Well, bandlimited to a bandwidth < fs/2 (but the distinction isn't useful for audio), and given perfect reconstruction circuitry. But as far as I can gather, Theo's concern is "what happens when, as is inevitable in practice, the reconstruction circuitry is imperfect?" And that is an interesting question, academically speaking, if there really isn't a body of theory to cover reconstructive imperfection - if only to be certain that all the improvements made to DAC technology in the last three decades have actually been _improvements_.
But I think all of this is probably covered by existing research anyway. Minimising phase disruption in digital filters is well understood; LSB errors and resistor chain nonlinearities are fairly obvious, sources of relatively predictable badness, and can be assessed in the same way as nonlinearity in general; clock jitter is easy to simulate... and then there are analogue reconstruction filters. Unless I've missed any, I don't think there's anything else to look at, unless he wants to disprove or augment Nyquist-Shannon. Which would be an achievement, true, but... I would humbly submit that there might be more fruitful avenues towards seeing "Verelst theorem" in the indices of 22nd-century audio textbooks. Still, I understand great white whales all too well; and if Theo _needs_ to harpoon this one, we should perhaps not stand in his way. On 05/06/2015, Stefan Stenzel <stefan.sten...@waldorfmusic.de> wrote: > Theo, > > Any continuous function bandlimited to frequencies < fs/2 is completely > determined by its samples. > That’s the essence of the sampling theorem, which answers all your > questions. > > Stefan > > >> On 03 Jun 2015, at 22:47 , 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 -- 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
