Re: Low pass filters revisited

[Dennis Doms <SynABit@everest.invalid>]

Supertimer wrote:

> Some years ago, some newsgroup readers made
> a big fuss that there was a low pass filter on the
> Apple IIGS.  The IIGS has a low pass filter at 26kHz
> frequencies.  What those people kept arguing was
> that this halved the sampling rate compared to CD.
> This is total nonsense.  The maximum frequency
> that can be accurately captured by a given rate of
> sampling is half the sampling rate.  This is denoted
> by the Nyquist theorem.
> 
> Fact is, practically all digital audio equipment has
> low pass filters.  CD players have them and PC
> sound cards have them.
> 
> Take a look at Tom's Hardware's review of the new
> Audigy2 card from Creative.  It specifically points
> out a low pass filter.
> 
> I'm just thinking how funny it was that people were
> blaming Apple for putting in the filter when in fact
> there's nothing to blame.  Without such a filter all
> you get is extra noise above 1/2 the sample rate.
> I even recall that someone came out with a IIGS
> emulator and promoted it saying that it lacked the
> low pass filter.  Shouldn't the Mac's audio out
> have one too?  It probably does.

I missed the earlier part of this discussion, but my $0.02...

Assuming a sampling rate of N, you have to have an analog filter that 
removes any frequency over N/2, the Nyquist criteria you refer to. It's 
not a matter of noise; what happens is that any frequency above the 
Nyquist threshold that that reaches the digitizer will be "folded" to a 
different frequency when reproduced. Best explanation of this I have 
seen is in Hal Chamberlin's _Musical Applications of Microprocessors_, 
in my mind a superb book for anyone really interested in the subject. 
(Chamberlin also built a wavetable synth card for the original Apple, 
maybe the first such consumer computer-based synth. Unfortunately I got 
rid of mine years ago.)

CD sampling frequency is set a bit above 44KHz so the Nyquist cutoff is 
22KHz. People can argue (and have argued) about whether this is 
suffcient, but it's what the industry is locked into. So the input 
filter should cut any input off below this, and more bandwidth on 
output shouldn't matter (if you sampled properly at 44KHz, anything 
about 22Kz on out put has to be noise or distortion.

Another problem is that an analog filter isn't going to cut off sharply 
at the defined frequency; it's actually going to effect a "rolloff" 
(hopefully rapidly) toward that frequency. It's just the physics of how 
things work. On the input side (analog-to-digital) any signal above the 
Nyquist cutoff is a potentially severe source of distortion, so the 
rolloff may have to sacrifice some accuracy below the cutoff to avoid 
that (some people, including me, think CDs should have been 
standardized at a higher sampling frequency; they probably went with an 
assumption that most people don't hear well above 10-12K which I also 
disagree with). On the output side (digital back to analog), 26K may be 
intended to let the entire digitzed signal knowing they may be allowing 
a little "noise" through in the 22K-26K range. (That is, they're 
allowing the filter a little "headroom" so the rolloff doesn't affect 
the high frequencies of the original signal as much; this is safe 
because folding isn't involved in this direction.)

-- 
Dennis Doms SynABit@Everest.invalid
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"We aren't here to rule. We aren't here to bring chaos or anarchy.
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