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A SOUND PLAYER FOR 8-BIT APPLES
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DAC522 - April, 1993
INTRODUCTION
Back in 1980, when I purchased my first (16 kB, cassette) Apple ][+,
I was intrigued by the possibility of using its cassette input to
digitize sound and its speaker to play it back. In fact, I wrote
mini-assembler routines to do just that, and an APPLESOFT program to
use them to "read" hex dumps to me so I could check my typing against
hex listings in magazines.
It worked, but the results could hardly be confused with hi-fi! Both
the input digitizer and the output device were limited to 1-bit
resolution, essentially capturing and reproducing only the zero
crossings of the input signal, so everything was infinitely clipped
or "fuzzed" to the very edge of recognition! A number of authors
since have used this approach in programs like "Audex", "Doubletalk",
and "Digicorder".
Apparently the Apple ][, for all its wondrous capabilities, had
serious limitations in recording and reproducing audio. These limits
were repeatedly tested by talented programmers like Paul Lutus, who
in 1981 wrote Electric Duet, which produced real two-voice, reedy
music! A host of other programs used similar techniques during the
80's, but the fundamental (harmonic?) tyranny of square waves
continued. (Paul has recently placed Electric Duet in the public
domain--check it out!)
Then, in 1990, Scott Alfter wrote a little suite of programs to play
Mac sound files on any Apple ][. I first ran across it on America
OnLine, in a little demo called "Insert Disk." This was attributed
to another author, but a perusal of the playback routine shows that
it is, in fact, Alfter's.
Scott's SoftDAC was a new high water mark for audio reproduction on
an 8-bit Apple. It played 11 kHz. sampled sound files through the
Apple speaker (or the cassette output) with tantalizing fidelity--not
great, still gravelly, but much better than I had ever heard before.
It inspired me to find out just how far you could go in making a
vanilla Apple ][ sound like a IIgs or a Mac WITHOUT adding hardware.
This is the result.
HOW IT'S DONE
As I've suggested, the problem is that it takes several bits of
precision in converting digital samples to sound to make "good"
sound, but the natural audio output capability of the Apple speaker
(prior to the IIgs) is only one bit. You can decide when to "toggle"
the speaker, but that's it--the cone is either all the way in (or
headed there) or all the way out (or headed there). Experiments have
shown that the human ear is essentially insensitive to the "polarity"
of sound, so "in" and "out" can be interchanged in all the discussion
that follows. (This is just as well, since the Apple I/O circuitry
doesn't give us control over the polarity anyway!)
Paul Lutus (and others) found that greater resolution in speaker
movement could be achieved by toggling the speaker (in and out) at a
high frequency, and then varying the "duty cycle" of the square wave.
Changing the duty cycle (the fraction of the time the speaker is
commanded to be "in," say) of a high frequency square wave can be
thought of as causing the speaker cone to move to a position
approximating the average value of the square wave, which is the duty
cycle. This allows us to generate multiple tones by changing the
duty cycle at an audio rate to approximate the value of the sum of
the two (or more) tones.
Scott Alfter refined this process sufficiently to produce 8
discrete positions for the speaker cone, effectively implementing a
3-bit digital-to-analog converter (DAC) by manipulating software
timing loops. Brilliant! Of course, there are some limitations.
First, it's limited in its sample rate to 11 kHZ, or 93 clock cycles
on an unaccelerated Apple ][. It could be slowed down, but the 11
kHz. "carrier" frequency is already marginal and quite annoyingly
audible. Second, with only 93 cycles to spend, it simulated only 3
bits of DAC resolution, so sounds are still somewhat "gritty." This
is a result of "quantization noise": the difference between what the
sound waveform value actually was and what is reproduced after
retaining only 3 bits of the sample. In the case of a 3-bit DAC, the
reproduction of each sample is off by an average of a little more
than 6%--not bad, but unfortunately still quite audible. (Postscript:
In Summer, 1992, Scott released a 4-bit version of his SoftDAC--half
the noise of the 3-bit, but twice as noisy as this 5-bit.)
HOW MANY BITS CAN DANCE ON THE CONE OF A SPEAKER?
After being inspired by Scott's code, I had to find out how many bits
of precision could be achieved in a software DAC, at 11 kHz., on a
"stock" Apple ][. Until April, 1993, I thought the answer was 5
bits--but I was wrong! Greg Templeman (Barnabas on America Online)
took my statement as a challenge (Right on, Greg!) and proceeded to
write a 6-bit DAC,again running at 11 kHz. A 5-bit DAC averages
about 1.5% quantization noise, while a 6-bit DAC halves this, to
0.75% noise. Errors this small are practically inaudible against the
background of the very loud 11 kHz. carrier tone, but more about that
in a moment...
Until March of 1993, I thought 5 bits was the limit. I viewed the
problem as a single loop which, in just 93 machine cycles, had to:
1) Toggle the speaker to start,
2) Delay a number of cycles proportional to the value of
the sound sample,
3) Toggle the speaker again,
4) Delay a complementary number of cycles to maintain a
constant carrier frequency,
5) Get the next sound sample (handling page crossings),
6) Test for the end of the sound, and
7) Use the sample to set up the next variable delays.
Doing all this within a single loop with a constant period of 93
cycles ruled out using more than 48 cycles for variable delay, while
still allowing enough time to get the next sample, test for the end,
and set up the delays.
What Greg saw that I didn't, was that for each sample, one of the
variable delays is at least half of the maximum delay. So he split
the loop into two loops, putting some of the work of steps 5) through
7) into the "long" delay! This allows some of the delay period to be
used for useful work, permitting a total variable delay of 64 cycles
out of 93. The result is 6-bit resolution and higher volume (64/93
instead of 48/93 for my previous 5-bit DAC). Very clever! He has
made the result available on America Online.
At this point, it seemed like the game was over--after all, with 93
cycles to divide up, and 1 cycle minimum resolution, 64 different
duty cycles are the best we can hope for. But there was still one
annoying problem which had not been solved: the ear-numbing 11 kHz.
"screech" of the carrier tone. The only way to eliminate it was to
raise the carrier frequency above the range of audibility, say to 22
kHz., which would cut the timing budget in half! That would require
trading off resolution for greater speed...
SoftDAC: THE NEXT GENERATION
Hearing Greg's 6-bit DAC opened some doors for me. First, splitting
the loop up got my gears turning about other ways to do useful work
during delay periods. Second, starting from 6-bit resolution meant
that doubling the carrier frequency would only require falling back
to 5-bit resolution, which seemed like a sacrifice I could live with
(an additional 0.75% quantization noise). Frankly, as Greg remarked
via e-mail, in the presence of the 11 kHz. carrier, it was difficult
to hear the difference between 5- and 6-bit resolution.
This latest DAC is composed of 16 different pulse generators, each of
which has the job of producing two identical pulses with "on" times
varying from 6 to 37 machine cycles and with a constant period of 46
cycles. The total period of the two pulses is 92 cycles, the closest
even approximation to 11.025 kHz. (Actually, 11.092 kHz.) At the
end of each generator, it jumps to the generator needed for the next
sound sample. It's only coincidental if it winds up "looping" by
vectoring to itself!
The appropriate generator is selected by the most significant 4 bits
of the sound sample, and the fifth-most significant bit is used to
lengthen the duty cycle by 1 cycle, if it is set. As a result, this
software DAC, which I call DAC522, converts with a precision of 5
bits and a "carrier" frequency of 22.05 kHz.
Dropping back to 5 bits to get rid of the 11 kHz. carrier is, I
think, a good tradeoff. Let your ears be the judge.
Since 16 different generators are used, each spreading the "work"
differently among the speaker toggles, DAC522 is larger than previous
DACs (1012 bytes). That's a problem for the sound editor, because
memory is already tight, and it would be a shame to cut into the mere
20 kB of space available for sampled sounds. The actual code for the
generators is more structured than tight, so it would be possible to
compress the code some by combining common "tails," but another
avenue seemed even more promising.
I decided to put the 16 generators, which break naturally into two
halves, into the 32 lines of hi-res page 1 which are hidden by the
four lines of text in "mixed" mode! The initialization and
termination code and a 16-byte table fit nicely into the leftover
spaces, since each "bottom line" is actually 48 bytes long. So in
this version of SOUND.EDITOR, all of DAC522 is in the hi-res screen
contained in the file SOUND.ED.OBJ, freeing page 3 for other uses.
This hi-res embedded form of DAC522 is a little awkward to use in
other programs (!), so I've included a single-file, contiguous
version, DAC522.8C, which is assembled to load at $8C00. The DAC is
called by setting up the start address at 6/7 and the end address at
8/9. The entry point is $2370 for the hi-res version, and $8C00 for
the contiguous version. (The requirement of previous versions that
the last byte of a sound be set to $00 has been dropped.) The source
for DAC522 is available upon request.
(You may be interested to know that the source code for the duty
cycle generators is itself generated by an Applesoft program, which
does all the dirty work of counting cycles and scheduling the work
between the timed events. This approach is a practical necessity for
experimentation with such large chunks of timed code! Verification
is done using an oscilloscope.)
I listen to my Apple //e through headphones, and the output of this
software DAC sounds GREAT! You can also attach an external speaker,
with or without amplification. (Sorry, the ability to send the sound
to the cassette output was dropped from this version.) If you feed
the output into your stereo, go easy with the volume control--you
don't want to harm your stereo! You will want to turn down the
"treble" response of your amplifier to reduce the power level of the
(inaudible) 22 kHz. carrier. Remember, tweeters can't handle
overloads!
NOTICE
This program is FREEWARE. You can distribute it any way you like,
but you can't remove this notice or make money on it! If you enjoy
the new sound capability this program gives your Apple, and you would
like to encourage me to create more sound-related tools, you can send
suggestions or a small contribution (or both!) to:
Michael Mahon
1975 Adele Place
San Jose, CA 95125
Internet: mahon@nsa.hp.com
AOL: MJMahon
GEnie: M.Mahon
Apple ][ forever!