The Design of the Roland Juno Syntheziser's Oscillators
blog.thea.codes
blog.thea.codes
It’s got some obvious shortcomings and wild browser inconsistencies, but lets you go through much of the same design process in making your own synth.
1] https://developer.mozilla.org/en-US/docs/Web/API/Web_Audio_A...
My college electronics prof was old-school enough who told us back in his day it was “standard practice” to use pp-amps to solve differential equations from their Calc class.
You can specify the sampling rate of the Teensy with a bit of fiddling, and the limits depend on what you're asking the audio library to do. The stock Chord Organ's set up to run at 44.1k, using a couple of submixes in the library to do things like set waveform levels independently.
You can also set an oscillator to drive the output pin directly, with just one waveform.
I've got a couple of 'em running at 2,822,400hz instead of 44,100hz. That's 2,822k for one oscillator (I can get four running at 768k), by telling the Teensy its sample rate is something hilariously high, just to run some square and 12-bit triangle and sawtooth waves.
I avoid aliasing pretty well :) and it's definitely a fully digital DAC output. It's just good at being free from aliasing because I'm not concerned about what the sampling rate 'means' in terms of 'usable notes'. The only thing I care about is getting my waves nicer. The Teensy also has a rectangular wave, which is PWM adjustable. That, at 2,822k or even 768k, is quite nice even when it's a really thin pulse…
And of course you could use the square to drive an integrator :)
The Cortex M4 in the Teensy runs at 200MHz. In the early 80s consumer-grade DSP didn't exist at all. There were some exotic studio processors with slow microprocessors supported by custom hardware multipliers, but 8MHz 16-bit microprocessors were considered fast, expensive, and exotic.
Roland had a stellar run with their hardware designs. The Junos may be one of the best synthesizers ever made hitting the bullseye for price, character, simple but flexible programmability, and a legendary sweet but powerful sound.
There's a finesse to this kind of audio design that IMO makes a lot of Eurorack seem clumsy and uninspired in comparison.
The thing with eurorack that can feel uninspiring because it's never one music instrument, especially if you rewire it often and it becomes this abstract blob of music tech that is never finished, which makes it both addictive and expensive.
Also, Teensy is amazing! I got one recently to play with some audio stuff and it’s so much fun. Amazingly capable board really, love that it can do USB MIDI etc.
Also, aliasing as a concept doesn’t show up in purely digital systems.
There are a lot of solutions to this in the literature, such as wavetables that are band-limited, but for simple virtual analog synthesizers, there's a technique that is close to magic in its simplicity and quality: PolyBLEP. Check it out.
Try drawing what would appear to be a perfect square wave in a digital wave. Up, flat, down, flat. Guess what: you've just introduced enormous amounts of aliasing.
"Lollypop" sampling vs. real DAC output: https://mk0soundguyshosprmrt.kinstacdn.com/wp-content/upload...
As you've observed, the output of a real digital circuit includes the flat parts, unlike the infinitely thin "lollypops" that you see in DSP textbooks.
But the jaggies themselves are not aliasing, they're actually the result of anti-aliasing. The sample-and-hold reconstruction filter that practically every DAC uses is an anti-aliasing filter, albeit a crude one, but if you've chosen your sampling frequency correctly, the harmonics from the jaggies exist entirely outside of your passband. A simple RC filter removes them almost perfectly.
This is aliasing: https://upload.wikimedia.org/wikipedia/commons/thumb/2/28/Al...
Digitally sampling an analog input signal is usually where you need to actually put some design effort into the AA filter, because you don't necessarily know whether the analog signal at your input has a lot of energy just outside your passband. Such an input can cause you to see an alias that's comparable to or louder than your signal of interest, and there's no way to get around that with direct sampling except for arbitrarily sharp AA filters.
But with a DAC, you know exactly what you're putting into your AA filter (your sampled signal convolved with a box), and you can easily arrange things so that the AA filter both works perfectly (sampling > nyquist) and is easy to design (sampling >> nyquist).
When you represent an ideal square or saw wave as a series of digital values you are effectively sampling it at a much lower sampling rate than the infinite rate required for a perfectly sharp square wave. This introduces aliasing is why a naive implementation of a square or saw wave will sound terrible.
There are a whole bunch of techniques you can use to solve this problem without excessive CPU usage but they are non-trivial.
Your ears
Your speakers
The op-amps in your fancypants analog synthesizers
--
More critically, signals having high frequency components is. not. aliasing. Neither is distortion.
Out-of-band signals being erroneously remapped into the passband via the sampling process is aliasing.
That's why it's called an alias. The remapped out-of-band signal is indistinguishable from a different in-band signal.
Any process that generates or distorts a waveform at any sample rate will generate aliasing in the digital domain - unless it has no >Nyquist components.
And most waveforms do have >Nyquist components. Sine waves <Nyquist don't, but ramps, steps, and virtually all forms of distortion do.
If you don't understand this go back and reread the basics, because hundreds of DSP engineers have spent countless hours devising ways to handle this problem.
An ideal signal that you want to approximate may contain infinite frequency components, but this property alone is not what gives you aliasing artifacts. Sampling incorrectly does. You can absolutely approximate this signal without aliasing artifacts, but you need to sample a band-limited approximation of the signal, not the signal itself. That's what BLEP does.
Attempting to sample the ideal signal directly (the naive approach) will indeed give you aliasing artifacts. But we already know that the ideal signal isn't band-limited, so we should also know that sampling it directly (at any frequency) is always folly.
Do you see what I was trying to highlight? "Oh no, the signal has high frequency components!" is not the problem. Incorrect sampling is the problem. Aliasing is an effect, not a cause. You don't "get aliasing" just because the ideal signal has high frequency components, you get aliasing because you sampled the wrong thing.
You can call it aliasing if you want... you wouldn't be wrong. It's just not particularly instructive, and referring to everything as aliasing without being more specific about where it's coming from is what leads people down rabbit holes like running a DAC at 2+ MHz because nobody showed them how to use a polyphase filter. Sure, it works, it's just wasteful, and you can accomplish the same thing by sampling better rather than faster.
Then again, your condescending response leads me to believe that you're not actually interested in being instructive.
http://www.martin-finke.de/blog/articles/audio-plugins-018-p...
I'm well aware.
This is because the "naive" approach to e.g. a digital square wave is to sample a logically continuous function defined as:
if (less than halfway through the cycle period) -1
else 1
Secondly, the sharp rising edge of the square wave, from a "sum of sines" perspective, requires sinusoid components that are not part of a conventional square wave to represent them digitally. If you were to digitally sample an analog square wave through an ADC it would look quite different from the result of this function.
The naive digital sawtooth wave suffers from similar issues due to its discontinuity.
An ideal square wave is not a signal that is band-limited to the audio range, so attempting to sample it directly (the naive approach) doesn't work. Instead, you want to sample a band-limited approximation of the square wave (which is what BLEP, etc. do).
If you're synthesizing, the naive approach doesn't work because the interaction that occurs between the square wave transitions and the sample rate introduces energy into the passband as a beat frequency. Yes, this interaction is aliasing, which is what we expect to get when sampling a signal that is not band-limited to our passband. That BLEP oscillator or other polyphase techniques are needed in order to synthesize a correctly sampled band-limited approximation of a square wave.
Similarly, if you're sampling an analog square wave with a high slew rate, you absolutely must have an analog anti-aliasing filter in front of your ADC, or you will end up with exactly the same beat frequencies in your sampled signal.
?? Aliasing doesn't just happen when you're converting an analog signal to a digital one. It can also be introduced when you're manually building or converting a digital signal with the intention of it sounding like a given analog signal, or like the ultimate output of another digital signal. It was this usage I was referring to. For example, if you downsample a digital signal from another digital signal without filtering out frequencies above Nyquist. Or in the example I gave, if you draw a square wave with the expectation that it sound like an analog square wave, not realizing that the sharp corners you've drawn didn't add in high-frequency odd harmonics, but rather partials with Nyquist-reflected aliased frequencies. It's this second case which causes problems for naive approaches to digital wave-design: you can't filter out the incorrectly-introduced reflected frequencies after the fact, but rather must build the wave in the first place to not have them.
> Up, flat, down, flat. Guess what: you've just introduced enormous amounts of aliasing.
I thought you were suggesting that the jagged, stair-step output of a DAC is what causes aliasing, which is a common misconception.
I was trying to point out that stair-step output is just the reconstruction filter of the DAC operating as intended, and that a reconstruction filter is an anti-aliasing filter. In the case of a DAC's sample-and-hold, it's an easy way to select the baseband alias. [1]
I think one reason this thread went off the rails is that there are two anti-aliasing filters in a digital synthesizer. I was initially referring to the hardware anti-aliasing filter at the output of the DAC, which is also called a reconstruction filter or an anti-imaging filter. Everybody else was referring to the digital anti-aliasing filter that you need in order to create a band-limited approximation of an infinite bandwidth ideal signal so that you can actually sample it, because attempting to sample the ideal signal directly is always incorrect.
Given that the article is about the precursor to digital synthesis, I suppose I should have realized that people were going to be more interested in discussing the latter. However, now we're getting to the second reason this thread went off the rails (and the reason I usually regret participating in audiophile threads): Differences in terminology, points of focus, and "Well, Ackchyually" audiophile-grade condescension cause people to read past each other and continue to argue despite largely being in agreement.
If you read my downstream responses (https://news.ycombinator.com/item?id=25601970 and https://news.ycombinator.com/item?id=25602267), I hope it's clear that I both understand and agree with the actual argument you wanted to make.
[1] Aside: If you were to insert sinusoids at twice the sampling frequency instead of flats in between each sample, you'd be selecting the alias centered around twice the sampling frequency instead of the one at baseband. This is (roughly) how a mixer works.
Oh, heavens no. Just describing the naive way to draw a square wave in PCM.
Once you introduce a master clock, especially one clocking an ADC, then aliasing can and does indeed show up.
So it's perfectly possible - in fact dangerously easy - to generate waveforms with components that are >Nyquist.
It doesn't matter if the hardware runs at gigahertz frequencies or subsonic frequencies. In fact it doesn't matter if there's never any hardware at all.
Because there is always an implied sample rate of 1 x fs, and any signal which generates components of more than 0.5 x fs will alias.
Here is my view of things: along the time axis, signals can be either continuous-time or discretized/discrete-time. Along the intensity axis, for example voltage, signals can be either continuously-variable or discretized/discrete-valued.
I consider an "analog signal" to be one that's continuous in time and in value. I consider a "digital signal" to be one that's continuous in time but discrete in value; for instance, the output of a (asynchronous) logic gate.
Your definition of "digital domain" seems to be discrete-time, discrete-valued signals; for example, the readings out of an ADC or commands into a DAC.
The difference between the two would nicely explain a lot of the confusion here.
If what you mean is "the artifact isn't 'aliasing' until it finally goes through the DAC", my answer to you is: that's a useless and counterproductive distinction. I inadvertently introduced an artifact into my digital signal that I cannot easily remove. That this artifact magically gains a label only once it passes through the DAC is pedantic nonsense that helps no one.
And aliasing does happens in digital oscillators when you're using a fixed clock and sample rate: If you have flexible clock (per-voice) you can just increment the output value in equal steps (and then set it to zero at the end of the "sawtooth") and you won't get aliasing. But if you have a fixed clock, you have to use a (very simple) equation to calculate the position of the soundwave at a given sample number. So you get aliasing when you approach Nyquist frequency, and you need the anti-aliasing filter to fix it.
And since it was 1982 the sampling rate of the chip was probably not that high, so you would get aliasing much earlier than at ~22kHz.
Digital AA is very hard to design, just the mathematics involved are extremely difficult to grasp, much harder than analog.
Aliasing shows up SPECIALLY in purely digital systems. Take a sample every half period of a periodic signal like a sinusoidal wave. Your signal output will be constant or zero.
Take a digital sample(calculate a frame) of a wheel in a 3D game (draw the wheel at a specific position), each 30th or 60th of a second. The wheel will go backwards at some speeds(stroboscopic effect, a form of alias).
Going from simple dc arduino inputs to high precision analog is a bear, but super rewarding. Get ready to get your soldering skills right and start caring about resistor tolerances!
Well thanks. There goes all my free time... But seriously, that website looks like an amazing resource
Another of my synth DIY mentors (with whom I worked on the Arturia MiniBrute) is Yves Usson: http://yusynth.net/index_en.php
For those interested in an open source design embodying these techniques, I have an open source hardware design here: https://github.com/russellmcc/dco with a blog write-up here: https://www.russellmcc.com/posts/2013-12-01-DCO.html .
Also of relevance is an open source hardware design for the later roland alpha juno digital oscillator design: https://github.com/russellmcc/alphaosc https://www.russellmcc.com/posts/2019-06-14-Alpha-DCO.html
It is clearly modeled after the Juno, and adds a lot of nice features (2 DCOs per voice, 2 more-capable LFOs, an arpeggiator, full FX suite...) and you can get the 12-voice keyboard model for about half of what you’d pay for a Juno 106.
It’s got a big screen in the middle, but the front panel is designed so that you almost never have to use it, even when building patches. They have a great shortcut system for assigning modulation that’s easy to pick up and very fast to use. It’s just a great synth all around.
Instability ironically prized and cherished by synth enthusiasts who will claim it makes old synthesizers sound "better" than modern ones...
Pre-COVID I had a semi-regular synth jam session with a dude 100% invested in software synths. First 30 minutes (no exaggeration) of every session was him fighting with Ableton or whatever, and rebooting his Mac, trying to get something trivial to work, like MIDI clock or input monitoring.
Meanwhile I just plugged my Minilogue into the power strip and mixer and did my own thing.
There's something to be said for a musical instrument not to be joined at the hip to a general-purpose networked computing device.
My only argument is that with software versions you’re much more likely to get upgrades when bugs occur. And I personally will simply no longer buy a Korg flagship because of my troubles.
Personally I'm from the camp that likes super-clean audio, so I was overjoyed when software synths fixed all the problems that we used to have with hardware, but there's definitely a camp that really likes the "warmth" or unpredictability of the original machine's output. Sometimes I think people spend more time adding plugins to dirty up their sound than they did making the original patch in the first place.
My first synthesizer was a Juno 60, and I owned a bunch of other vintage and modern ones over the years. With hardware, it was a whole ritual to turn everything on, each instrument had its own smell, it put me into a mood of "let's play with this machine and see what happens".
When I moved to software, I finally had all the sounds I always wanted but could never afford, I finally no longer had to futz around trying to reprogram a patch I liked, I finally could send any instrument to any effects box... but there were less happy accidents. It felt a bit more like my day job, which also just involves sitting in front of a computer.
I think it can be like that for a lot of people, where the tactility and limitations of the gear can inspire a different approach to music-making. I imagine that aspect also plays in to the emotion that some people have that hardware instruments "sound" better.
All that said, I would never go back to hardware. As you say, it's hard to beat the convenience of a laptop.
With a VST, everything goes through a mouse. And you'll probably spend some of your time getting distracted by moving windows around to show/hide other VSTs.
It's a much more cerebral experience.
My biggest problem with software is that it's so limited. VSTs and DAWs ape hardware studios far too literally.
I'd like to be able to connect anything to anything - including VST internals to the internals in other VSTs. And add some generative/programmed elements. But most DAWs either don't allow that at all, or they only allow it with severe limitations.
I’m excited to see what happens in VR. The tactile feedback isn’t there, but I bet the muscle memory is. I don’t have a VR setup, but Synthspace might convince me to get one this year—it looks better every time I check on its progress. A VR modular synth kit without the insane cost? Yes please!
Yes, but there's also noise inside the Juno at the DAC, chorus, etc.
And as someone who makes digital synths for a living even 100% accurate fully digital oscillators are difficult to fully realize in practice. Aliasing concerns abound at every stage of a softsynth- there are well-known formulas for calculating alias-free waveforms at a fixed frequency, but these start to get expensive when you also are considering PWM and frequency modulation which are essential tools for achieving a variety of different sounds. And aliasing sounds a lot worse than analog imperfections.
But there's more to that analog sound. The opamps and the rest of the circuitry, including supposedly passive elements like resistors and capacitors, all add tiny amounts of distortion and other parasitic interaction with the rest of the synth which varies with frequency content, level, and dynamics.
Human ears are incredibly sensitive to these variations, and the circuits in 70s and 80s synths had a lot of components, all adding their own colour. Which is why if you A/B the hardware with the software, the software rarely wins.
In DSP terms there are differences between functional/abstract models, component-level models, and component-level models that include these complications and imperfections. There hasn't been a lot of work done on the latter, and if they were modelled accurately they would likely need an order of magnitude more DSP cycles than current VSTs.
The Commodore Amiga has the crudest possible anti-aliasing filter: a single fixed-frequency low-pass filter shared by all 4 channels. It does not work very well, so aliasing is a defining characteristic of the Amiga sound. Aliasing adds high frequency content that compensates for the low sample rates required by memory limitations, and extra harmonic complexity that compensates for the low channel count. I think Amiga modules sound worse if played by something with good anti-aliasing filters.
Aliasing (a sampling artifact) is an issue in synthesizers which run at low/fixed sampling rates and sample waveforms to produce output (often using frequency registers). This includes modern software synthesis, and also hardware like DS (ZOH, samples, almost like Amiga), N163 (ZOH, short wavetables), Yamaha (FM on sine waves, IDK the details), and to a lesser extent SNES (Gaussian reconstruction, samples).
Reconstruction artifacts (extra frequencies at x * fundamental, may exceed sampling rate) are different from sampling/aliasing artifacts (frequencies are taken modulo the sampling rate). But they can combine (like on DS hardware).
> Whatever you now find weird, ugly, uncomfortable and nasty about a new medium will surely become its signature. CD distortion, the jitteriness of digital video, the crap sound of 8-bit - all of these will be cherished and emulated as soon as they can be avoided.
For this kind of circuitry I would reduce temperature drift by enclosing it into a heated thermostat kept well above room temperature. This way after initial warm up period there is very little drift.
If I understand correctly, the output from the sawtooth has a voltage offset? Can that lead to DC passing through speakers? And would the pulse-width comparator input need an equivalent voltage offset?
It motivates me to try it back.
I have to find a little time to do something interesting now that I have the resources that I had not in the past(if only I had the time I had then).