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**bandpass** At 44kHz+ rates, neither aliasing nor transient artefacts should be audible, as they both occur at 20kHz+.

And yet they are when you click "allow aliasing".

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You seem an expert on sampling theory, so I would like to ask if you could help clarify the information in this Lavry Engineering white paper?

I'm hardly an expert, but I know a bit.

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He talks about 'connecting the dots' and the fact that the 'non technical' person assumes that the more dots (higher sample rate) the more accurate the re-creation of the waveform.

The basic idea is that a sine wave is one frequency, pure and unpolluted. All other variations of waveforms are multiple frequencies combined (look up Fourier Transform). It's not quite the absolute truth... I mean, you can't feed a bunch of sine waves together to get a perfect square wave, but if you filter a square wave down to its fundamental, only a sine wave will be left. A sine wave has a positive peak and a negative peak, so you should be able to sample a 20KHz wave with only a 40KHz sample rate. That's one sample for the peak and one sample for the trough. The output will still be 20KHz. A 20KHz wave sampled at 40KHz would yield a triangle wave, but a low-pass filter will get rid of the digital "junk". If you have a 10KHz sine wave digitally sampled at 40KHz, you still have a triangle wave on the output, right? Well, that triangle wave still contains the original information (10K sine wave), but it's been polluted by false, odd harmonics. The first harmonic of a 10K triangle wave is 30KHz, so if you filter out everything above 20KHz, it's a sine wave again.

There's also a matter of quantization distortion. Since you only have so many levels to represent your signal, they're not perfect representations of the input signal. Since those steps are discrete and predictable, they can somewhat be reversed by subtracting the calculated error from the output signal.

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Is it just that the maths is so advanced its impossible to explain without formula? Its driving me crazy, but i haven't got time to quickly go and do a 4 year maths degree How does something come out of nothing?

When did "maths" become a word? I'm not insulting you, I just see it a lot now when I never did a few years ago. It's explainable without math, but that's not how engineers think I guess.

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edit just got the best quote yet, straight from John Watkinson's book 'Introducing Digital Audio', still don't get it:

This is tougher to explain in layman's terms. He's talking about oversampling DACs. Go back to our 40KHz sample rate. The input signal has been limited to 20KHz by the magical "perfect" anti-aliasing filter, which is really just a filter that blocks absolutely everything above a certain frequency without harming anything in the audible range. Perfect filters don't exist and they never can, but let's pretend they do. If you convert this 40KHz signal to analogue directly, it takes an equally "perfect" reconstruction filter (yet another low-pass filter) at 20KHz to get rid of the junk. On top of false harmonics, you have the reverse of aliasing, which is imaging. Anything BELOW the Nyquist frequency (20KHz in this case) is reflected above the Nyquist frequency, so 10KHz is now output as both 10KHz and 30KHz. Still, a perfect filter doesn't exist for reconstruction either. What they do is over-sample the signal, usually by 8x, so now 40KHz is 320KHz. This creates an "impulse" of sorts where you have a spike in the signal that represents the 40KHz digital signal followed by seven samples of "zeroes". Issues have been pushed 8x out into no-man's-land where very simple filters can gracefully dispose of them. The original signal only contained audio below 20KHz, so all that information has been smoothed into something recognizable.

I'm giving the quick'n'dirty of all this stuff, but that's the jest of it. I know some people "in the know" will tear me apart because I even seen experts tear each other apart for trying to paraphrase. Of course, it all works well assuming you have perfect A/D conversion and perfect D/A conversion. In reality, there is no perfection and I really do think 96KHz sounds better than 44.1KHz in almost all situations. The main reason for that, of course, is because more of the errors introduced by the ADC and DAC are well beyond your hearing range. On that note, I think it's hilarious that the same people who created 64x (and higher) oversampling ADCs, 8X oversampling DACs and oversampling plugins claim anything higher than 44.1KHz is stupid. "Really? So as long as the A/D converters are running at 2.8MHz, the D/A converters at 352.8KHz and anything doing any processing is running at, say 176.4KHz, 44.1K is totally perfect for everything. It sounds like you guys are saying 44.1K SUCKS!" Now I KNOW I'm going to get it for that!