gmx.net
>> <mailto:elfenjunge at gmx.net>> wrote:
>>
>> Have a look at this paper on page 64, Multimode Ladder Filter
>> https://www.native-instruments.com/fileadmin/ni_media/
>> downloads/pdf/VAFilterDesign_1.1.1.pdf
>> <https://www.native-instruments.com/fileadmin/ni_media/
>> downloads/pdf/VAFilterDesign_1.1.1.pdf>
>>
>> You can mix the different poles with a simple opamp mixer.
>> input -4 * Pole1 + 6 * Pole 2 -4 * Pole 3 + Pole 4 will
>> yield a funky looking HP filter
>>
>> julian
>>
>>
>> Am 31.07.2017 um 20:10 schrieb Michael Zacherl:
>>
>> Hi,
>> I discussed that briefly in one of the last SDIY meetings,
>> did some experiments but never came to a sound conclusion:
>>
>> Is there a ‘cheap’ way of turning a low pass filter into
>> a high pass?
>>
>> How’s that possibly approached?
>> Just something like subtracting the LP’s output from its
>> input signal?
>> If so, what about resonance?
>>
>> My point about doing that cheaply is the (upcoming)
>> release of two synths with Moog ladder filter featuring
>> a switchable high pass mode.
>> To my knowledge, there was no resonating HP filter from
>> Moog so far in any synth.
>> Until now.
>> Since both synths (Moog Mother-32 and Behringer Model D)
>> are on the budget side in terms of money I’d rather
>> expect a simple solution compared to a, say, DSI Pro-2
>> with two fully featured filters in it.
>>
>> Any hints?
>> Thanks, Michael.
>>
>>
>> --
>> http://mz.klingt.org
>>
>>
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