[sdiy] converting white noise to pink noise

[Eric Brombaugh]

Andre Majorel wrote:
> On 2008-03-04 15:17 -0800, Dave Manley wrote:
>> Andre Majorel wrote:
>>> But note that long period does not imply good sound. For example,
>>> http://www.maxim-ic.com/appnotes.cfm?appnote_number=1743&CMP=WP-9
>>> is a 32-bit LFSR with a 2**32 period that does not sound very
>>> white.
>> Interesting, do you have a sound file you can share?
> 
> http://www.teaser.fr/~amajorel/noise/
> 
> I'll make another clip using just one bit per iteration as
> suggested by Achim.

Hi Andre,

Thanks for posting your code. Looking through it I can see two problems:

1) You're outputting all 32 bits at every iteration, even though the 
algorithm only generates one new bit. Since your generator shifts down 
this results in sequences of decreasing logarithmic ramps that give it 
an interesting resonant sound.

2) The LFSR polynomial is implemented incorrectly. To write the 
implemented algorithm out in pseudocode would look like this:

  If bit 0 is set
    flip each bit in the shift register with a 1 in the tapmask
    shift register down 1 bit
    set bit 31
  else
    shift register down 1 bit

The actual LFSR algorithm is more like this

  sample each bit in the shift register with a 1 in the tapmask
  xor all the sampled bits
  shift the register down 1 bit
  put the result of the XOR operation into bit 31

Interestingly, your algorithm actually does generate a PRN sequence, but 
it isn't maximal-length. I analyzed its repeat rate and found that it is 
107359437 cycles long - about 40x shorter than a maximal-length 32-bit LFSR.

By changing the code for updating the register from

     if (r & 1)
       r = (1 << 31) | ((r ^ tapsmask) >> 1);
     else
       r >>= 1;

to
     r = r<<1 | (((r>>1)^(r>>5)^(r>>6)^(r>>31))&1);

I got a repeat interval of 4294967295 cycles as expected. Unfortunately, 
this code doesn't allow arbitrary taps to be defined at run time though, 
so it's not nearly as flexible as your approach. You probably ought to 
patent it. :)

Eric