Re: Is higher oversampling ratio better in signal fidelity in digital world?

Thomas Magma said the following on 19/05/2006 19:21:
"Jerry Avins" <jya@xxxxxxxx> wrote in message news:_LCdnWcTNJg7ZvDZnZ2dnUVZ_sGdnZ2d@xxxxxxxxxx
Thomas Magma wrote:

I'm not sure if I exactly agree with the statement of not being able to get
closer to the original signal then simply satisfying Nyquist. It seems to me
that if you sampled (lets say) a 100 Hz perfect sinusoidal wave form at 200
Hz or so, that during playback (DAC process), this will appear as a very
chunky square wave that contains tons of harmonics. It you oversampled that
same 100 Hz sine wave at 44kHz then you have better represented the original
sine wave and playback would contain vary little harmonic content. The two
methods will sound different.
The output of the DAC is not what you need to be thinking about. You
ignored the role of the reconstruction filter. If the sampling frequency
is 200 Hz, everything above 100 Hz must be removed from the analog
output. What harmonics did you mean?

The sampling frequency must be greater that twice the highest signal
component. When sampling at 200 Hz, 100 Hz can't be reliably
reconstructed. 200.001 Hz is sufficient, but only if the sampling lasts
a good part of 1000 seconds and the signal remains unchanged for that
time. The bit of oversampling that is always needed to allow practical
anti-alias and reconstruction filters also assures reasonable resolution
times, but in theoretical cases that don't call for filters, resolution
time has to be accounted for.


Thinking in the time domain, as you lower the sample rate you increase the digitization (Your sampled sine wave will start to look like a square wave). Clocking that data through a DAC at the same rate will produce strong harmonics (3rd 5th 7th etc).

Harmonics? Aliasing frequencies are not harmonically related (except in degenerate cases).


You can't regenerate the original sine wave out of a DAC no matter what digital reconstruction filtering you use if the playback rate is too slow.

If you mean without using an analogue filter, then you can't reconstruct the original sine wave 100% at *any* sample rate (except infinity!).


The output of a DAC will always start digitizing

"Digitising" is probably the wrong word here. What you're describing (the staircase-like waveform) is actually an artifact of the impulse-response of a zero-order hold, which itself is just a filter.


--
Oli
.

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