Generate Pink Noise Efficiently

On Sun, 24 Mar 2013 00:43:43 GMT, no-one@notreal.invalid (Robert
Scott) wrote:

>OK, here is the method that I ended up using.  I generate a square
>wave of random period, or rather a random half-period.  I start with a
>randon number uniformly distribute between 400 and 655.  This number
>is multiplied by a value that ranges from 635 nsec to 1134 nsec,
>depending on the parameter value I am trying to communicate.  The
>resulting time is the length of the next square wave Hi or Low time.
>After that time I toggle the output and generate another random number
>for the next half-period.  The result sounds about right.
>
>The spectrum of the frequency-jittered square wave is not just a
>single wide peak but has significant harmonics that are also
>spread-spectrum.  But the overall sensation of rising or falling pitch
>is conveyed, much like the Shepard Tones mentioned earlier.
>
>Robert Scott
>Hopkins, MN

That's nice, since it's easy to generate and accomplishes the task.


Eric Jacobsen
Anchor Hill Communications
http://www.anchorhill.com

Robert Scott <no-one@notreal.invalid> wrote:
> OK, here is the method that I ended up using.  I generate a square
> wave of random period, or rather a random half-period.  I start with a
> randon number uniformly distribute between 400 and 655.  This number
> is multiplied by a value that ranges from 635 nsec to 1134 nsec,
> depending on the parameter value I am trying to communicate.  The
> resulting time is the length of the next square wave Hi or Low time.
> After that time I toggle the output and generate another random number
> for the next half-period.  The result sounds about right.

So, the inverse of a phase accumulator.

The usual way would be to generate a number, which is the phase
increment, so proportional to frequency, then add it to a 
(possibly large word size) accumulator, modulo some value
(usually a power of two). For a square wave output, you just
take the high bit. For a sine, you use the high bits for a
sine lookup table.
 
> The spectrum of the frequency-jittered square wave is not just a
> single wide peak but has significant harmonics that are also
> spread-spectrum.  But the overall sensation of rising or falling pitch
> is conveyed, much like the Shepard Tones mentioned earlier.

-- glen