[sdiy] More on Xpander modes was Re: HP from LP ?
David G Dixon
dixon at mail.ubc.ca
Wed Nov 15 08:56:51 CET 2017
This is exactly how the Intellijel Polaris is done as well, although that
one has about 29 modes, I think. I have a nifty Excel spreadsheet which
draws all the transfer functions for the various modes, when you enter the
five gain factors. That's how I generated all the graphs in the Polaris
user's manual.
_____
From: Synth-diy [mailto:synth-diy-bounces at synth-diy.org] On Behalf Of Andrew
Simper
Sent: Tuesday, November 14, 2017 9:23 PM
To: David Moylan
Cc: SDIY List
Subject: Re: [sdiy] More on Xpander modes was Re: HP from LP ?
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/
<https://cytomic.com/files/dsp/cascade-tapped-filter-responses.pdf>
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.ne
<https://mutable-instruments.net/archive/documents/pole_mixing.pdf>
t/archive/documents/pole_mixing.pdf <https://mutable-instruments.n
<https://mutable-instruments.net/archive/documents/pole_mixing.pdf>
et/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
<https://www.native-instruments.com/fileadmin/ni_media/downloads/pdf/VAFilte
rDesign_1.1.1.pdf>
.com/fileadmin/ni_media/downloads/pdf/VAFilterDesign_1.1.1.pdf
<https://www.native-instrument
<https://www.native-instruments.com/fileadmin/ni_media/downloads/pdf/VAFilte
rDesign_1.1.1.pdf>
s.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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