"Perfect" sinusoids/square waves/etc. only exist as mathematical abstractions. A good starting point would be to get a feel for what, say, the "square wave" coming out of an analog synthesizer actually looks like - the noise floor, the distribution of harmonics, frequency jitter, under/overshoot, etc. I think you'll find that modern digital equipment generally can produce much, much closer approximations to these ideals than we ever see from analogue synthesizers.
But more generally the answers to your questions depend on the specifics of the A/D/As in question. There are many different designs with different oversampling and interpolation stages, different noise shaping strategies, etc. So the question of where the quantization noise ends up doesn't have a general answer - it depends in on both the design of the A/D/A components, and on the specifics of the signal in question (these are nonlinear, time-variant operations we're talking about). Likewise, the effect of applying a half-sample delay depends heavily on how you do that. If you're talking about signals that are simply computed directly or delay in the analog domain, then you'll simply see a half-sample delay at the output. But if you're talking about sampling a signal and applying a half-sample delay, then it depends on what technique you use to implement that delay. Also, note that the function a*exp(b*x+c) is not, by itself, a well-defined test signal, since it has infinite energy. The sampling theorem does not apply to such signals in the first place. You would need to apply some kind of window/truncation to ensure finite energy and bandlimiting. More generally, these issues are all quite well studied and understood, and not particularly relevant to music-dsp as such. So I'm not sure what is the point of repeatedly bringing them up in this context. It sounds like what you want is more like a book or class on mixed-signal circuits. The main reference I use for that is "Analog Integrated Circuit Design" by Johns and Martin. It's a bit dated by now, so it's not going to cover the latest-greatest converter designs (not sure that any book really does), but the chapters on the noise modeling, theory of oversampled conversion, etc. are all still valid for learning the theoretical underpinnings of this stuff. E On Wed, Jun 3, 2015 at 1:47 PM, Theo Verelst <theo...@theover.org> wrote: > Hi, > > Playing with analog and digital processing, I came to the conclusion I'd > like to contemplate about certain digital signal processing considerations, > I'm sure have been in the minds of pioneering people quite a while ago, > concerning let's say how accurate theoretically and practically all kinds > of basic DSP subjects really are. > > For instance, I care about what happens with a perfect sine wave getting > either digitized or mathematically and with an accurate computer program > put into a sequence of "signal samples". When a close to perfect sample (in > the sense of a list of signal samples) gets played over a Digital to Analog > Converter, how perfect is the analog signal getting out of there? And if it > isn't all perfect, where are the errors? > > As a very crude thinking example, suppose a square wave oscillator like in > a synthesizer or an electronic circuit test generator is creating a near > perfect square wave, and it is also digitized or an attempt is made in > software to somehow turn the two voltages of the square wave into samples. > > Maybe a more reasonable idea is to take into account what a DAC will do > with the signal represented in the samples that are taken as music, speech, > a musical instrument's tones, or sound effects. For instance, what does the > digital reconstruction window and the build in "oversampling" make of a > exponential curve (like the part of an envelope could easily be) with it's > given (usually FIR) filter length. > > In that context, you could wonder what happens if we shift a given > exponential signal (or signal component) by "half" a sample ? Add to the > consideration that a function a*exp(b*x+c) defines a unique function for > each a,b and c. > > Anyone here think and/or work on these kinds of subjects, I'd like to > hear. (I think it's an interesting subject, so I'm serious about it) > > T. Verelst > > -- > dupswapdrop -- the music-dsp mailing list and website: > subscription info, FAQ, source code archive, list archive, book reviews, > dsp links > http://music.columbia.edu/cmc/music-dsp > http://music.columbia.edu/mailman/listinfo/music-dsp > -- dupswapdrop -- the music-dsp mailing list and website: subscription info, FAQ, source code archive, list archive, book reviews, dsp links http://music.columbia.edu/cmc/music-dsp http://music.columbia.edu/mailman/listinfo/music-dsp
