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<p>Don't feel you *have* to get tangled up in maths - I could do
maths up through my technical university course, but frankly it
never conveyed spirit to me & I rarely go anywhere deep with
it in any of my designing.<br>
I was also going to suggest looking up the CGS Dome Filter (the
phase shift network mentioned) but don't think schematics were
presented - it does, however, state the Electronotes article I
referred to - #83<br>
<a class="moz-txt-link-freetext" href="https://sdiy.info/wiki/CGS_dome_filter">https://sdiy.info/wiki/CGS_dome_filter</a><br>
</p>
<div class="moz-cite-prefix">On 11/03/2020 15:22, ColinMuirDorward
wrote:<br>
</div>
<blockquote type="cite"
cite="mid:CAGV3gy5HVULAW7xeSjdnZtteA2EhQ+iHpy3iHE==p1-P38XEaw@mail.gmail.com">
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<div>I'm still working on these replies, folks, thanks for the
discussion! <br>
</div>
<div>OK, TBH, I'm pretty lost. It's probably beyond me without
having the math. Is it anything like barber-poling a series of
APF filters?<br>
</div>
<div><br>
</div>
</div>
<br>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">On Wed, Mar 11, 2020 at 9:43
AM Quincas Moreira <<a href="mailto:quincas@gmail.com"
moz-do-not-send="true">quincas@gmail.com</a>> wrote:<br>
</div>
<blockquote class="gmail_quote" style="margin:0px 0px 0px
0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
<div dir="auto">This is a celebrated one, by JHaible. I have
the pcb, waiting for the day when i’ll have time to source
the parts...
<div><br>
</div>
<div><a
href="http://jhaible.com/legacy/frequency_shifter_fs1a/fs1a"
target="_blank" moz-do-not-send="true">http://jhaible.com/legacy/frequency_shifter_fs1a/fs1a</a><br>
<div><br>
<br>
<div dir="ltr">Sent from my iPhone</div>
<div dir="ltr"><br>
<blockquote type="cite">On 11 Mar 2020, at 4:11, Tom
Bugs <<a href="mailto:admin@bugbrand.co.uk"
target="_blank" moz-do-not-send="true">admin@bugbrand.co.uk</a>>
wrote:<br>
<br>
</blockquote>
</div>
<blockquote type="cite">
<div dir="ltr">
<p>My brain is not awake enough to closely follow
Dave's description! But I remember there's a good
basis in an old Electronotes - I didn't follow it
exactly by any stretch but it really helped me
design my own, the theory I took being:<br>
1) make a quadrature sine/cosine VCO<br>
2) audio input splits to two 6-stage all-pass
filter<br>
3) each filter-chain is followed by a
RingMod/Multiplier with the modulating input
coming one from sine / one from cosine<br>
4) then you do sum & difference of the two
ring mods to get up & down shifts.</p>
<p>What I really enjoyed was adding feedback! In
fact, redeveloping the ideas at the moment &
adding in a bit of extra control + output
mixing/panning. Really great audio processor, even
at LFO rates where it becomes a wonderful phaser
type machine.<br>
</p>
<div>On 11/03/2020 07:28, David G Dixon wrote:<br>
</div>
<blockquote type="cite">
<div>
<p class="MsoNormal"><font size="2" face="Arial"
color="navy"><span
style="font-size:10pt;font-family:Arial;color:navy">I
built a frequency shifter following the
Bode plan. This is frequency shifting by
manifesting certain trigonometric
product-to-sum formulae using electronic
circuits:</span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"
color="navy"><span
style="font-size:10pt;font-family:Arial;color:navy"> </span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"
color="navy"><span
style="font-size:10pt;font-family:Arial;color:navy"
lang="PT-BR">sin u sin v = 0.5 [cos(u – v)
– cos (u + v)]</span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"
color="navy"><span
style="font-size:10pt;font-family:Arial;color:navy"
lang="PT-BR"> </span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"
color="navy"><span
style="font-size:10pt;font-family:Arial;color:navy"
lang="PT-BR">cos u cos v = 0.5 [cos(u – v)
+ cos (u + v)]</span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"
color="navy"><span
style="font-size:10pt;font-family:Arial;color:navy"
lang="PT-BR"> </span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"
color="navy"><span
style="font-size:10pt;font-family:Arial;color:navy">So,
if you have two signals with their
90-degree quadrature signals (say, u is
the audio you want to shift and v is the
on-board quadrature oscillator), then if
you multiply the signals together (using a
four-quadrant multiplier) and also
multiply their quadrature signals together
(using a second four-quadrant multiplier)
then you can sum the multiplier outputs
together, and you will get the following
(by adding the two equations together):</span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"
color="navy"><span
style="font-size:10pt;font-family:Arial;color:navy"> </span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"
color="navy"><span
style="font-size:10pt;font-family:Arial;color:navy">cos
(u – v)</span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"
color="navy"><span
style="font-size:10pt;font-family:Arial;color:navy"> </span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"
color="navy"><span
style="font-size:10pt;font-family:Arial;color:navy">This
represents the audio signal u which has
been frequency-shifted downward by the
frequency of the oscillator signal v. Of
course, the audio signal probably has many
frequencies u occurring simultaneously,
and they will all be shifted down by v.
That’s what makes frequency shifting sound
so alien and weird.</span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"
color="navy"><span
style="font-size:10pt;font-family:Arial;color:navy"> </span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"
color="navy"><span
style="font-size:10pt;font-family:Arial;color:navy">By
being clever with the summations of the
multiplier output signals (based on a
little bit of algebra), you can also
recover the up-shifted audio:</span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"
color="navy"><span
style="font-size:10pt;font-family:Arial;color:navy"> </span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"
color="navy"><span
style="font-size:10pt;font-family:Arial;color:navy">cos
(u + v) </span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"
color="navy"><span
style="font-size:10pt;font-family:Arial;color:navy"> </span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"
color="navy"><span
style="font-size:10pt;font-family:Arial;color:navy">With
both the down- and up-shifted signals, you
can get a stereo effect.</span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"
color="navy"><span
style="font-size:10pt;font-family:Arial;color:navy"> </span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"
color="navy"><span
style="font-size:10pt;font-family:Arial;color:navy">The
entire circuit consists of a 90-degree
phase displacement network to generate the
cosine of the incoming audio (I designed
mine with 12 stages from 15 Hz to 15 kHz
using a little thing I found on the
internet called QuadNet), a quadrature
oscillator to generate both sine and
cosine waves at frequency v (mine is TZFM
and consists of two Rubicon cores with
sine shapers, with one syncing the other
in such a way that the two are always 90
degrees out of phase), two four-quadrant
multipliers (I built a dual unit from a
single 2164 chip – two linearized VCAs),
and a couple of output amplifier stages
for doing the summing. The key to success
is to AC couple the signals into the
multipliers to eliminate DC offsets in the
incoming signal, which is the single
largest source of error in the circuit.
If that is done properly, the multipliers
require no trimming (if accurate summing
resistors are chosen).</span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"
color="navy"><span
style="font-size:10pt;font-family:Arial;color:navy"> </span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"
color="navy"><span
style="font-size:10pt;font-family:Arial;color:navy">The
circuit works great and sounds super
freaky. I’m going to be building another
one for one of our members here shortly.</span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"
color="navy"><span
style="font-size:10pt;font-family:Arial;color:navy"> </span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"
color="navy"><span
style="font-size:10pt;font-family:Arial;color:navy"> </span></font></p>
<div>
<div class="MsoNormal"
style="text-align:center" align="center"><font
size="3" face="Times New Roman"><span
style="font-size:12pt">
<hr width="100%" size="2" align="center">
</span></font></div>
<p class="MsoNormal"><b><font size="2"
face="Tahoma"><span
style="font-size:10pt;font-family:Tahoma;font-weight:bold">From:</span></font></b><font
size="2" face="Tahoma"><span
style="font-size:10pt;font-family:Tahoma">
Synth-diy [<a
href="mailto:synth-diy-bounces@synth-diy.org"
target="_blank" moz-do-not-send="true">mailto:synth-diy-bounces@synth-diy.org</a>]
<b><span style="font-weight:bold">On
Behalf Of </span></b>ColinMuirDorward<br>
<b><span style="font-weight:bold">Sent:</span></b>
Tuesday, March 10, 2020 7:01 PM<br>
<b><span style="font-weight:bold">To:</span></b>
*SYNTH DIY<br>
<b><span style="font-weight:bold">Subject:</span></b>
[sdiy] frequency shifter</span></font></p>
</div>
<p class="MsoNormal"><font size="3" face="Times
New Roman"><span style="font-size:12pt"> </span></font></p>
<div>
<div>
<p class="MsoNormal"><font size="3"
face="Times New Roman"><span
style="font-size:12pt">Hi, I got a
little lost trying to understand what
a frequency shifter is. I mean the
pre-digital method used by Moog (I
think?).</span></font></p>
</div>
<div>
<p class="MsoNormal"><font size="3"
face="Times New Roman"><span
style="font-size:12pt">I recently
built a 4pole APF, and was really
impressed with some of the pitching
effects I could achieve with it. I'm
guessing this is an entirely different
method than the frequency shifters
like Moog and JH have done.</span></font></p>
</div>
<div>
<p class="MsoNormal"><font size="3"
face="Times New Roman"><span
style="font-size:12pt">Is the APF
method used by anyone? What are its
limitations, and what is it even
doing? </span></font></p>
</div>
<div>
<p class="MsoNormal"><font size="3"
face="Times New Roman"><span
style="font-size:12pt">Well, I guess
I'm just looking for some conversation
on the topic of analog frequency/pitch
shifting methods. If anyone has any
thoughts/experience they'd like to
share.</span></font></p>
</div>
<div>
<p class="MsoNormal"><font size="3"
face="Times New Roman"><span
style="font-size:12pt">Cheers,</span></font></p>
</div>
<div>
<p class="MsoNormal"><font size="3"
face="Times New Roman"><span
style="font-size:12pt">Colin</span></font></p>
</div>
<div>
<p class="MsoNormal"><font size="3"
face="Times New Roman"><span
style="font-size:12pt"><br>
-- </span></font></p>
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