>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 ?

I think this is less of a DAC issue than the various quirks of the analog
VCO designs. Like the classic function-generator style ones that start with
a sawtooth oscillator, then use comparators to generate a pulse wave,
full-wave rectifier to get triangle output, and wave shaping on triangle to
generate a sinusoidal output. Do VA people simulate these circuits
explicitly? Most of what I recall has been BLIT based stuff, or for digital
synthesis of specific waveform types the wavetable approach described by
RBJ is pretty straightforward and compelling.

For those who don't recall from undergrad EE lab:

The sawtooth oscillator is, basically, a variable current source feeding a
capacitor, which dumps when its voltage reaches a constant (say 1V). So you
get a linear rise (constant current feeding constant capacitance) and
control the frequency by altering the input current. The capacitor has to
drain through a non-zero resistor, so there is some finite discharge time
to reset, and also temperature compensation is required on the current
source, etc. You probably also put a DC-blocking cap at the output, so
there is some fixed highpass characteristic built in there (but maybe not
if this is an LFO). You can implement hard sync with another oscillator by
dumping the cap whenever the master oscillator hits some level.

To get the pulse output, you run this through a comparator circuit, with
the comparison voltage determining the pulse width (0V for square wave,
assuming a +/-1V sawtooth).

To get a triangle wave output, you full-wave rectify the sawtooth (and then
need to add another DC blocker)

To get a sinusoidal output, you use some diodes or other nonlinear
components to do an approximate instantaneous wave shaping on the triangle.

The fun bit in a modular synth is that all these synchronized outputs are
available simultaneously, and can be run through different
filter/modulation paths downstream, etc.

E



On Wed, Jun 13, 2018 at 9:06 AM, Theo Verelst <theo...@theover.org> wrote:

> Neil Goldman wrote:
>
>>  > 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....
>>
>> Even assuming a magically perfect and noiseless analog square wave
>> generator, at the very
>> least your speaker cones can't teleport between two positions.
>>
>
> Sure, there's a lot of stuff not just happening with speakers, but with
> acoustics of
> any kind as well, always very audible.
>
> For me when I started building musical circuits of the kinds I described,
> in high school,
> there were perfect enough squares available: electronics "function
> generators" would offer near perfect square waves with rise times orders of
> magnitude faster than an audio circuit would normally require, and crystal
> oscillators would keep jitter pretty low for
> creating square tones.
>
> It's true the imperfections I mean are the "digitally created" ones, which
> includes the exact filtering in the DAC, the linearity of it, which filter
> components have been (and not been) used like for DC coupling and analogue
> (mean IIR automatically) anti-aliasing filtering. The converter chip I use
> often at the moment (a PCM5102A DAC with up to 50MHz very low jitter and
> ground separated clock) is analog filtered with a single high quality
> component analog filter, DC coupled with a very high quality OPA627 OpAmp,
> with no subsequent electrolytic capacitors in the signal path. On my big
> monitoring or studio headphones it should be able to be very accurate.
>
> It's hard to explain, but it's possible to take the given filtering inside
> a DAC (to begin with the standard "oversampling" digital one) and try to
> invert it to the extend that the streaming filter inversion allows you to
> control the signal at oversampling clock speed to some level of accuracy.
> This might cost headroom: some inversions might take a lot of amplitude
> which is lost in the out coming signal, but nevertheless there are a few
> ways to try to do this.
>
> So taking a square wave with a given limitation of zero harmonics above a
> certain frequency (like can be created with additive synthesis)
> approximating the "perfect reconstruction" at the output of the DAC
> oversampling filter output is a real possibility. Unfortunately inversion
> of such a FIR or IIR filter with near bit-accuracy
> at the streaming signal output might not be easy, is hard to verify
> (unless you have
> and accurate model of the filter) and requires also a signal example (the
> required output) which is up sampled or otherwise known to or at the over
> sample frequency.
>
> Now if you've got that, for the DAC being used, you could indeed worry
> about if the "all harmonics up to Niquist" is perfect and good sounding.
> And certainly: do I want to
> include some sort of analogue filter simulation in the signal path for
> better sound, etc.
>
> I've got a (very complicated) setup that certainly will work with
> pre-inversions of DAC
> reconstruction/anti-alias/oversampling filtering, which IMO is absolutely
> necessary to
> get the quality I want, but mainly the kind of processing prepares signals
> to sound
> alright in *any* normal, small or big, damped or reverberating, acoustic
> space. And I
> found a lot of high quality recorded (commercial) music contains
> preparations for that
> principle of letting acoustics not get in the way of music enjoyment.
> Probably a domain
> Lexicon has been one of the main players in, and indeed my Lexicon digital
> reverberation
> unit almost cries and sings when these "signal preparations" start to
> sound good.
>
> I'm sure a lot of modern speakers are very prepared for use with digital
> signals, and
> often, I wish they would be more neutral and the reconstruction filters in
> DAC better.
>
> TV
>
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