Does anyone know of any purely digital techniques for oscillators or filters that aren't based on trying to emulate an analog circuit?
Surely there must be some good sounding oscillators/filters that are derived from
scratch in the digital domain rather than using bi-linear transforms etc.
It seems that pretty much all digital filters are based on transformed analog designs rather than direct z-domain pole placement and I was wondering if anyone knows why (is it hard or do they sound crap)?
FM is the only one that comes to mind but there must be others.

"Good sounding" is subjective and the subjective consensus of people is that they seem to prefer whatever the ancient analog equipment did.

There are. Tons.

once you realize what i'm about to say, your mind will be blown.

electronic circuits are approximating the same functions.

it's maths all the way down.

see this for example:


this has been xhip's description since i think about late 2005.

Actually it's the other way around. Analog synths were designed to approximate mathematical models (i.e. digital sound). Now for whatever reason we sometimes choose to digitally approximate analog approximations of digital models. Sounds like Silent Hill 5, a computer game that was made after a movie that was made after a computer game.

sure you're posting that as a joke but you might not realize how true it is. "digital" means "discrete" though. it has nothing to do with math. you can have discrete math, or continuous (analog) math.

you're mixing them up. they're not the same thing!

an electronic circuit doesn't start executing spells and have faeries fly around inside the components or anything like that.

a lot of the first electronic music pioneers were working based upon designs on paper. the concept of the ramp and pulse (even and odd harmonic at 1/f) are fundamental mathematical concepts. they happen to be some of the easiest to reproduce and most versatile in both electronic and software formats!



most of the first efforts were additive, inspired by existing technology found in pipe organs for example. a lot of technology was developed for radio broadcast and analog computers using tube circuits. things really took off with the transistor, of course.

When I said digital what I really mean is discrete time it's just easier to imply digital/analog = discrete/continuous.

It just seems to me that most of the discrete time techniques center around transforming from the equivalent continuous time version and I was wondering about the reasons for this. Is it difficult to design things directly in the discrete time domain?

These
http://www.image-line.com/documents/harmless.html

and these

http://www.image-line.com/documents/harmor.html

Analog designers tried to get a close as possible to perfect wave forms. Digital designers try to emulate the failed attempts analog designers had. Ho ho.

I do think the direct conversion of a continuous function to discrete results in what is called a 'naive' implementation. The problem with that is error in the signal is introduced in the form of aliasing. Even filters have aliasing, as the matched-z transform will generate a lowpass with a frequency response that wraps around the nyquist frequency.

So any function which takes a digital approach to change aliasing behavior is rightfully fully digital. A naive function is still digital obviously, yet naive.

Those both look quite interesting are they just directly setting the spectrum and doing short time IFFTs?

the problem with any "fully discrete" implementation is that our ears are not discrete. no matter what you do, there are still going to be issues like distortion. whether it's harmonic, aliasing, quantization or whatever.

i'm sure we've seen claims that in some cases these can be desirable, but do any of us believe that? in my opinion any time you get a desirable result out of aliasing for example it just happens to be lining up to approximate something you could have done some other way.

ultimately anything we do in audio is going to be a continuous function.

cool discrete stuff? well, what about if we take a system that could be considered discrete like melody? then we can look at very interesting completely digital/software techniques like trackers, "virtual life".

http://www.youtube.com/watch?v=XcuBvj0pw-E

*shrug* Didn't Planck & Co. already demonstrate that the universe is digital?

Digital approximations of analog approximations of mathematical approximations of digital behavior as perceived by nonlinear wetware which is itself digital... what a funny world this is.

Anyhoo, to answer the OP, it's because synth guys can be as bad and stupid as the guitar guys who think that good tone only comes from a misbehaving tube. Yes, (virtual) analog can sound warm and amazing -- but so can digital, dammit (Yamaha's DX series comes first to my mind, but that's just me). Some synth guys think that good tone only comes from a misbehaving transistor -- you know, the same part which guitar guys revile.

In short, it's because too many people don't trust their ears enough. If it sounds good, it is good.

Or maybe it's because analog synths are so optimized towards a few sounds, like a traditional music instrument. They have such limited possibilities that they can give you just a few options that are almost guaranteed to sound good. If you just want to play your music, analog is prolly the way to go. Digital takes special discipline and training which go beyond the song; it can be much harder to control, but it can do so much more than analog.

Well, the actual answer is more complicated, but in the end what it boils down to is that most sound, pre-electronic, was created by plucking a string under tension (oscillator) or striking a membrane (osc/noise) and altering those with some sort of resonant chamber (filter) It's also the way the human voice works except you're pushing air past a membrane to create a waveform (osc) and your mouth/sinus system to filter it. There were also ways to resonate chambers of air by forcing air past them, ala flutes and such. In a sense you're basically creating acoustic subtractive synthesis in all these examples so when they started doing it with voltage, it just made sense.

Then, there's the way a pipe organ makes sound which is by exciting air in a resonant chamber. In a crude way it's an "additive" synth which can be done with analog voltage based synths, but it would cost a huge amount of money because you'd need an osc for each harmonic (stop) So it didn't really come into fashion (aside from organs) until digital systems became powerful enough to do it.

FM is more or less the same kind of thing. Can (and is) done with analog, but Yamaha just figured out a way to do it digitally. There's nothing "digital" about FM itself, it's just a more convenient way of doing it.

I guess the only "digital" synthesis types (I don't count sampling) are granular, but really that's just a tricky sampler technique.

Anyway, "analog" is in vogue now because of how it, as Jafo says, "misbehaves." I think as humans we like it better because it reminds us more about how natural acoustic systems make sound than how pure digital ones do, but I agree with Jafo, you can make very nice digital sounds as well.

Let me ask a slightly more specific question. Is anyone aware of purely discrete time method of designing (placing z-domain poles) a digital filter?
All the usual examples (eg RBJ biquads) involve converting continuous time versions.