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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