Wacky HF Aliasing!

[FarleyCZ]

Imagine a signal at exactly Nyquist. One sample will be +1 and the other -1 and so on. Instead of thinking it's a square it might as well be a sine! And it is. Two points is all that you need to describe a sine. You can derive both frequency and amplitude from those two points. By sinc interpolation.

Ok, I addmit I was thinking about linear interpolation. But even with band limited signal, even with better interpolations, I still kind of can imagine signal, where for example amplitude is missinterpreted badly. The most exact one: If we try to describe sine at exact Nyguist by 2 poinsts as you said, but we do not hit highest and lowest points.
Ok when you have 3 or 4 points per period, some good interpolation algorithm propably will be capable of true interpetation of signal, but even though DSP programers seem to be really careful in thet frequency area.

[jupiter8]

The example above was just the easiest to explain. I'm not completely sure it holds for exactly Nyquist or "only" below Nyquist. Anyways if you're just below you have like 2.0001 points per cycle and that is enough to reconstruct the wave 100% perfect. No ifs or buts. This was proven 60 years ago.

http://www.lavryengineering.com/documen ... Theory.pdf
This PDF may or may not be of interest to you.

Mathematically the input and output are exactly identical.

This assumes infinite long filters and infinite long bitdepth and we don't have that in real life. Infinity is no problem in maths but is a real show stopper for computers.

Fortunately the human senses have limits too so the question is:how much is enough ? Well we don't hear anything above 20k hz or so. Add some for the sinc filters and then some extra just for safety. That gives a samplerate say 60 kHz. The difference between the loudest and faintest sounds that humans can hear is about 120 dB. That is 20 bits.

Plus you have limits on the analog circuit as well. The highest dynamic range i've ever seen on a AD converter is 127 decibels. So 24 bits 96 kHz is way beyond what you'll ever need.

So how about CD standard ? 16 bits 44.1 kHz seems like it should be pretty bad. Turns out it isn't. Technically it's cutting it a bit close however in listening tests it turns out that few, if any ,can hear the difference between CD standard and higher quality ones.

So what about plugins that boasts 64 bit precision and internal oversampling?
That is a whole other story that i won't go into now. It has nothing to do with the delivery format.

[FarleyCZ]

Ok, I'm silent.
But Lenard know what he does. Sylenth1 is still beast!

[tuzemec]

This turned into a really nice and informative discussion
Something that we don't see every day here, at KVR
Thank you, guys