Re: sample rate

[Bill Fox <billyfox@soundscapes.us>]

Adrian Bartholomew wrote:

> this is where SOME info is worse than NO info.
> dude think about it.
> u have a wave at 1/2 the sample frequency. think about it like 
> connect-the-dots.
> the only ones u can plot are the max(positive) and min(negative) 
> points of the wave. NOW connect the dots and what do u have. thats 
> right a sawtooth wave. even if the original was a sine.
> but at least u have the frequency. forget about phase what about shape 
> or tone?
> even if u sampled at a frequency high enough to give u three or even 4 
> points to connect, its STILL approximate, very far from the shape of 
> the original and certainly not "all the information of the original 
> signal".

Dude, there is no connect the dots in a sampled system.  Electronically, 
the dots AREN'T connected.  The DAC outputs a stepped series of voltages 
that feed a reconstruction filter, i.e. an LPF.  This filter takes your 
so-called sawtooth, filters out everything above the LPF's pernamently 
set cutoff frequency and voila, you get a sine wave!  Think about it a 
minute.  The LPF is set to filter out everything above (0.5)fs, where fs 
is the sampling frequency.  fs is the first possible overtone of ANY 
waveform that isn't a sine.  What you think is a sawtooth is actually a 
square wave.  But you won't hear anything except the original sine wave 
being reconstructed.

The lack of information or understanding is yours.  I can't give you the 
engineering background required to prove that I'm right.  You'll have to 
spend a few years first, learning higher mathematics andinformation 
theory.  But every CD player, every DVD player, every minidisc, DAT, and 
iPod prove me right.

Cheers,

Bill