[sdiy] samp. freq for ADSR ?

[ASSI]

On Sunday 04 April 2004 23:16, Magnus Danielson wrote:
> > From: ASSI <Stromeko at compuserve.de>
> > On Friday 02 April 2004 22:13, mark verbos wrote:
> > > Creating a 500Hz sampling frequency. Nyquist's theory is that the
> > > maximum sampled frequency is half the sample rate, leaving the
> > > Buchla MARF with a maximum of 250Hz (real low for audio).
> >
> > This is a common misinterpretation of the Nyquist Theorem.
>
> Actually no, it is a correct interpretation of the Nyquist Theorem,
> but it is not a practical interpretation of the Nyquist Theorem as
> you want to point out.

My apologies to Mark if I have overextended his statement, but I took 
it to read: "if the sampling frequency is fs, then the maximum 
frequency in the reconstructed signal is fs/2". This simply does not 
follow from the Nyquist Theorem and is actually quite harmful in this 
shortened form.

The Nyquist Theorem states that the samples obtained at a rate of fs 
from any signal that is bandlimited to fs/2 can be used to fully 
reconstruct the original signal provided the reconstruction process 
matches the sampling process and both sampling and reconstruction are 
error-free. Since the discrete samples itself have an infinite and 
periodic spectrum, the reconstruction process involves filtering, most 
commonly a low-pass (if the frequency band of interest starts at zero). 
If the signal is not actually sampled and the samples obtained by 
computation instead, the reconstructed signal is only guaranteed to be 
bandlimited if the samples could have been obtained from a bandlimited 
signal via tha sampling process for which the reconstruction filter was 
designed.

To go back to the ADSR example, the MARF can easily produce frequency 
components much higher than fs/2, as the sample sequences it uses are 
not restricted to follow the Nyquist Theorem. Similarly, a "perfect 
sawtooth" or "perfect square" sample stream won't sound all that 
perfect playing through your soundcard and the horrible aliasing you're 
gonna hear is not the soundcard's fault.


Achim.
-- 
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