Path: utzoo!attcan!uunet!lll-winken!lll-lcc!ames!pasteur!ucbvax!decwrl!labrea!polya!rokicki
From: rokicki@polya.STANFORD.EDU (Tomas G. Rokicki)
Newsgroups: comp.sys.amiga
Subject: Re: Sampling at 29KHz (long)
Message-ID: <2850@polya.STANFORD.EDU>
Date: 18 May 88 23:24:16 GMT
References: <2845@polya.STANFORD.EDU> <734@eos.UUCP>
Reply-To: rokicki@polya.Stanford.EDU (Tomas G. Rokicki)
Organization: Stanford University
Lines: 81

> 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).

But if you try to play back a waveform that *includes* high frequencies
by undersampling, those high frequencies come back and haunt you.  That
is the point I am trying to make.

> 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).

As chuck said, a square wave at 14KHz should be filtered to a very
nice little sine wave; that is what the filter is for.  A square
wave at frequency f looks something like

	sin(ft+a_1) + 1/3 sin(3ft+a_2) + 1/5 sin(5ft+a_3) . . .

where the a_i's are phase shifts.  The filter should attenuate
the third and fifth etc. harmonics almost entirely, leaving you
with a very nice sine wave.

> 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(!)

Correct, assuming you stick with that 256 sample table.

> With this same sine wave and a variable (intergral.fractional) sampling
> increment, one could generate a maximum frequency of 14 KHz!

Yes, but because of the integral.fractional nature of your incrementing,
you are guaranteed to introduce some amount of garbage into your
sound; all your peaks won't peak at the same point, etc.  Although
this effect probably won't become really bothersome until you are up
to about 1/8 of the maximum frequency or so.

> 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).

But the sampling rate is variable; this is what makes it a win.
I really don't understand what is so hard about having multiple tables;
if you do octave tables, you need only twice the storage of the original
table (1+1/2+1/4...~=2).

> 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.

Ever feed the 6502-generated signal into a spectrum analyzer?

> 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?")

But it only needs be done once for each sample . . . even a full FFT,
filter, and reverse FFT doesn't take long for a 256 byte sample.  Not
real time, true, but for synthesis?  Faster than you can figure parameters
for the sample.

> >	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? :-)

Well, I'm trying to learn myself, so I presented what I think I
understand to be the case, and I hope to be corrected where I am
wrong.

> 		Phil Stone	(I still love the Amiga sound driver)

-- 
    /-- Tomas Rokicki         ///  Box 2081  Stanford, CA  94309
   / o  Radical Eye Software ///                  (415) 326-5312
\ /  |  . . . or I       \\\///   Gig 'em, Aggies! (TAMU EE '85)
 V   |  won't get dressed \XX/ Bay area Amiga Developer's GroupE