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2021 Aug 12

Nonlinear DSP is good, fun, and hard

From day to day, my job is to take care of my son, and will be for the foreseeable future. While I enjoy him trotting up to me, book in hand, speaking the unfathomable, I anticipate a break. When I get a break, I like to spend it on something that unites all of my skills, interests, and concerns, and lately that has been digital signal processing.

Though I spent the past year focusing on hardware, especially analog circuits, it’s not the best thing for me to focus on right now, for many reasons. I love analog electronics, so this was a bittersweet realization. But DSP makes me more content.

Even before I became a software developer, analog prototyping felt inconvenient and awkward. Fishing around for components just to tweak something, debugging by squinting at wires and probes; dare I say, analog prototyping can be demanding of one’s eyesight. You also need specialized equipment, some of which can be hard to find. Many times I’ve wanted a high-impedance audio probe—a way to poke any node in a circuit to hear the signal—but never procured one. You can spend a lot of money and time building a lab without getting any work done.

Analog prototyping can differ significantly from production. If you want to be more than just a hobbyist, you ought to make prototypes using the same technology you intend to use for production. This requires making a tough decision up front, which increases pressure to get it right the first time. PCB manufacture is pretty affordable for hobbyists, but automated PCB assembly can cost thousands of dollars and is not cost-effective for low volumes. When you’re spending your own cash, it is daunting.

If you want to design for robustness and repairability, you should prefer through-hole construction. It kicks surface-mount technology’s ass in terms of longevity; that’s the reason military and aerospace applications use it. I also know this first-hand from all the mid-20th century gear I’ve peered into. The boards were made with a highly accessible technology.

But through-hole is bulky (→ costly) and suffers from a limited selection of components. Just the other month, the through-hole package of the LM13700 operational transconductance amplifier (OTA)—on which I was basing a recent design—was EOL’d by Texas Instruments. Bam, my design has just been invalidated. OK, I’ll look into THAT Corporation ICs. If it’s good enough for Elektron Music Machines, it’s probably good enough for me.

But wait, why are we doing this? You love analog so much you’re willing to use expensive components offered by only one company? OK, I’ll use discrete transistors to build my own OTAs—no, you can’t get good enough matching for that. GAH. OK, transistor arrays? Good luck finding them. Fuck it, just use pots; they’ll have less noise.

Nevermind the troubles of the bill of materials. Hardware production is problematic to any person who is concerned about e-waste. We already overproduce electronics and throw them out for bad reasons (to make money); so how are we going to justify producing more electronics? I might say I have a uniquely analog design that can’t be realized by any other means. But I doubt the claim; can one prove that an idea cannot be realized by mere software? (And how can one guarantee that the customer isn’t going to dump it in the landfill when it breaks?)

Mere software is quite attractive from the perspective of hardware reuse. I can write platform-agnostic DSP code and run it on salvaged hardware, no new production required. Still sounds awesome, assuming I did my job right. Plus, it can be updated. Hard decisions can be postponed.

That feels familiar. DSP development is software development, something I actually did for a living. I learned many powerful techniques to assist me in that endeavor, many of which have no place in analog circuit design. DSP can be developed with a rapid feedback loop, making it much more fun to work on. Need to tweak something? Just edit the code, build it, and listen.

DSP has challenges that analog doesn’t, especially if you’re modeling nonlinear analog systems. This is far from simply applying a bilinear transform; you need much more insight into the system being modeled. And because you’re choosing the model based on what might be useful for musical expression, there is a lot of freedom in the design.

That makes it a bit fun, because many things can be tried. But it also exposes you to a much larger mathematical universe, which means you’re not guaranteed to succeed. Modeling nonlinear dynamical systems is hard work, and people who are good at it are well compensated. Even they encounter problems they cannot solve. There is a reason that accurately predicting the weather two weeks from now is impossible: complexity.

You might have success over certain ranges of parameters, but not others, and be left scratching your head; why does the model absolutely flip shit when the cutoff frequency is too high? The intuition by which analog circuits can be designed is not useful in such cases; it requires insight into how nonlinear time-varying discrete-time dynamical systems work, and what conditions are required for their stability. This means you have to read thick textbooks, which you may shut with more questions than answers.

Sometimes the difficulty of nonlinear DSP gives me pause; maybe this is the reason to insist on analog hardware. But I don’t think that’s a good answer. I want to see the state of the art advance to the point that analog hardware is never necessary from an auditory perspective. Arguably we have already attained this long ago. Yet somehow a shred of doubt remains (which markets have noticed). Yes, I agree, simulation generally has limitations. It wouldn’t be sensible to require a supercomputer to get an ear-accurate simulation of an analog circuit.

Fine then, technology always has limits—but part of the job of a creative person is to exploit them for the sake of expression. Constraints are important to creativity, so ultimately musicians should not be disturbed by the fact that instruments made with DSP have limitations. The constraints might differ from those of other technologies, but this just requires acclimation, not a technological miracle.

After all, that’s exactly how analog became so beloved in the first place.


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