3 Feb
1999
3 Feb
'99
6:52 a.m.
Philip.Belben(a)pgen.com wrote:
That said, oversampling and filtering is _not_ hard.
People nowadays think
only in terms of digital, discrete working and analogue, continuous
working. IMHO the place to do oversampling is in between - in the
Analogue, Discrete domain.
After you do the D/A, you have a huge amount of sampling noise at Fs/2 (and
its harmonics). For a CD player, Fs is 44.1 KHz, so the sampling noise is at
22.05 KHz. Since the desired audio frequency response extends to 20 KHz, a
non-oversampled player needs "brick wall" analog filters, with a pass band to
20 KHz, and a stop band starting below 22.05 KHz.
Digital oversampling is used to move the sampling noise to a higher
frequency. 4x oversampling moves it to 88.2 KHz. The oversampling filter
is a low-pass filter, so the audio content still has a frequency response
to somewhere above 20 KHz. But now your analog filter can have a much
shallower slope, which is easier to implement and introduces much less
phase distortion.
Your analog oversampling scheme does not eliminate the noise at Fs/2,
and in fact introduces more sampling noise at higher frequencies. It does
not help reduce the requirements of the analog filter.
Further notes on oversampling:
The digital oversampling filter can effectively implement a tradeoff between
the quantization and time domains. For instance, many early CD players used
14-bit D/A converters with 4x oversampling. It can be shown that this does
not lose any of the data on the disc, and ignoring the analog filtering
issues, is fully equivalent to a non-oversampled 16-bit D/A. But due to
two factors, the 4x 14-bit converter actually produces a *more* accurate
reproduction than the 1x 16-bit converter:
1) The reduced requirements on the analog filter,
2) It is easier to get precision in the time domain (using a crystal
oscillator clock source) than in the quantization. D/A converters
have inherent problems with linearity of output across changes at
power-of-two boundaries. This is most noticable at the midpoint
(or zero) crossing, where it is crucial that a change of the most
significant bit must have exactly the same weighting as the change
of all of the lower order bits plus one LSB.
Most audiophiles seemed not to believe it, and thought that it was important
to get 16-bit converters, even if they weren't oversampled.
Of course, a 4x 16-bit converter is even better than a 4x 14-bit converter.
The logical extreme of oversampling is to use such a high factor that you only
need one bit of data. This is called a delta-sigma D/A converter. For 16-bit
source data this would require at least 65536x oversampling, but there are
some tricks to reduce this to e.g. 128x. This is the basis of the so-called
"1-bit" D/A converters. The advantage is that you only need a single-pole
analog filter (and in practice can get by without even that), and that the
tradeoff from quantization to time domain has been maximized, which is good
because it is much easier to get high precision in the time domain as
described above.
Note that many of the same audiophiles that thought that they were being
cheated by 4x 14-bit converters have been completely "taken in" by 1-bit
converters, even though their own reasoning should suggest that they are
being cheated 7.5 times as much as by the 4x 14-bit converter.