Dear All

After having spent a frustrating hour searching around to find some
simple code that would generate 1/f noise, or more generally 1/f^alpha
noise, I decided to write it myself. So here goes:

http://www.eng.ox.ac.uk/samp/powernoise_soft.html

I hope you enjoy it. Comments and feedback welcome.

All the best,
Max

max wrote:
> Dear All
>
> After having spent a frustrating hour searching around to find some
> simple code that would generate 1/f noise, or more generally 1/f^alpha
> noise, I decided to write it myself. So here goes:
>
> http://www.eng.ox.ac.uk/samp/powernoise_soft.html
>
> I hope you enjoy it. Comments and feedback welcome.

Hello Max

You must have looked in the wrong places. Searching for "pink noise" I
immediately found

http://www.firstpr.com.au/dsp/pink-noise/

There's also [1], which is interesting.

Regards,
Andor

[1] Kasdin, N.J., Discrete simulation of colored noise and stochastic
processes and1/fá power law noise generation, Proceedings of the IEEE,
Volume 83, Issue 5, May 1995 Page(s):802 - 827.


>
> All the best,
> Max

Andor wrote:

> You must have looked in the wrong places. Searching for "pink noise" I
> immediately found
> 
> http://www.firstpr.com.au/dsp/pink-noise/

Yep, thats a good easily accessible resource.

> [1] Kasdin, N.J., Discrete simulation of colored noise and stochastic
> processes and1/f? power law noise generation, Proceedings of the IEEE,
> Volume 83, Issue 5, May 1995 Page(s):802 - 827.

Unfortunately, that one is well hidden behind the IEEE knowledge firewall.

Erik
-- 
-----------------------------------------------------------------
Erik de Castro Lopo
-----------------------------------------------------------------
"In my opinion, shareware tends to combine the worst of
commercial software (no sources) with the worst of free
software (no finishing touches). I simply do not believe
in the shareware market at all."  -- Linus Torvalds

On 22 Mar, 22:27, Erik de Castro Lopo <er...@mega-nerd.com> wrote:
> Andor wrote:
> > You must have looked in the wrong places. Searching for "pink noise" I
> > immediately found
>
> >http://www.firstpr.com.au/dsp/pink-noise/
>
> Yep, thats a good easily accessible resource.
>
> > [1] Kasdin, N.J., Discrete simulation of colored noise and stochastic
> > processes and1/f? power law noise generation, Proceedings of the IEEE,
> > Volume 83, Issue 5, May 1995 Page(s):802 - 827.
>
> Unfortunately, that one is well hidden behind the IEEE knowledge firewall.
>
> Erik
> --
> -----------------------------------------------------------------
> Erik de Castro Lopo
> -----------------------------------------------------------------
> "In my opinion, shareware tends to combine the worst of
> commercial software (no sources) with the worst of free
> software (no finishing touches). I simply do not believe
> in the shareware market at all."  -- Linus Torvalds

Ah, well I did find those resources, but no simple "one pager" of
Matlab code for generating perfect 1/f^alpha noise. These pages all
seem to be geared to solving the problem with filters: nothing wrong
in that of course for certain applications but it's a bit long-winded.
The solution I'm proposing just constructs the appropriate power
spectrum and randomised phases, then uses the IFFT to get the 1/
f^alpha signal.

There is an interesting residual issue is the DC component or signal
mean: should this be zero? If so, it violates the full power-law
behaviour across the entire spectrum. The main problem though is that
1/f^alpha is undefined at f = 0.

Max

m...@googlemail.com wrote:
> On 22 Mar, 22:27, Erik de Castro Lopo <er...@mega-nerd.com> wrote:
>> Andor wrote:
>>> You must have looked in the wrong places. Searching for "pink noise" I
>>> immediately found
>>> http://www.firstpr.com.au/dsp/pink-noise/
>> Yep, thats a good easily accessible resource.
>>
>>> [1] Kasdin, N.J., Discrete simulation of colored noise and stochastic
>>> processes and1/f? power law noise generation, Proceedings of the IEEE,
>>> Volume 83, Issue 5, May 1995 Page(s):802 - 827.
>> Unfortunately, that one is well hidden behind the IEEE knowledge firewall.
>>
>> Erik
>> --
>> -----------------------------------------------------------------
>> Erik de Castro Lopo
>> -----------------------------------------------------------------
>> "In my opinion, shareware tends to combine the worst of
>> commercial software (no sources) with the worst of free
>> software (no finishing touches). I simply do not believe
>> in the shareware market at all."  -- Linus Torvalds
> 
> Ah, well I did find those resources, but no simple "one pager" of
> Matlab code for generating perfect 1/f^alpha noise. These pages all
> seem to be geared to solving the problem with filters: nothing wrong
> in that of course for certain applications but it's a bit long-winded.
> The solution I'm proposing just constructs the appropriate power
> spectrum and randomised phases, then uses the IFFT to get the 1/
> f^alpha signal.
> 
> There is an interesting residual issue is the DC component or signal
> mean: should this be zero? If so, it violates the full power-law
> behaviour across the entire spectrum. The main problem though is that
> 1/f^alpha is undefined at f = 0.

There's an elegant non-filter approach that combines a series of PRNGs 
running at different rates. Each running at half the rate of the one 
just faster than it seems yo be an adequately small spread and easy to 
implement.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

On Sat, 22 Mar 2008 16:03:44 -0700 (PDT), m...@googlemail.com
wrote:

>On 22 Mar, 22:27, Erik de Castro Lopo <er...@mega-nerd.com> wrote:
>> Andor wrote:
>> > You must have looked in the wrong places. Searching for "pink noise" I
>> > immediately found
>>
>> >http://www.firstpr.com.au/dsp/pink-noise/
>>
>> Yep, thats a good easily accessible resource.
>>
>> > [1] Kasdin, N.J., Discrete simulation of colored noise and stochastic
>> > processes and1/f? power law noise generation, Proceedings of the IEEE,
>> > Volume 83, Issue 5, May 1995 Page(s):802 - 827.
>>
>> Unfortunately, that one is well hidden behind the IEEE knowledge firewall.
>>
>> Erik
>> --
>> -----------------------------------------------------------------
>> Erik de Castro Lopo
>> -----------------------------------------------------------------
>> "In my opinion, shareware tends to combine the worst of
>> commercial software (no sources) with the worst of free
>> software (no finishing touches). I simply do not believe
>> in the shareware market at all."  -- Linus Torvalds
>
>Ah, well I did find those resources, but no simple "one pager" of
>Matlab code for generating perfect 1/f^alpha noise. These pages all
>seem to be geared to solving the problem with filters: nothing wrong
>in that of course for certain applications but it's a bit long-winded.
>The solution I'm proposing just constructs the appropriate power
>spectrum and randomised phases, then uses the IFFT to get the 1/
>f^alpha signal.
>
>There is an interesting residual issue is the DC component or signal
>mean: should this be zero? If so, it violates the full power-law
>behaviour across the entire spectrum. The main problem though is that
>1/f^alpha is undefined at f = 0.

Max,

Thanks for the free toy. I thought it would be interesting to listen
to the noises and look at them, so I made one-second bursts for a
Windows system ...

for alpha = 1:3;
 mySound = powernoise(alpha , 44100);
 m = mean(mySound)
 rms = norm(mySound)/sqrt(44100)
 wavwrite(mySound,44100,strcat('PN', num2str(alpha), '.wav'));
 plot(1:44100,mySound);
 hold all;
end

 I found that the darker-colored noises (alpha = 2 or 3) were
inaudible, until I later multiplied them by quite a bit. The rms
amplitude was lots smaller than for the white noise, and maybe the
sound system or ear doesn't respond as well either. 
On the DC question, I found that the DC level was always positive,
always at a mean of .0048. Shouldn't the DC polarity be random?

-- 
John

On Sat, 22 Mar 2008 22:23:59 -0400, Jerry Avins <j...@ieee.org> wrote:

>m...@googlemail.com wrote:
>> On 22 Mar, 22:27, Erik de Castro Lopo <er...@mega-nerd.com> wrote:
>>> Andor wrote:
>>>> You must have looked in the wrong places. Searching for "pink noise"
I
>>>> immediately found
>>>> http://www.firstpr.com.au/dsp/pink-noise/
>>> Yep, thats a good easily accessible resource.
>>>
>>>> [1] Kasdin, N.J., Discrete simulation of colored noise and stochastic
>>>> processes and1/f? power law noise generation, Proceedings of the IEEE,
>>>> Volume 83, Issue 5, May 1995 Page(s):802 - 827.
>>> Unfortunately, that one is well hidden behind the IEEE knowledge firewall.
>>>
>>> Erik
>>> --
>>> -----------------------------------------------------------------
>>> Erik de Castro Lopo
>>> -----------------------------------------------------------------
>>> "In my opinion, shareware tends to combine the worst of
>>> commercial software (no sources) with the worst of free
>>> software (no finishing touches). I simply do not believe
>>> in the shareware market at all."  -- Linus Torvalds
>> 
>> Ah, well I did find those resources, but no simple "one pager" of
>> Matlab code for generating perfect 1/f^alpha noise. These pages all
>> seem to be geared to solving the problem with filters: nothing wrong
>> in that of course for certain applications but it's a bit long-winded.
>> The solution I'm proposing just constructs the appropriate power
>> spectrum and randomised phases, then uses the IFFT to get the 1/
>> f^alpha signal.
>> 
>> There is an interesting residual issue is the DC component or signal
>> mean: should this be zero? If so, it violates the full power-law
>> behaviour across the entire spectrum. The main problem though is that
>> 1/f^alpha is undefined at f = 0.
>
>There's an elegant non-filter approach that combines a series of PRNGs 
>running at different rates. Each running at half the rate of the one 
>just faster than it seems yo be an adequately small spread and easy to 
>implement.

That's known as the Voss pink noise generator.  It's described here:
http://www.firstpr.com.au/dsp/pink-noise/

I wrote this about it:
http://www.firstpr.com.au/dsp/pink-noise/allan-2/spectrum2.html

Regards,
Allan

Allan Herriman wrote:
> On Sat, 22 Mar 2008 22:23:59 -0400, Jerry Avins <j...@ieee.org> wrote:

   ...

>> There's an elegant non-filter approach that combines a series of PRNGs 
>> running at different rates. Each running at half the rate of the one 
>> just faster than it seems yo be an adequately small spread and easy to 
>> implement.
> 
> That's known as the Voss pink noise generator.  It's described here:
> http://www.firstpr.com.au/dsp/pink-noise/
> 
> I wrote this about it:
> http://www.firstpr.com.au/dsp/pink-noise/allan-2/spectrum2.html

Thanks, Allan. I knew it was one of the real smart guys here, but I 
couldn't remember which one. It tickled me when you showed it to us.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

m...@googlemail.com wrote:

> After having spent a frustrating hour searching around to find some
> simple code that would generate 1/f noise, or more generally 1/f^alpha
> noise, I decided to write it myself. So here goes:
> 
> http://www.eng.ox.ac.uk/samp/powernoise_soft.html
> 
> I hope you enjoy it. Comments and feedback welcome.

Nice tool, thanks!

I do, anyway, have a question.

How did you test the function in order to be sure
it is generating the noise shape you wanted?

Thanks again,

bye,

-- 

piergiorgio

On Mar 23, 6:06 am, John O'Flaherty <quias...@yeeha.com> wrote:
> On Sat, 22 Mar 2008 16:03:44 -0700 (PDT), maxlittle2...@googlemail.com
> wrote:
>
>
>
> >On 22 Mar, 22:27, Erik de Castro Lopo <er...@mega-nerd.com> wrote:
> >> Andor wrote:
> >> > You must have looked in the wrong places. Searching for "pink
noise" I
> >> > immediately found
>
> >> >http://www.firstpr.com.au/dsp/pink-noise/
>
> >> Yep, thats a good easily accessible resource.
>
> >> > [1] Kasdin, N.J., Discrete simulation of colored noise and stochastic
> >> > processes and1/f? power law noise generation, Proceedings of the IEEE,
> >> > Volume 83, Issue 5, May 1995 Page(s):802 - 827.
>
> >> Unfortunately, that one is well hidden behind the IEEE knowledge firewall.
>
> >> Erik
> >> --
> >> -----------------------------------------------------------------
> >> Erik de Castro Lopo
> >> -----------------------------------------------------------------
> >> "In my opinion, shareware tends to combine the worst of
> >> commercial software (no sources) with the worst of free
> >> software (no finishing touches). I simply do not believe
> >> in the shareware market at all."  -- Linus Torvalds
>
> >Ah, well I did find those resources, but no simple "one pager" of
> >Matlab code for generating perfect 1/f^alpha noise. These pages all
> >seem to be geared to solving the problem with filters: nothing wrong
> >in that of course for certain applications but it's a bit long-winded.
> >The solution I'm proposing just constructs the appropriate power
> >spectrum and randomised phases, then uses the IFFT to get the 1/
> >f^alpha signal.
>
> >There is an interesting residual issue is the DC component or signal
> >mean: should this be zero? If so, it violates the full power-law
> >behaviour across the entire spectrum. The main problem though is that
> >1/f^alpha is undefined at f = 0.
>
> Max,
>
> Thanks for the free toy. I thought it would be interesting to listen
> to the noises and look at them, so I made one-second bursts for a
> Windows system ...
>
> for alpha = 1:3;
>  mySound = powernoise(alpha , 44100);
>  m = mean(mySound)
>  rms = norm(mySound)/sqrt(44100)
>  wavwrite(mySound,44100,strcat('PN', num2str(alpha), '.wav'));
>  plot(1:44100,mySound);
>  hold all;
> end
>
>  I found that the darker-colored noises (alpha = 2 or 3) were
> inaudible, until I later multiplied them by quite a bit. The rms
> amplitude was lots smaller than for the white noise, and maybe the
> sound system or ear doesn't respond as well either.
> On the DC question, I found that the DC level was always positive,
> always at a mean of .0048. Shouldn't the DC polarity be random?
>
> --
> John

Thanks John.

All this is to be expected: by definition, increasing alpha means that
higher frequency components fall off more and more rapidly with
increasing frequency. Eventually all the very low frequencies around
DC dominate, so I wouldn't expect good reproduction from a sound
system.

The DC level is fixed in the algorithm, regardless of alpha. My
question was more: how should we expect to deal with the issue that if
f=0, 1/f^alpha is undefined? I've settled for |P(0)|^2 = 1, where P(f)
is the Fourier transform of the signal, and that makes the entire
power spectrum follow the power law. But often, signals people prefer
mean zero, so no DC component. This seems to be more a matter of
convenience/application/convention rather than mathematical
consistency.

Max