On 2015-06-11, Theo Verelst wrote:
[...] I don't recommend any of the guys I've read from here to presume they'll make it high up the mathematical pecking order by assuming all kinds of previous century generalities, while being even more imprecise about Hilbert Space related math than already at the undergrad EE sampling theory and standard signal analysis and differential equations solving.
Could you be any more condescending?For your information, at least distribution spaces do not admit an inner product, much less a complete topology induced by it. Hell, in general they aren't even metrizable.
And as for last century mathematics, yes, well anything prior to 2000 technically is just that. But let me point out that math doesn't exactly age, and that 21st century math tends to be beyond most PhD's in its rigor, generality and methods. An EE could well stop at 1800 AD and make do. What we're talking about here is a theory which even now isn't really complete, what with Lojasiewicz and Hörmander doing their seminal work only in '58-'59, and many of the problems of distributional division continuing to generate papers to this date. That being the stuff that lets you operate on rational system functions in this setting, ferfucksake...
There are three main operations involved in the relevant sampling theory at hand, the digitization, where the bandwidth limitation should be effective, [...]
Yes.
[...] the digital processing, which whether you like it or not is very far from perfect (really, it is often, no matter how you insist in fantasies on owning perfect mathematical filter in the sense of the parallel with idealized analog filters), [...]
But the problems can be regularized/mollified out of practical significance using 1800s maths.
[...] and the reconstruction, which in the absence of processing can be guaranteed to yield back the input signal when it's properly bandwidth limited.
Yes, and with deep delta-sigma converters we know how to achieve that as well, over any useful audio bandwidth. Exactly enough for the resulting error to *always* fall under thermionic noise, in practical circuits.
[...] without going through the proper motions of understand the academic EE basics, it's a free world, at least in the West, so fine.
In fact we do our homework, often without it being in any way connected to a lucrative endeavour. When we don't get it, we ask for help on fora such as these. Which are then supposed to be easy to enter, *precisely* because there's strength in community.
I don't believe it is us who are climbing some imaginary ladder of power and prestige. We've been talking math, pure and simple. What you're doing here is pooping on a perfectly vibrant party of others. Please don't do that.
I repeat the main error at hand here: it's important to have bandwidth limited synthesis forms, but it is equally important to *quantify* [...]
We know, and we have.
[...] THEN you could try to get EEs/musicians opinions about inverting and partially preventing the errors in common DAC reconstruction filtering.
There is no error, as shown by tens of double-blind empirical tests over the years. If that's your persuasion.
Start with the basics, and goof of into some strange faith in miraculous mathematics to solve complexities that are inherent in the problem.
Oh, and you just happen to hold the magic key? Math bedamned? Seriously, man.
Even worse idea is to mash such idea up with the signal generators and filters, without concern for sample shifting, filtering errors, generator waveform reconstruction issues, and so on. That's not going to be my dream virtual anything. just saying.
That's sheer gobbledygook, and as an EE you ought to know so.
[...] but it may also kill information that is subsequently lost for later processing, and it will impose a character that probably is boring.
Show me the information theoretical argument to that effect. I can follow that kind as well, as I'd surmise quite a number of people here can.
But I don't need to worry about accusing the teacher of humiliating me, because I'd be fine good at it.
I am reasonably sure it is you who is humiliating himself. But of course I'm open to being proved wrong. Why not do the test?
-- Sampo Syreeni, aka decoy - de...@iki.fi, http://decoy.iki.fi/front +358-40-3255353, 025E D175 ABE5 027C 9494 EEB0 E090 8BA9 0509 85C2
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