Re: randomized white noise = white noise?

acannell@xxxxxxx wrote:
Thanks for your very interesting posts Tom. I think I have found a
"target" so to speak, to focus my efforts on. This algorithm:

b0 = 0.99765 * b0 + white * 0.0990460;
b1 = 0.96300 * b1 + white * 0.2965164;
b2 = 0.57000 * b2 + white * 1.0526913;
tmp = b0 + b1 + b2 + white * 0.1848;

Takes white noise samples and outputs pink noise samples. If I can find
a way to perform it using the 400 or so instructions I have to work
with on the ATTINY13, I have a way to generate pink noise real time
using it! Maybe I can use a look up table or somehow do it so I dont
need floating point....hmm
....

You might try a crude approximation like the following, which uses
16-bit fixed point arithmetic, with binary point at middle.
unsigned int b0, b1, b2, tmp, white, tw;
do {
<generate white>
tw = white/16;
tmp = tw*3;
b0 = b0 - b0/256 + tmp/2;
b1 = b1 - b1/16 + tw/4;
b2 = b2/2 + white + tw;
tmp += b0 + b1 + b2;
outp (tmp/256, PORTB);
while (1);
In code produced by the avr gcc port, this loop is around 75
instructions and 80 cycles if <generate white> is quite crude,
eg white = ADDP + 16 * white;
and around 75 instructions and 80+m+d cycles if <generate white>
is less crude, eg white = (ADDP + MULP * white) % MODP;
where m=cycles for rcall __mulhi3, d=cycles for rcall __udivmodhi4,
and ADDP, MULP, MODP are appropriate numbers, eg numbers that might
look like 2539, 27943, and 65521. [I don't know if the avr gcc port
has a random() function; if it does, it's probably better and faster.]

You can calculate the values the above code corresponds to. Eg,
b0-b0/256 is 0.99610*b0, vs. your desired 0.99765*b0, while 3*white/16
is white*0.1875 vs. desired white*0.1848, and so forth. Also, the loop
is fast enough that it should be ok with more filter stages (b3=...,
b4=...). Perhaps that would give you more leeway with the constants.

-jiw
.