Re: [linux-audio-dev] Direct Stream Digital / Pulse Density Modulation musing/questions

From: Mickael Vardo <m.vardo@email-addr-hidden>
Date: Sat Jun 11 2005 - 22:46:23 EEST

Hi there.

>Actually a correct explanation isn't that simple. Yours is much
>_too_ simple. Theoretically a 20 kHz bandlimited signal can be
>represented _exactly_ as a 40 kHz PCM stream. In order to not
>have to use a very steep lowpass filter in the DAC it is better
>to use a somewhat higher sampling frequency. 48 kHz should be
>enough most of the time.

No. Nyquist frequency allow original _sampled_ signal to be
fully reconstructed using a IDFT. It does not mean that the
reconstructed signal will have anything more than the original
samples.

If you sample an incoming analog signal at 2 samples per second
(sps), you'll definitely not be able to reconstruct ALL the
phases and ALL the frequencies between 0 and 1 Hz. You'll get,
however, a correct reconstruction of a periodic signal if it
lasts long enough. This is due to the inherent impossibility,
using a DFT, to get both accurate space and time resolutions
at the same time.

Just try this "simple" experience: sample a 1 Hz pulse that
is triggered after a random non-quantized delay that is less
than four seconds. Sample it at a rate of 2 sps and then,
try to get the original signal back with all its components
(phase and frequency). Good luck.

This is just as impossible as saying that you can compress the
information stored in any analog signal in a finite number
of samples.

Mickael Vardo
Received on Wed Jun 15 20:15:08 2005

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