🚀 go-pugleaf

minich@a.cs.okstate.edu (MINICH ROBERT JOHN) writes:

>From article by bas+@andrew.cmu.edu (Bruce Sherwood):
>> The analogy with audio is that a CD with frequency response out to 10
>> MHz would not sound better than one with frequency response out to 20
>> KHz, because the human ear can't hear the higher frequencies.

>  Well, it probably would sound a bit better. Consider this:

>A 20KHz sample on CD looks something like this

> * * * * * * * * * *
>* * * * * * * * * *

>which is just a dumb square wave. Sure, it's at high enough of a pitch 
>that most people wouldn't be able to discriminate between it and a pure sine 

I can't take this any more!  You  don't  just  feed  the  samples
through  an audio amlifier and see the square wave!  You put them
through  a  `reconstruction  filter'   which   reconstructs   the
waveform.   An  ideal reconstruction filter, with a step function
low pass frequency response at 20kHz will reconstruct  the  20kHz
waveform  as  a  *perfect* sine wave.  It will also reconstruct a
19.99 kHz waveform *perfectly*,  notwithstanding  the  fact  that
there  is  a  beat between the sample frequency and the frequency
represented (the sample  points  `walk'  slowly  along  the  wave
shape).

So if the basilar membrane in your ear responds up to  20kHz  you
_will not hear_  the  difference between a properly reconstructed
signal from 44.1kHz samples and a signal reconstructed from 20MHz
samples!   Most  adults'  hearing is far below this limit, in any
case (15kHz is considered good -- if  you  have  often:  operated
heavy  machinery, fired a gun, driven a car with the window open,
or listened to loud music with headphones on, 8 to 12 kHz  may be
more like it!)

Before someone asks what if the original were not  a  sine  wave:
recall that complex waveforms may be considered as a summation of
sine waveforms of different amplitudes and frequencies, so  in  a
linear system it is valid to think only in terms of the behaviour
of the individual sine wave components.

Of course, perfect reconstruction filters are hard  build,  so  a
44.1  kHz  sample  rate  permits reconstruction filters to have a
finite roll off starting at 20kHz and being essentially fully cut
at 22.05kHz (the limit for a 44.1 kHz filter), and *still* repro-
duce all frequencies up to 20kHz *perfectly*.  Now if the  filter
did  not cut off frequencies above 22.05 kHz, some of that 20 kHz
signal would appear as a 24.1 kHz signal (reflected in  frequency
about the Nyquist frequency).  This would be undesirable.

Oversampling (no one sells CD players that don't `oversample' any
longer, do they?) permits some of the reconstruction filtering to
be done using a digital filter.  Consider  4x  resampling:   each
sample is replicated four times in a row at 176.4 kHz.  A digital
filter with a cut off frequency of 20 kHz can  be  applied.   Now
when  reconstructing,  the  analog filter still has to be flat to
20kHz, but need not be fully cut until 88.2 kHz, the Nyquist rate
for  the 4x oversampled signal.  Since the digital filter has en-
sured that there will be no frequency components in  the  digital
signal  between  20kHz  and 88.2kHz, a much lower Q filter may be
used, which is much easier and cheaper to design.

Now what about those 18 bit players?  CDs only have 16  bit  sam-
ples  dont they?  but if you use oversampling and digital filter-
ing, you can `interpolate' between the original samples and  sam-
ple  quantisation.   But what does it buy you?  The reconstructed
signal is only as good as the orignal digital material.   A  good
advertising  gimmick,  in  my opinion.  (What about the precision
and linearity of those 18 bit A-D converters?)

Neil/.		Neil%teleos.com@ai.sri.com

Note that our mail feed  via  SRI  is  currently  dead,  so  that
flames,  questions  and  assertions  that  `my hearing is good to
37.496e29 MhZ -- medically verified' (you must be an alien)  will
be thrown into the bit bucket.