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From: turk@media-lab.media.mit.edu (Matthew Turk)
Newsgroups: sci.electronics,comp.std.internat,rec.video,comp.graphics
Subject: Re: I don't need HDTV!
Summary: Sampling theory
Message-ID: <1948@mit-amt.MEDIA.MIT.EDU>
Date: 21 Mar 90 16:29:11 GMT
References: <sa0KhqO00Uh7M2R25C@andrew.cmu.edu> <5478@okstate.UUCP>
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Organization: MIT Media Lab
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In-reply-to: minich@a.cs.okstate.edu's message of 20 Mar 90 18:52:05 GMT

In article <5478@okstate.UUCP> minich@a.cs.okstate.edu (MINICH ROBERT JOHN) writes:
>
>    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
>  of the same requency, but what happens if, say, you have a 20,001Hz waveform? 
>  Then, 20KHz just isn't enough to provide a nice, "symetric" waveform. Thus, 
>  you get a somewhat harsh sound. If I were really after a "human limits" sample, 
>  I'd bump the rate up to around 30KHz to minimize the distortion. (Assuming that 
>  a 40KHz sample is "wasteful".) 
...
>  The truth is, we CAN hear the effects BELOW the maximum frequency. 


The problem is quite a bit better understood than you are assuming.
The aliasing you describe is eliminated by prefiltering the signal
with a lowpass filter.  Also, digital signals are not reproduced as
square waves.  If the human ear was indeed insensitive to signals
above 20kHz, then an ideal system would prefilter the signal (lowpass
at 20kHz), sample at 40kHz, then reconstruct the (filtered) analog
signal exactly to be amplified and sent to your speakers.

The real issues here are: (1) a perfect low-pass filter is not
realizable, so you either have to accept some aliasing or filter at a
higher rate; (2) the human frequency response isn't an ideal low-pass
system, so there's no clear and clean cutoff point.  ~20kHz is, I
believe, the -3dB point.  Since the CD sampling rate is 44.1kHz,
there's a little room for variation -- perfect filtering would fully
represent signals < 22.05kHz.  In real systems, we can definitely
avoid any noticable aliasing, but this reduces the frequence response.
Anyone know how tight the filters used in digital recording are?

	Matthew