Path: utzoo!attcan!uunet!lll-winken!lll-tis!ames!pasteur!agate!eos!phil
From: phil@eos.UUCP (Phil Stone)
Newsgroups: comp.sys.amiga
Subject: Re: Sampling at 29KHz (long)
Message-ID: <734@eos.UUCP>
Date: 18 May 88 22:08:55 GMT
References: <2845@polya.STANFORD.EDU>
Reply-To: phil@eos.UUCP (Phil Stone)
Organization: NASA Ames Research Center, Calif.
Lines: 59

In article <2845@polya.STANFORD.EDU> rokicki@polya.STANFORD.EDU (Tomas G. Rokicki) writes:
>
>	Why Sampling At 29K Is Usually Sufficient
>
>.....Lecture on sampling theory omitted.....
>
>	If you undersample such a waveform, aliasing will cause
>some strange effects.  Let us say our sampling rate that we are
>undersampling at is m (samples per second.)  According to Nyquist,
>our sampling rate should be at least twice the frequency of the
>highest component sine wave.  Any components that have a
>frequency greater than 2/m will have some portion of their energy
>aliased or mirrored down to a lower frequency.
>
>.....7 paragraphs on the evils of undersampling omitted.....

Obviously, one should not try to play frequencies higher than the Nyquist
frequency; this is what you so laboriously illustrate.  Your examples are
not very realistic, however.  Let's take a simple sine-wave synthesis
instead (not the most realistic scenario either, but so simple as to be
an example of what an audio driver *should* be able to handle).

Compute a 256-point sine wave and put it in memory (32-byte sine waves
don't cut it in my book - even a tin ear can hear the interpolation
noise in fixed, jagged steps that big).  With a fixed sample-playback
increment and a maximum rate of 29 KHz, the highest frequency you can
generate is 29000/256 = 113 Hz! - just about TWO OCTAVES below A440(!)
With this same sine wave and a variable (intergral.fractional) sampling
increment, one could generate a maximum frequency of 14 KHz!  Now, I
realize that more complex waveforms will alias at this frequency, but
at more reasonable, musical frequencies, say 1 KHz, fairly complex
waveforms can be easily generated with no Nyquist aliasing, and without
the need to spin-off shorter tables just to get higher frequencies.

My point is, it is the combination of a relatively low sampling rate
*and* a simple increment method that makes the sound driver so
inconvenient to use.  Fix one or the other if you want a high quality
and flexible sound device (I'd pick the increment as the easier to fix,
though I don't appreciate the subtleties of the Amiga's DMA).

Also, I'm all for multi-sampling, if what you are trying to do is
*re-create* a musical instrument.  Not everyone is using the Amiga as
a sampler, though.  I enjoy playing with its synthesis capabilities, and
wouldn't mind if one waveform of say, 256 bytes, could be used over five
octaves - not a tall order.  I used to be able to do *that* with a 6502.

Your postscript tosses off a reference to *making* the other octaves of
sound - this is called interpolation, a process which has earned many Ph.D's
over the last ten years.  Try interpolating 4 octaves from one sample *live*
sometime (can you say "Cray killer?")

>	Any further comments?

Yes.  Why is it that articles that start out with "I really don't know
much about this but..." always turn out to be the longest ones? :-)

		Phil Stone	(I still love the Amiga sound driver)
phil@eos.arc.nasa.gov
phil@eos.UUCP
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