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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>
                            <div>
                              <div>
                                <div>
                                  <div>
                                    <div>
                                      <div>
                                        <div>
                                          <p class="MsoNormal"><font
                                              size="3" face="Times New
                                              Roman"><span
                                                style="font-size:12pt"><a
href="https://www.instagram.com/colinmuirdorward/" target="_blank"
                                                  moz-do-not-send="true">https://www.instagram.com/colinmuirdorward/</a></span></font></p>
                                        </div>
                                        <div>
                                          <p class="MsoNormal"><font
                                              size="3" face="Times New
                                              Roman"><span
                                                style="font-size:12pt"><a
href="https://www.instagram.com/colinmuirdorward/" target="_blank"
                                                  moz-do-not-send="true">-<br>
                                                </a></span></font></p>
                                        </div>
                                        <div>
                                          <p class="MsoNormal"><font
                                              size="3" face="Times New
                                              Roman"><span
                                                style="font-size:12pt"><a
href="https://www.instagram.com/ssdp_synthesis/" target="_blank"
                                                  moz-do-not-send="true">https://www.instagram.com/ssdp_synthesis/</a></span></font></p>
                                        </div>
                                      </div>
                                    </div>
                                  </div>
                                </div>
                              </div>
                            </div>
                          </div>
                        </div>
                      </div>
                      <br>
                      <fieldset></fieldset>
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            moz-do-not-send="true">Synth-diy@synth-diy.org</a><br>
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            rel="noreferrer" target="_blank" moz-do-not-send="true">http://synth-diy.org/mailman/listinfo/synth-diy</a><br>
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                  <div><a
                      href="https://www.instagram.com/colinmuirdorward/"
                      target="_blank" moz-do-not-send="true">https://www.instagram.com/colinmuirdorward/</a></div>
                  <div><a
                      href="https://www.instagram.com/colinmuirdorward/"
                      target="_blank" moz-do-not-send="true">-<br>
                    </a></div>
                  <div><a
                      href="https://www.instagram.com/ssdp_synthesis/"
                      target="_blank" moz-do-not-send="true">https://www.instagram.com/ssdp_synthesis/</a></div>
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    <pre class="moz-signature" cols="72">-- 
BugBrand LTD
UK company No. 07199808
VAT No. GB 988 2629 57
1 Ninetree Hill
BRISTOL BS1 3SB
United Kingdom
<a class="moz-txt-link-abbreviated" href="http://www.bugbrand.co.uk">www.bugbrand.co.uk</a></pre>
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