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F#READY

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    PWM experiments

    in Atari 5200 / 8-bit Programming

    Posted

     

    SAMPLING
 
By The Gatekeeper
 
Last issue, there where three great articles about sampling ( by AlphaSys and Frankenstein ! ) This time I would like to tell some more.
 
 
6-Bits play routine?
--------------------
First of all, I would like to give some more details about the, which Frankenstein called, 6-bit play method which I also used in my MOD-Player. Within the Pokey chip, the four audio channels are mixed together like this:
 
 
Channel1--|
          |
Channel2--|
          |------Audio Out
Channel3--|
          |
Channel4--|
 
 
This way, if Channel1 has a volume of 15 and Channel2 one of 15 ( 3 and 4 are zero ) the Audio Out has a volume of 30 ! A little math tells us that 4 channels of 16 different volumes can give us 4*16=64 different Audio Out volumes. Right! Well, not exactly. :-)
 
C1:15 C2:00 C3:00 C4:00
C1:00 C2:15 C3:00 C4:00
C1:00 C2:00 C3:15 C4:00
C1:00 C2:00 C3:00 C4:15
 
have the same Audio Out. O.K. then it's three less. You still have 61 different output values. Alas, the XL isn't fast enough to output four values at 'almost' the same time. Take a look at this :-Q
 
     LDA C1
     LDX C2
     LDY C3
     STA $D201
     STX $D203
     STY $D205
     LDA C4
     STA $D207
 
The fourth channel is 'poked' to the right value 9.03 ms after channel one. In practice this turned out to be too slow... This means the XL can only use up to three channels which gives 46 different output values. Here they are:
 
C1 C2 C3 Result
---------------
00 00 00 00
01 00 00 01
02 00 00 02
.  .  .  .
.  .  .  .
14 00 00 14
15 00 00 15
15 01 00 16      <-- !!!
15 02 00 17
15 03 00 18
.  .  .  .
.  .  .  .
15 14 00 29
15 15 00 30
15 15 01 31      <-- !!!
15 15 02 32
15 15 03 33
.  .  .  .
.  .  .  .
15 15 14 44
15 15 15 45
 
 
This is not 6-bits but LOG(46)/LOG(2) = 5.52 bits. This is very unhandy. For example, take the MOD-Player. It has four channels, playing a sample in a resoltion of 4 bits. 4*(2^4) ends up into 64 different combinations, which needs 6 bits to be played without quality loss. Sadly, we only have 5.52 bits... We have to calculate 6 bits into 5.52 bits with this formula :
 
X=6-bits value
Y=5.52-bits value
 
Y = X / 64 * 46
 
Well, try this in Machine Language, and you'll be happy if you get a replay speed of 1 kHz ! Solution : Look-Up Table !!!
 
 
The Look-Up Table
-----------------
You build up three tables, one for each channel, containing 64 values, the values that have to be played for that 6-bits combination. Then, a certain sample can be played by this small routine :
 
TABLE1    EQU $2000
TABLE2    EQU $2040
TABLE3    EQU $2080
 
PLAY      LDX VALUE
 
          LDA TABLE1,X
          PHA
          LDY TABLE3,X
          LDA TABLE2,X
          TAX
          PLA
 
          STA $D201
          STX $D203
          STY $D205
 
          RTS
 
VALUE     DFB 0
 
 
On Side-B you'll find a small Turbo-Basic program which builds up these three tables. It'S briefly documented, so I won't tell anything more about it here...
 
 
Oversampling
------------
Frankenstein mentioned the term oversampling in his theory article. I really agree with him, that the meaning of it is getting vague. A lot of people use it in a different context and don't tell what they actually mean. I'm sorry to say, but to my opinion, Frankenstein is also wrong. He combined two subjects into one. The method of calculating values between to samples and the result of that, having a higher replay frequency. Let's get a clear mind ! (?)
 
Oversampling : When you digitaly record an audio signal, with a frequency spectrum ranging from 20 Hz to 20 kHz, the theory of Nyquist tells us you need a recording frequency of at least 40 kHz. Two times the highest input frequency that is. Now, it's called oversampling when the samplefrequency is not twice the input frequency, but e.g. 5 or 10 times. It's used to lessen the terrible effect of high frequencies.
 
But what about that calculating of values between two taken samples ? Well, that is called interpolation. CD-Players use interpolation technics to 'recover' lost data. Take this situation. An (imaginairy) 2-bits CD-Player has read the following values :
 
 
A  11|*   *l  
^  10|**  *o *
|  01|** **s**
   00|*****t**
   ----------
          abc    --> t
 
 
After the second occurance of %11, the player wasn't able to regain the sample information. Now it can just play the %11 again ( 0-order ), but it can also calculate the so called 'expected value'.
 
b = ( a + c ) / 2
 
This is interpolation of the first order. ( Lineair Interpolation. ) There are also higher order interpolation technics using logarithmic functions, sines and cosines etc.
 
As Freddy told us, it's possible to calculate all averages of two samples, and play this one between the two known samples. The resulting data-stream has to be played twive as fast as the original, that results in 1 time oversampling. Processing the 1 time oversampled data stream once again results in 2 times oversampling etc.
 
 
Analog Filters
--------------
With two components, a resistor and a capacitor, you can filter out either low and high frequencies. Take a look ate the following two schemes :
 
         ----
In -----| R1 |-------- Out
         ----     |
                  |
                 ___
                 ___ C1
                  |
                  |
                 GND        _figure 1_
 
        ||C1
In -----||------------ Out
        ||        |
                  -
                 | |
                 |R|
                 |1|
                 | |
                  -
                  |
                 GND        _figure 2_
 
Figure 1 will push down high frequencies above a certain f(R,C) and figure 2 pushes down all frequencies below f(R,C).
 
f(R,C) = 1 / ( 2*pi*R*C )
 
e.g.  R=1K  C=10 pF --> f=15.9 kHz
 
All frequencies above or under 15.9 kHz will be pushed down.
 
 
Digtal Filtering
----------------
First of all, you don't need to use oversampling for digtal filtering. It's based on taking not a 100% of the next sample taken. That way, high frequencies will fade away. You can simulate both RC-Filters seperately, but not together.
 
The essention of this algorithm is to add only a fraction of the new sample to a fraction of the old one. Watch this :-) a=1/2  b=1/2  (-:
 
Last Sample  New Sample  Calculated...
   (Y)          (X)        (aY+bX)
 
128          140         134
134 (!)      144         139
139          151         145
145          143         144
 
 
Mention that a+b=1 and a>=b. All quick changes of amplitudo will dissapear. The imaginairy f(R,C) is very low when a>>b. To simulate the other RC-filter, bY has to be subtracted from aX. ( aX - bY | a+b=1 v a>=b ). All sorts of exotic filters are possible.
 
 
Modulation Technics
-------------------
There is a whole range of different modulation methods. Named here are only a few...
 
 
PAM - Pulse Amplitudo Modulation
 
%11 |*
%10 |**
%01 |***
%00 -----
     abcd
 
 
PPM - Pulse Place Modulation
 
Pls |   *  *  *
    -----------------
     a   b   c   d
 
 
PWM - Pulse Width Modulation
 
Pls |*** **  *
    -----------------
     a   b   c   d
 
 
PNM - Pulse Number Modulation
 
Pls |* * *   * *     *
    ---------------------------------
     a       b       c       d
 
 
PCM - Pulse Code Modulation
 
Pls |***  *
    ---------
     a b c d
 
 
PAM is used on our XL/XE and so it is on ST(E)'s, Amigoes, MSX(2) and C64s. You can generate and n number of pulses, all with a different amplitudo. IBM compatible PC'S could use PAM, but they only have one bit and can therefore only generate block-waves. But wait a minute, all the other modulation technics only require two states. ( Pulse or no pulse ! ) That's why MOD-Players on PC use PWM. They just vary the width of the pulse. Be carefull, every pulse, no matter the length of the one before, starts at a certain frequency! Offcourse, there are a lot of disadvantages. The frequency of the starting points have to be very high so that one pulse sounds like PAM. Luckily the PC sound producer is VERY VERY BAD. It isn't able to produce sounds higher than 8kHz, therefore a starting point frequency of about 10 kHz is fine. Still you need at least a 12 MHz AT. Imagine you want an 4-bit play routine. The length of one period is 16. ( e.g. 15 times 1 and one time 0. ) Now the replay rate of all zeroes and ones is 160 kHz !!! ( This is still slow compared to the 2.56 MHz for an 8-bits player !!! )
 
Probably you think, why do you tell me this ? Our XL/XE is much too slow for this ! Then I must admit that you are right, but this last paragraph about modulation is not meant to be used in practice on an XL. It's just some more theoretical background. Maybe it inspires somebody to get one of these modulation technics working on a XL. ( What about some external hardware, producing a 1-bit PWM output from an 8-bit paralell digital input ? )
 
 
Well, this is the end. ( Finally. ) Let me tell you this, Frankenstein, I can secure you that there were two people that liked your article. ( Me and you that is ! ) I hope we like this one also !
 
Editor: Yes, I liked it. Thanx!

     

     

    Hehe, nice! Megazine #5 and #6 had some good articles about sampling :P

    http://www.ataripreservation.org/websites/freddy.offenga/megazine/

    Outlove 128 Bytes, released at Outline 2k18

    in Atari 5200 / 8-bit Programming

    Posted

     

    yep good one. I guess if I would try to program this scroller, my version would easily fill up 48 KB. At this point I would consider to switch off OS to gain some extra 10 KB or so :)

    I wonder how the approach works. First to make it run and then as small as possible? Or smallest possible right from the beginning?

     

    Thank you :)

     

    Usually I have a crude idea for something which I "think" would fit. The first step is to make it work and not care too much about clever tricks (which would make the code less understandable). Then optimise it and come to the conclusion it won't fit. Sometimes the next day after a good night sleep more optimisations will pop up. Eventually it's like optimising until it fits or come to the conclusion the idea simply won't fit.

    But it doesn't end there. When it fits, there is this urge to add more. E.g. when it has no sound, I want to add a bleep or two.

     

    So, we are lucky there are demo compo's with a deadline, otherwise one could go on forever adding, changing, optimising ;)

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