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a k butler wrote:
>
>> Bell Labs researcher Harry Nyquist develops Sampling Theory. It states
>> provides that if a signal is sampled at twice its nominal highest
>> frequency, the samples will contain all of the information in the
>> original signal.
Which is true! Millions of mathematicians have prooved it.
> Which is clearly not true :-)
> There's no way to keep the phase information for a signal sampled
> at only twice it's frequency.
> Only the amplitude.
guess what students ask their teachers of sampling theorems? They
usually ask the same as you do and they get an answer they can
understand. You have to do the mathematics. I do not know anybody who
does the mathematics behind it, still claims that its not possible.
What usually is forgotten, is that the Nyquist theorem is aimed at
infinite observation time.
> Or, alternatively, as Jon explained,
> a 22050Hz signal is only captured by 44100Hz sampling if the sampling
> happens to occur at the peaks and troughs of the signal, and not
> at the zero crossing points.
Which is only true for exact 22050 Hz at 44100 Hz sampling rate.
Do you really want to sample exactly a 22050 Hz signal with a 44100 Hz
sampling rate? The phase weirdness happens with the analog filters
before the converter. 22050 Hz is the theoratical border which cannot be
passed, the amplitude and phase you get for this one frequency is
arbitrary. But we are talking about real world problems don't we ;-)
Stefan
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Stefan Tiedje
Klanggestalter
Electronic Composition
&
Improvisation
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