Clipping in the digital domain like this introduces an extremely hard corner, effectively corresponding to a set of signals near the sampling frequency and its harmonics that are required to perform the shaping. That's where the "interesting distortion" comes from.
Real diodes are not quite as sharp, because there's an exponential region between forward voltages of 0V and the forward voltage of the junction (~0.7V for P-N diodes, ~0.3 for Schottky).
And vaccum tubes are softer still, with a considerable rolloff region.
Cliff Chase, the guy who started Fractal Audio [1] to build the Axe-Fx digital guitar processor, often writes about these types of disparities [2] since his business is modeling analog components in the digital domain. I'm not a trained EE and have a very surface-level understanding of the subject matter but I find these types of talks fascinating nonetheless.
Some still insist on old-school germanium diodes and transistors for things like clones of the classic guitar effects pedals. Those are also ~0.3 V, but their proponents argue that the shape of the "knee" and other parameters are different to silicon, thus leading to a perceptible difference in sound quality (in this application, the devices are often intentionally operated in non-linear regions) I've also heard that the specs for old germanium devices varied a lot more than modern silicon ones, thus leading to stories that (e.g.) Jimi Hendrix would order a dozen pedals and pick the one he thought sounded best.
> Some still insist on old-school germanium diodes and transistors for things like clones of the classic guitar effects pedals. Those are also ~0.3 V, but their proponents argue that the shape of the "knee" and other parameters are different to silicon
This is true. The important feature of germanium diodes, wrt this application, isn't their lower forward voltage as Schottky diodes are even better at that , but rather their characteristic V/I curve which is softer than silicon (0) and produces less odd harmonics which would otherwise contribute to a harsher sound.
Regarding germanium transistors, they're mostly used to replicate old school fuzz guitar pedals. In that application, aside the above characteristic, the particular configuration in which they're employed contributes to the sound: old fuzz pedal produce a very pleasant asymmetric distortion in which one half wave is much less distorted than the other, so that the output can contain a blend of clean and distorted sound.
R.G. Keen at Geofex (.com) wrote a thoroughly informative article about how that circuit works which anyone interested in building guitar pedals will find very informative (1).
That reminds me about podcast with some mic guru that was talking about zener diodes. They used ones to stabilize high voltage used for a capacitive microphone and found out that while initially they didn't care much as long as voltage matches, some models had harder or softer knee and the softer ones reduced the noise level coz they provided more noise-free power.
I said this in another comment, but the fundamental difference is that the frequency spectrum in discrete time is periodic and therefore finite in the range that the DAC can recreate, while distortion creates infinite spectra beyond the confines of that period. This is a fundamental limitation of DSP.
The way around it is to make sure the upper harmonics generated by distortion beyond the limit is below the audible threshold, either by making the period larger (over sampling) or modifying the distortion process. It's not lossless and a difficult design problem when factoring in computational limits. It's often cheaper to use discrete analog components with all their flaws than a good-enough processing chain and computer that can evaluate it.
Even offline whitebox modeling tools like SPICE, and realtime black box tools like Volterra series models are limited by this.
you can find very high dynamic range ADCs and DACs that cover the audio spectrum plus a few megahertz. Distortion due to spectral aliases above the Nyquist frequency is simply not an issue that one needs to worry about with decent hardware.
As for the cost efficiency of DSP emulation vs using genuine parts - sure maybe it makes sense to use real analog hardware. It depends on the specific requirements of your design.
Agree with all those who have raised the issue of problems with aliasing. Just to flush things out, it's worth mentioning what effect aliasing has on the quality of the audio output. Nobody seems to have address that issue yet.
Aliasing causes higher harmonics to reflect at the Nyquist sampling rate and be heard as a signal with lower frequency. e.g. a 25khz signal with a sampling rate of 24khz will end up sounding like a 23khz signal instead. A 26khz signal will sound like a 22khz signal. And so forth. Because there are exponentially more harmonics as frequency increases, aliased harmonics can end up reflecting a startling amount of energy into audio frequency ranges, even if the amplitude of each harmonic is much lower than the amplitude of the fundamental harmonic.
Because the harmonics are reflected, they no longer form a harmonic series, so they end up adding a metallic sound to the overall output signal. The sound of inharmonic aliased signals alone is not unlike the sound of striking a metal dinner plate with a spoon, or a copper pipe with a wrench. Not a pleasant sound.
We have very inexact vocabularies for describing sound. But clipped signals with heavy aliasing are usually described in terms like the following: "harsh", "metallic", "cold", "fizzy".
In fairness, this is a toy example. One would hope that in a mature ecosystem, those few who are capable of doing the very significant heavy math lifting required to implement better clipping will contribute components that can be shared and reused by everyone.
You've done a fantastic job of describing what I couldn't put my finger on! One of the issues I had when developing this code was what I referred to as a "jarring" noise when distortion gain was turned up. It's like you describe: almost "metallic." I alluded to the "jarring" sound in the article, and it's great to know the culprit! There weren't a lot of repos, articles, or forum posts that had examples of solid, straightforward distortion implementations, and now I can see why.
Hopefully, we'll see someone get some code out there that helps clean this up!
OP here! I'm admittedly new to the world of digital signal processing and don't have a math background. But what I _do_ have is a background in programming and guitar effect pedal building.
My hope with this site and series is to get people like me exposed to the possibilities a little bit of code and a Teensy can unlock for them. The lower the barrier of entry, the more cool things people can create. :)
That being said, I'd love to get feedback on good sources to learn more about signal processing/theory or any resources folks would suggest for covering the topic even better!
I’ve recently started to work through implementing DSP as VST plugins. But I never really thought that a pedal type DSP unit was tractable as a hobbyist. I’m pretty excited to follow your work and see if I can do some pedal style effect or basic synth work in hardware.
Thanks for the post! Right before I saw this on HN I was watching a video on how to build a Klon clone, so this write-up couldn't have come at a better time.
It did a great job! It has a lot of processing power and since it's bare-metal, latency and variance concerns are easily avoided.
I was disappointed that there didn't seem to be a good ecosystem of SPDIF/Toslink-based audio I/O for the Teensy, at least at that point. I had to make the Toslink hardware myself.
Toslink is an awesome connector for this type of thing, and I think it would be great if people started using it for Eurorack-style audio processing modules instead of analog signals.
You can get stereo pretty easily this way, and if someone could write up some ADAT lightpipe code, you could even get 8-channel polyphony!
Glad to see some posts about using Teensy for this purpose.
As an EE who uses Teensies occasionally in embedded and industrial contexts, I'm always surprised by the expectation of "the audio guys" regarding hardware/software solutions.
For most users of these chips, "making the X hardware yourself" is the expected outcome, the fact that there's a convenient compute module that has USB power, the processor, a debug interface, a USB connector, and an open-source toolchain to quickly reach the "blink LED" stage is just a small leg up on the normal way of doing things.
I think it's so cool that there's a whole culture of people building little mixers, synths, and guitar pedals and so on in their garage. That's kind of tangential to the high school kids learning to code on Arduinos. And that's kind of tangential to those of us using these development boards professionally, either for prototyping or for low-volume custom stuff.
Side note: You might be interested in the TMDX5535EZDSP DSP eval board (still active, now over 10 years old, but it was a great platform for me to learn the fundamentals of DSP) or the newer TMDSOSKL137 eval board (more appropriate for building a giant mixer), they integrate a lot more audio processing power and have FFT accelerators/SOC audio interfaces that are better than even the Teensy 4.0/4.1.
Any waveform can be composed by a (sometimes infinite) series of sinewaves. The goal of distortion is to create a set of such sinewaves that sound pleasing to the ear. A much more complicated problem is to create such waveforms that fit optimally in a given mix with other instruments.
It does. Oversampling is the classic way to reduce that problem, but some newer techniques to mitigate hard clipping aliasing (or any transfer function aliasing) with GitHub repo examples here:
Hey there, no aliasing in this case. As for the clipping, this is effectively just hard clipping like you'd see from two alternating diodes in series on an analog gain circuit.
Admittedly, I'm early into moving from analog circuits to digital signal processing, so I could be off the mark on my answer. :) Hope it helps, though.
When you clip in continuous time you're pushing additional energy into the harmonics of the baseband signal being clipped. Since spectra in continuous time is infinite, you don't get any aliasing (a better way to say it is that "aliasing" isn't as meaningful in continuous time)
When you clip in discrete time, the spectra is finite (more technically, it's periodic with a period of the sample rate frequency). That means the energy that would go into harmonics past nyquist gets "wrapped" around.
This is the big difference between analog and digital distortion. In analog, it's really quite difficult to create energy at non-harmonic frequencies of the signal. In digital clippers like you have here, it's trivial, and the design problem is figuring out how to deal with it. Most products will use some kind of anti-aliasing strategy (usually oversampling before clipping) to handle it.
Oversampling won't help with the brickwall clipping being attempted here.
This circuit is not a diode emulator, it's a comparator. It's the worst-sounding of all distortions. It sounds even worse in digital because of the aliasing.
And it will always alias, no matter how much you oversample it, because a vertical edge - aka "Heaviside Step Function" - has an infinite harmonic series. If you oversample it enough it won't alias much because the series terms become smaller. But they never disappear.
A better way to do this kind of clipping is with a tanh (logistic/s-curve) approximation. That can give you a variety of valve-like [1] smooth clipping curves. Unfortunately tanh is pretty expensive computationally, so a more practical alternative is a piecewise curve, perhaps with some interpolation.
Although if you only have 8-bit or 16-bit resolution you may as well just use a lookup table.
OP might want to consider learning a little more about signal theory and practical DSP before posting more how-tos.
[1] Not really because real valves are more complicated. But it will do for a first approximation.
I appreciate your feedback and sharing your knowledge! I'll definitely be digging more into some of the things your mentioned to get a better understanding. The topic is a super deep one–though my goal (at least at this point) is to stay high level enough so that anyone could get started in making their own sounds/effects.
The lower the barrier of entry, the more cool things that people can come up with! I'm hoping that more without a math/EE/audio background like myself can get started and explore some more of these deeper topics :)
It will help, though! Commercial products will use 4-16x oversampling internally. Most useful distortions will have infinite harmonic series, but the hard clipper is certainly one of the worst because of the high amount of total harmonic distortion (THD). There's a lot of energy in those upper harmonics.
The classic soft clipper is something like
tanh(kx) / tanh(k)
which gives you a normalized output. It's not that expensive in the grand scheme of things, and is certainly cheaper than oversampling.
If you want something even more valve-like, a bit of DC bias to the signal before tanh will give you even order harmonic distortion, which sounds warmer (it beefs up the signal and puts energy into the octave harmonics, where as hard clippers usually only shove energy into the odd harmonics which sound harsher).
Interesting, I was under the impression that aliasing was something on the presentation layer (e.g. plotting on an oscilloscope). Have some breadcrumbs/links to share that would be a good resource on understanding aliasing in your context? Would be excited to learn more!
Take a sine wave below your system's Nyquist frequency. Chop off the top. Take the continuous Fourier transform. You will notice that there are now frequency components above the Nyquist limit of your system. Those will now be aliased down to lower frequencies.
One trick for doing nonlinear waveshaping without introducing too much aliasing is to perform the wave shaping at a higher sample rate than the rest of your system and then downsampling with a low pass filter. Thankfully, the high frequency components introduced by nonlinearity tend to decrease in magnitude reasonably quickly.
In the analogue realm - or more correctly, in the continuous-time realm, because an analogue sample-and-hold will show the same issues, it doesn't. It just introduces more harmonics at high frequencies.
In the digital (or again more correctly discrete-time, you have a sample rate) realm it totally makes a difference, because many of the harmonics you generate will extend above the Nyquist frequency, half the sample rate, and "reflect" back down.
What I don't get is, isn't that an inevitability of working with a digital signal? That is, if you were to sample a signal that was clipped in continuous time, wouldn't you get the same pattern of samples than if had clipped the signal after sampling?
Take the fourier transform of a clipped signal - it will have high frequency components.
In general, the more pointy edges you introduce to a waveform, the more high frequency artifacts you get.
This aspect of pontryagin duality (narrow in one domain means wide in the other) is also what underlies the heisenberg uncertainty principle. If you "hard clip" a photon's position (with a slit) you get a lot of frequency domain (momentum) noise, leading to a spread-out beam.
Why isn't there any aliasing? You're flattening off the peaks of the signal which absolutely must generate more harmonics, and at some point those are going to extend far beyond Nyquist.
I don't see you doing anything in particular to bandlimit your waveshaping, but I might well have missed it.
Yes, it matters a lot. A mild amount of low aliased crunch sounds very different from a mild amount of very aliased distortion, and people pay a bunch of money for software that sounds good.
Audiophiles also drop a lot of money on gear that intentionally distorts the signal. Aliasing is one reason why they buy tube amplifiers instead of tube modelers in their receivers, although I don't doubt the latter exists.
I play electric guitar.. I really doubt what you're saying.
I'd bet I could ask 10 other people who play guitar and none of them even know what aliasing is.
And none would be able to talk intelligently about what it means and what sounds good when thinking about a transistor distorting, an op-amp distorting, diode or LED clipping, a tube causing clipping/distortion, or a digital algorithm clipping. Most just try something and fiddle with the knobs, decide whether it sounds good or not, and move on with trying to figure out what music to create.
I actually find the stuff that gives more options around clipping tends to just be annoying. I prefer the designer to just pick the best sounding one and just go with that. Pretty much every time I've had an effect that offered a clipping switch or rotary dial one sounds the best, it takes a couple minutes to decide, after that I just wish the designer had left only that best one in the product without a switch.
I'd kind of argue intentional aliasing as a purposeful strategy to get a unique sound is probably something that has been overlooked. I guess "bit crushing" counts and that is somewhat common though.
Audiophiles are a whole different thing. I love tubes for playing guitar where everything is very non-audiophile but it's still really hard to wrap my head around it for audio reproduction.
I agree with a lot of what you’re saying here. But there are two opposing points: if you doubt that removing aliasing would matter, then you can’t also hold that aliasing on purpose is an overlooked effect idea!
I have been doing tons of anti-aliasing and saturation DSP lately and agree you mostly should be picking a vibe and sticking to it as a DSP sound designer. However the hell that comes together in the math is irrelevant, as long as the minimal set of controls you provide to the musician are fun to tweak and you’re not delivering an airplane cockpit.
There is a lot of marketing blather about analog this legendary that but at the end of the day, a unique sound that is fun for musicians to “play” or intuitively useful for the tradespeople (mixers, mastering engineers, trackers) to use is all that matters!
This is something that designers know and care about, and translates into "this box/plugin sounds good" vs "this box/plugin sounds bad" when hearing reviews or asking the dude at guitar center what to try out.
For example, if you were comparing AxeFX, Kemper, or Line6 Pod none of this would be on the labeling, but it's deeply tied to how they were designed.
For sure and I'd imagine these have to be designed with pretty high sampling rates internally to make sure they don't introduce too many artifacts and sampling issues.
But beyond musicians being able to hear what they like and don't like I don't think anybody understands what is going on. It's quite possible aliasing is part of "sounds digital" when a musician uses that as a pejorative... newer digital processing sounds less digital through better algorithms and likely things like better handling of aliasing.
Most distortion effects aim to add frequencies that are harmonics of the incoming signal. DSP, with a finite sample rate, can add frequencies that are not harmonics of the incoming signal, unless care is taken to avoid this.
Real diodes are not quite as sharp, because there's an exponential region between forward voltages of 0V and the forward voltage of the junction (~0.7V for P-N diodes, ~0.3 for Schottky).
And vaccum tubes are softer still, with a considerable rolloff region.