Octave up mechanics - please explain

[yeeshkul]

Guys please can anyone explain to me how the octave-up works in Octavia (transformer + diodes) and in Univox Superfuzz (two trannies facing each other). Or just gimme a link. Thank you very much.

[km-r]

its somewhat like the signal is rectified...
the negative portion of the signal is inverted.
if you can picture this out... the octave comes from the signal/harmonics produced by the peaks of the rectified signal...

im sorry i could not really put this into decent words...

[yeeshkul]

i see ..  thanks

[R.G.]

Kimar is correct - it's exactly because the signal is full wave rectified.

All the bottom halves are flipped over so they're identical to the top halves. There are two peaks/valleys where there was only one, so we hear an octave up. It's not a pure sine wave, so we also get the harmonic series of the rectification, plus the cross-products of any multiple frequencies that were there.

Look here: http://www.allaboutcircuits.com/vol_2/chpt_7/3.html

[Ice-9]

I can fully understand how flipping half of the wave over creates a frequency doubled wave giving the ocatve up, which leads me to how does the octave down work.  I am thinking that you cwould take say the positve half of the wave cycle and rectify this using a fullwave rectifier voltage doubler circuit ( which i think) would flip half the wave over, halving the frequency, but this would double the output as well On the plus side you should get a good sine output.
Is this right or wrong ??

[yeeshkul]

Yes i understand, thank you. I wasn't sarcastic, i may have sound like that. What is the role of the transformer by the way?

[R.G.]

I can fully understand how flipping half of the wave over creates a frequency doubled wave giving the ocatve up, which leads me to how does the octave down work.  I am thinking that you cwould take say the positve half of the wave cycle and rectify this using a fullwave rectifier voltage doubler circuit ( which i think) would flip half the wave over, halving the frequency, but this would double the output as well On the plus side you should get a good sine output.
Is this right or wrong ??

Good thinking, but no, it won't work. For octave up, you need the signal to do something twice as often. For octave down, you need it to do something half as often, in the "goes-up" or "goes-down" sense. Full wave rectifying makes the negative (or positive) half into a replica of the positive (or negative) half, so it makes for a twice-as-often. There are no simple rectifier schemes that make for half-as-often. The simplest octave down involves some kind of counting circuit to count events and produce an output change every other input change. That's why every simple octave down uses something like the CD4013 CMOS dual flipflop. Flipflop circuits do exactly the every-other-one counting needed.

[Ice-9]

Yeah ! after further thought on that octave down idea i see exactly what your saying. I would end up with a signal of the same frequency as i started with as what i had in mind would actually first double the frequencys then i was flipping it back over giving exactly what i put in. If this makes sense. Next time i get an eureka moment i will think it through a bit longer. 

[R.G.]

No embarassment is needed - you should encourage your eureka moments.

The vast majority of my creative thoughts are flatly worthless or impractical if not impossible. I throw away about seven out of ten. It's worth the work of evaluating and trashing to get the three out of ten that are worth working on.

[yeeshkul]

Guys could you tell me what is the transformer for and how important for the octavia sound are its parameters? Does it change the signal level before it comes to the rectifier?

[yeeshkul]

ah i see, i found it here http://www.allaboutcircuits.com/vol_3/chpt_3/4.html#03261.png

[PoopLoops]

Good thinking, but no, it won't work. For octave up, you need the signal to do something twice as often. For octave down, you need it to do something half as often, in the "goes-up" or "goes-down" sense. Full wave rectifying makes the negative (or positive) half into a replica of the positive (or negative) half, so it makes for a twice-as-often. There are no simple rectifier schemes that make for half-as-often. The simplest octave down involves some kind of counting circuit to count events and produce an output change every other input change. That's why every simple octave down uses something like the CD4013 CMOS dual flipflop. Flipflop circuits do exactly the every-other-one counting needed.

Could you explain this a bit more?  I get how full-wave rectifying it doubles the frequency (although not perfectly, the bottom troughs are sharp), but not how a flipflop would halve the frequency.  I guess the way I am thinking of it is that you let one full wave through, then the flipflop blocks the signal and skips a full wave, and then lets the next one through, etc.  Which would be weird but not a real half-frequency.

I was thinking I could use an FFT to transform frequency into amplitude, use a divider to cut the amplitude in half, and stick it through another FFT to get the now halved frequency.

But I don't think that would work for a guitar signal, since it has all these overtones and harmonics...

[Mark Hammer]

The diodes are used so that the final output essentially "ignores" one half cycle from each of the two contributing sources.

Note that what happens electronically, and what happens psychoacoustically can be different.  Just because you have electronically rectified and "folded over" the incoming waveform does not automatically mean that the listener will perceive an octave up. The listener tracks (albeit unconsciously)  all those peaks in the output signal, and if every second peak in a doubled signal is juuuuuuuust a bot louder, then you won't hear the octave in any distinct manner; you'll just simply hear a brighter-sounding fuzz.  This is why things like some versions of the Superfuzz, or the nicely modded Green Ringer found at the viva analog site, include trimmers: to balance off the two rectified copies of the signal so that an octave can be heard.

It is rare that octave-up fuzzes include any pre-rectifier tonal shaping.  As a result, you get doubling of stuff you really don't want doubled.  It is also sometimes the case that the diodes used to do the rectification introduce some crossover distortion.  For instance, in the Green Ringer ( http://www.generalguitargadgets.com/pdf/ggg_gro_sc.pdf ), the signal MUST pass through D1 or D2 to get to the output.  But D1 and D2 insist that the signal must be greater than around 500mv to pass at all, which means that for each half cycle any part of the signal that is less than 500mv goes unheard and then almost instantly, once the signal passes that threshold, the signal appears magically.  This clips the "sides" of the waveform, rather than the top, producing a different kind of distortion.  In the Foxx Tone Machine ( http://www.generalguitargadgets.com/diagrams/ftmsc.gif ), this crossover distortionis supplemented by more conventional chop-the-top clipping via D3 and D4.  Since Q3 adds some gain between the first and second set of diodes, you hear more of the one kind of distortion than the other in the FTM.  In the GR you hear only the one type.

The Tycho Brahe ( http://www.generalguitargadgets.com/pdf/ggg_toct_sc.pdf ) uses the transformer to produce two complementary versions of the signal at the output, and the diodes lop off one half cycle each at the very last point of intervention in the circuit before the volume pot.  Everything up to that point is essentially signal conditioning in anticipation of the transformer.

One of the things that happens with octave-up units as well is a primitive sort of sideband product.  Fret two strings and bend the lower one upwards, while using an octave-up unit.  What you will hear is a bizarre sideband product that goes downward, even as you're bending the string upward!  That crude ring modulation effect is why the Green Ringer is called a "ringer", even though it is ostensibly an octave-up fuzz.

The problem that ALL rectifier-based octave-up units are faced with is that what they produce is not a mere doubling of the input.  The lower half of the resulting waveform does not look like the top half.  Indeed, if we were to feed a pure sine wave into an octave-up fuzz double it, then look at the fast fourier transform of the top and bottom halves of the resulting waveform, we'd see that one half has much more harmonic content than the other.

[zyxwyvu]

Could you explain this a bit more?  I get how full-wave rectifying it doubles the frequency (although not perfectly, the bottom troughs are sharp), but not how a flipflop would halve the frequency.  I guess the way I am thinking of it is that you let one full wave through, then the flipflop blocks the signal and skips a full wave, and then lets the next one through, etc.  Which would be weird but not a real half-frequency.

For a flip-flop based octave down effect, there are two ways to go about it. Both first convert the input signal into a square wave suitable for driving logic gates (such as the 4013 flip-flop). They differ in how that is used later:

Option 1: Feed the square wave into a 4013 (or two for two octaves down). Every time the input goes from low to high, the output of the flip-flop switches states. This halves the frequency, but we still have a square wave. A lot of filtering is usually added afterwards to soften up the square wave. This is the approach used in the MXR Blue Box, among others.

Option 2: Create the octave-down square wave like option 1, but instead of using that as the output, multiply it with the clean signal. In other words, when the octave down square wave is high, let the output through, when it is low, mute the input. A sine wave fed into this will result in a full period of the wave, then a full period of nothing, then another period of sine wave, etc. This sounds much cleaner than option 1, and is the approach used in the Boss OC-2. This also sounds like what you described.

An important part of both circuits is the conversion from a guitar signal with lots of harmonics to a square wave. Lots of low-pass filtering is usually used to remove the harmonics, leaving mostly just the fundamental frequency.

The schematics of both should be pretty easy to find with a quick google search, or a search here.

I was thinking I could use an FFT to transform frequency into amplitude, use a divider to cut the amplitude in half, and stick it through another FFT to get the now halved frequency.

But I don't think that would work for a guitar signal, since it has all these overtones and harmonics...

An FFT is pretty hard to do - it requires a powerful microcontroller, most likely with external ADC and DAC. I don't see any reason it wouldn't work otherwise. Pitch shifting is generally a lot more complicated than it appears, though. There are numerous subtle difficulties that arise due to the discrete nature of the processing. I remember there were a couple good threads on this in the DSP section here, but I can't seem to find them right now.

[R.G.]

Could you explain this a bit more?  I get how full-wave rectifying it doubles the frequency (although not perfectly, the bottom troughs are sharp), but not how a flipflop would halve the frequency.  I guess the way I am thinking of it is that you let one full wave through, then the flipflop blocks the signal and skips a full wave, and then lets the next one through, etc.  Which would be weird but not a real half-frequency.

Sure. I think you may be confused about what a flip flop does. It does not let anything through. It generates an output based on a clock signal. The output goes up on one clock, then down on the next, then up on the next, and so on as long as there are clocks. The way we make this be an octave down is to mess with the guitar signal until we get it to make one pulse (or pulse edge) per cycle. That pulse is then supplied to the flipflop as the clock. The output then contains half as many positive going parts as it gets clocks. This produces a square wave that is half the frequency of the guitar signal, if you've done everything just right. The "just right" consists of filtering to get only one zero crossing per half-wave. The filtered signal is usually run into a comparator and the comparator gives out a logic signal which is high whenever the guitar signal is above ground, and low whenever the guitar signal is below ground. That's about optimum for sending to a flipflop clock.

I was thinking I could use an FFT to transform frequency into amplitude, use a divider to cut the amplitude in half, and stick it through another FFT to get the now halved frequency.

That isn't exactly how FFTs work I don't think. Fourier transforms convert amplitude per time to amplitude per frequency, with time implicitly being so large that it doesn't affect the calculations. Cutting the amplitude per frequency then inverting the transform just gives you back half the amplitude as a function of time, since all the amplitudes were cut in half. I always thought it was time and frequency that were transposed, not time and amplitude.

The other problem is that if you go to all the trouble to be able to do an FFT, as a practical matter it will involve using an A/D, some computation/storage and then D/A. If you already have all that stuff, you can simply use DSP methods to generate a half-speed replica of each wave and get not only octave down, but good (ish!) fidelity to the original.

[frank_p]

Is it me or a FFT does not work in real time (well the sort I know) ?  To have a dynamic FFT you would have to apply a repeated sampling at given intervals and for a given interval (time window) each time.  If you sample too fast you wont be able to have a convenient time frame to compute the "correct" frequencies unless you have some overlapping of the windows in the time domain.  Otherwise the time windows are too small and you run in the Nyquist problem.  There may be other sort of DFT that might do what you are talking about... perhaps (?). But, for what I know, FFT is a pain with fast ever changing frequencies.  But we are not talking analog stuff anyway...   

[PoopLoops]

That isn't exactly how FFTs work I don't think. Fourier transforms convert amplitude per time to amplitude per frequency, with time implicitly being so large that it doesn't affect the calculations. Cutting the amplitude per frequency then inverting the transform just gives you back half the amplitude as a function of time, since all the amplitudes were cut in half. I always thought it was time and frequency that were transposed, not time and amplitude.

You're right, a Fourier Transform goes from -inf to +inf...  A milisecond isn't close enough. :p

The other problem is that if you go to all the trouble to be able to do an FFT, as a practical matter it will involve using an A/D, some computation/storage and then D/A. If you already have all that stuff, you can simply use DSP methods to generate a half-speed replica of each wave and get not only octave down, but good (ish!) fidelity to the original.

I see.  I want to stay away from any computation (of the kind that requires me to input code), since that gets really complex really fast...