My tl;dr answer to your question is it's difficult because even if it's
digital, it's not digital. Ever. It's always analog.

Like you, I'm a university EE (and Comp. Sci.) because I wanted to go into
chip design. This was back in the early 80's. So maybe my classwork was
different than yours. It was always amusing to deal with my computer
science classmates when something that dealt with the inherent analogness
of even digital logic came up.

In the late 70's, when I was in high school, I also tried to build an
organ. But back then, I had few resources, monetary or otherwise. I didn't
know about top octave chips or anything. So what I used were TTL inverter
circuits to make square wave oscillators, and fed those into J/K
flip-flops for dividers (a bit overkill, that). I also used some other TTL
logic to take those square waves and make some very steppy sawtooth waves
(which I then filtered to make them smoother.)

Currently, I emulate one of those old MOSTEK chips + dividers on an FPGA.
I'm not using much of the FPGA, but since I need oodles of output pins, I
have to use something fairly stout. No DACs necessary. I may try a version
sometime that mixes the signals internally to a single bus, then use a DAC
on that, but I fear I won't get it to sound as nice.

Neil Gilmore

> There's this preoccupation I have since the advent of going "digital",
> let's say since I
> heard music being played on CD in the early 80s. I grew up with access to
> electronics
> equipment that would generate "square waves" in some sorts of analogue
> fashion, including
> originally "digital" chips, even driven from frequency stable crystals and
> so on. In fact
> I built my own organ/synthesizer based on a top octave synthesizer chip
> around 1980 which
> I gave CMOS divider chips to get well symmetrical, pure and pretty
> undistorted square
> waves to a analog mixing rail construction, and I must say (I was a
> teenager) I recall the
> different sounds. the feel if you like, of all those different square
> waves by themselves
> and some the filter and modulation constructs I made quite well.
> Now, like everybody else, I'm used to listening to a lot of audio in some
> form of digital
> source format, ending up at one of the varying types of Digital to Analog
> Converters, to
> enjoy digital music on for instance a smart phone, a HDMI based digital
> stream converted
> by a TV/Monitor, a very high quality DIY kit based converter setup,
> standard computer and
> bluray player outputs (both not bad) and known brand studio quality USB
> ADC/DAC units
> (Lexicon, Yamaha, and a Burr Brown/TI chip based DIY kit) and finally from
> some variety of
> digital music synthesizers (a.o. a Kurzweil and a Yamaha).
> The simple question that forced itself on me often, as I"m sure some can
> relate, after
> having been used to all those early signal sources including a host of
> analog synthesizers
> I had in the past, and a lot of music in various analog forms from
> standard pop to G. Duke
> and Rose Royce to mention a few of my favorites from an earlier era, is
> how can it be that
> such a simple wave like the square wave, just two signal levels with a
> near instantaneous
> jump between them, can be so hard to make digital, if you listen with a
> HiFi system and
> some normal musical signal discernment ?
> The answer is relatively simple: a digital square wave for musical
> application comes out
> of all current standard DACs with imperfections that I recognize and have
> an immediate
> form of musical dislike about. Not that a software synth can't be put on,
> played and
> create some fun with square waves, I'm sure it can to some degree be fun
> and played with
> in some music, but for sound enthusiasts, all that digital signal
> processing does come
> across as often the same sounding and not as musical as I remember it can
> be by far.
> Is it possible to do something about that? I'm an univ. EE so im y
> official background
> knowledge, there's enough to understand some of the reasons for these
> sound limitations
> easily. Solving all of them will prove to be very hard, given standard DSP
> and normal
> current DACs, so there is that. To begin with the understanding *why* such
> a simple
> "digital" square wave doesn't sound warm and nicely flutey from a digital
> system in many
> cases: the wave as to be "rounded" to fit in the sample timing, and the
> DAC essentially
> doesn't necessarily "know" how to create those up and down signal edges
> with accurate
> timing. So for instance 1 standard 1kHz square wave coming out of a
> CD-rate (44.1e3
> samples per second) DAC will have maximum up and down square wave edge
> timing errors in
> the order of 1000/44100 * 100% ~= a few percent timing errors. Doesn't
> sound like much,
> but all the harmonics might be involved, and for a High Fidelity system,
> and error of 1/10
> of a percent nowadays just like in the early days of tube HiFi is
> considered quite
> noticeable or even unacceptable.
> Can a DAC do a better job ? Yes, but not by just feeding it a pure square
> wave, rounded to
> the samples. One could make use of serious oversampling, and a much higher
> rate DAC, for
> instance I've tested a very high quality DAC with adjustable type of built
> in
> "oversampling" filter (low pass or short, hard window reconstruction) at
> almost 10 times
> CD rate (384k s/s),and surely this makes the sound more acceptable. The
> monitoring and
> pre-amplification as well as the analogue (electronics based) DAC
> filtering will matter
> for the sound, too.
> Now recently I've worked on quite a different type of problem, not
> important for this
> sharing at the moment, which as one of it's (complicated) side effects can
> produce
> components to a digital signal that try to use the (limited) DAC
> filtering, usually some
> internal up-sampling ("oversampling") with either a built in DSP  FIR
> (some short impulse
> with at least some low-pass qualities) or IIR (some standard low pass
> response) to create
> a purer sounding square wave approximation from a frequency limited
> digital wave source.
> Anyone else worked on this to some extend ?
> T.V.
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