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 ?

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