[A6] Rich, rich, rich

[Leary, John]

MelloT (Brian), then UnderTow:

>> Note that you can easily hear the difference between a square wave
>> and a sine wave at 10kHz. Nothing too special, it seems. Yet, the
>> compoent that makes them different is harmonics - the first of which
>> is a 30kHz tone above the 10k base fundamental.

> It isn't that simple. According to what you say, recording a square
> wave at 44.1 or 48 Khz would give us a pure sine at playback. That
> obviously isn't the case.

UnderTow, your statement, while completely intuitive, is also incorrect.  If the ADC and DAC are properly constructed, you *will* get a pure sine at playback (provided the square's fundamental is between 7.35 and 22.05 kHz).  If there is *any* other harmonic content, it means that the converters are -- simply put -- f*cked by design.

A brief aside -- there *are* some tweakhead ADCs that deliberately let a small amount of content above 22.05 in.  They do so deliberately, because of other side benefits you get thereby.  But it's almost always a special mode of these converters, to be enabled only in circumstances that the user *knows* are appropriate for it.  I've never seen a consumer or pro/sumer A/D with this option.


> What happens is that the harmonics inter-modulate the base waveform
> (which is still at it's original frequency). This is akin to FM and AM.
> What you _do_ get is digital quantisation errors (distortion)
> depending on the frequency of the intermodulation and the quality of
> the converters.

But that's not quantization error, that's aliasing.  (It's quite akin to AM, nothing like FM.


> The thing is that you always get quantisation errors
> to a certain degree.

Of course, no analog process is perfect.  At the same time, please keep the categories straight!


> Hence the oversampling DACs at the output. With an 8 times oversampling
> DAC you have an anti-aliasing filter starting at arround 176 Khz or so
> going down to about 20Khz.

An DAC (oversampling or not) won't be able to fix a damn thing if you feed it with signal that wasn't properly sampled to begin with.  And if the signal in the ADC had *any* content above 22.05 kHz when it left the antialiasing filter and entered the quantizer, then it wasn't sampled properly *by definition*.


>> So the body can (somehow) perceive things above 20k, just as
>> we can also perceive things below 20Hz without "hearing" it.

> It has nothing to do with the body perceiving stuff as explained
> above. The reason why we perceive loud frequencies below 20Hz has
> nothing to do with hearing. Its just the kinetic energy of the
> accoustic waves shaking our bodies.

UnderTow, I think you just restated Brian's point while claiming to contradict it.  Brian never mentioned "hearing"!

And regarding Brian's point, consider there may also be mechanisms that bring the 30kHz content of the 10kHz square wave back into the 20-20k realm of human hearing.  Amplifier nonlinearities, IMD, and the strange things that speakers do when they get excited.  Basically, everything UnderTow said, except without Nyquist's theorem getting in the way...

For example, Earthworks speakers have no protection whatsoever on the tweeters (purists!), and so one way to "perceive" super-HF content is by the smell of smoke they emit when dying.  Thanks to a supersonic feedback loop, this (exactly) happened to them at one of their demos!

Peace to all,
John