Nyquist Frequency

["Rainer Thelonius Balthasar Straschill" <rs@moinlabs.de>]

Jon,

(in my following ramblings, I will only talk about pure sine waves if
not mentioned otherwise. Also, I'm talking about theory, not about real
converters or other real devices):

> Stephen -  It is my understanding that the Nyquist theorum actually 
> specifies the theoretical maximum frequency that can be represented
with a 
> digital signal.  It says nothing of the quality of that
representation. 
> There's a key issue that makes the nyquist theorum all important to
the A/D 
> conversion process - frequencies higher than the Nyquist freq. will
manifest 
> themselves in the resultant digital signal as much lower frequency
noise. 
> That noise is basically garbage and is nearly unpredictable.

Frequencies higher than the Nyquist frequencie will come out as a
so-called alias at a lower frequency (and incidentally, also at higher
frequencies). But not as noise, but as a pure sine wave. This signal is
predictable. 

> Furthermore, frequencies that are close to but still less than the
Nyquist 
> frequency will be represented, however the amplitude of the
representation 
> will vary over time based on the _difference_ in frequencies.  How
much the 
> output varies in amplitude is a more complex equasion - important
thing is 
> that frequencies close to the Nyquist freq. (even though they are
still less 
> than) will be VERY distorted but will still be represented "perfectly 
> in-tune".  Example: 48KHz digital A/D converter could capture a 23KHz
pure 
> sine wave, and output a 23KHz sine wave whose amplitude varies at 1Khz
- you 
> would hear that 1Khz signal for sure!

Frequencies below Nyquist come through without any change.