>  such a simple wave like the square wave, just two signal levels with a
near instantaneous
jump between them

I think I disagree with this definition of a square wave. This is what a
perfect, ideal one would look like, but even in reality I don't think any
system (digital or analog) can exactly produce a perfect square and the
infinite bandwidth it takes for the infinite number of harmonics.

Even assuming a magically perfect and noiseless analog square wave
generator, at the very least your speaker cones can't teleport between two
positions. And I'm no electrical engineer but the circuitry must also have
some kind of damping effect on the extreme ranges? I mean even the
infinitesimally faint harmonics that will exist in the Mhz range, Ghz
range, etc up to infinity.

If you remove or dampen any of those higher harmonics, even ones well
beyond the range of human hearing, this perfect square shape takes on a bit
of a ripple shape. At what point is it no longer a "true" square wave?

So I would argue that a perfect square wave doesn't exist anywhere except
in theory, and it's more useful to define it by its harmonic series. And at
that point it doesn't look easier or more complex than any other common

I also don't know the answer but agree with the guess that it's probably
analog imperfections that make it sound good, rather than analog perfection.


On Wed, Jun 13, 2018 at 10:51 AM <ra...@raito.com> wrote:

> Theo,
> 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
> ra...@raito.com
> >
> > 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
> > 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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> > music-dsp@music.columbia.edu
> > https://lists.columbia.edu/mailman/listinfo/music-dsp
> >
> >
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