Jerry Avins wrote:

(snip)

> "The generation of random numbers is too important to be left to chance 
> - Robert R. Coveyou" is from http://www.firstpr.com.au/dsp/rand31/ which 
> might be worth reading for other reasons.

Somewhere in Knuth's "Art of Computer Programming" he has an example
of random number generators being left to chance.  He designs a very
complicated generator which after a short while settles on a nice short
repeating pattern.

-- glen

Randy Yates wrote:

   ...

> The OP is attempting to apply function-based autocorrelation 
> in order to gain probabilistic results, and it just ain't
> gonna happen.

"The generation of random numbers is too important to be left to chance 
- Robert R. Coveyou" is from http://www.firstpr.com.au/dsp/rand31/ which 
might be worth reading for other reasons.

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

glen herrmannsfeldt <gah@ugcs.caltech.edu> writes:

> jeroen_trip wrote:
>
>
>> I'm trying to simulate a small sample, say 15 numbers, of white noise. But
>> due to chance, the autocorrelation is not exactly 0. Of course the standard
>> deviation is also not exacty 1 but I can fix that. Is there transformation
>> to get rid of the unwanted autocorrelation??
>
> I would say that if you did that, that they aren't random anymore.
>
> Well, at least one of them isn't, and another one if you normalize
> the standard deviation.
>
> Zero autocorrelation and the appropriate standard deviation is only
> true in the limit as the length of the sequence goes to infinity.

I agree with you, Glen (sorry, I just can't bring myself to write
"glen").

I think the key here is to realize that the probabilistic
autocorrelation function is not a time-domain function. It 
is computed from the joint PDF(s) of the underlying random 
variables. 

The OP is attempting to apply function-based autocorrelation 
in order to gain probabilistic results, and it just ain't
gonna happen.
-- 
%  Randy Yates                  % "Though you ride on the wheels of tomorrow,
%% Fuquay-Varina, NC            %  you still wander the fields of your
%%% 919-577-9882                %  sorrow."
%%%% <yates@ieee.org>           % '21st Century Man', *Time*, ELO
http://home.earthlink.net/~yatescr

jeroen_trip wrote:


> I'm trying to simulate a small sample, say 15 numbers, of white noise. But
> due to chance, the autocorrelation is not exactly 0. Of course the standard
> deviation is also not exacty 1 but I can fix that. Is there transformation
> to get rid of the unwanted autocorrelation??

I would say that if you did that, that they aren't random anymore.

Well, at least one of them isn't, and another one if you normalize
the standard deviation.

Zero autocorrelation and the appropriate standard deviation is only
true in the limit as the length of the sequence goes to infinity.

-- glen

MY SUGGESTION
                            go for chaotic map generators.

logical map
bernoulli map
or other chaotic maps
which generate almost near to zero A.C
refere kenichi kitayama paper of AFRICON 2002

of related properties of CHAOTIC SEQUENCES

regards
particle

Oli Filth said the following on 05/09/2006 17:33:
> robert bristow-johnson said the following on 05/09/2006 17:04:
>> Oli Filth wrote:
>>> Andre said the following on 04/09/2006 15:54:
>>>
>>>> You may consider using maximum length sequences instead.
>>>
>>> Maximum length sequences don't have zero autocorrelation anywhere.
>>
>> they can be biased upward a little so that they are zero everywhere
>> except the zero lag and lags that are an integer multiple of the
>> period.
> 
> How so?  Surely MLS are always odd in length, so they must always 
> contain a slight DC offset, and hence a slight DC offset in the 
> autocorrelation?

Ah, of course.  You mean by subtracting the DC value from each sample 
(with the proviso that the samples are no longer {+1,-1}).


-- 
Oli

robert bristow-johnson said the following on 05/09/2006 17:04:
> Oli Filth wrote:
>> Andre said the following on 04/09/2006 15:54:
>>
>>> You may consider using maximum length sequences instead.
>>
>> Maximum length sequences don't have zero autocorrelation anywhere.
> 
> they can be biased upward a little so that they are zero everywhere
> except the zero lag and lags that are an integer multiple of the
> period.

How so?  Surely MLS are always odd in length, so they must always 
contain a slight DC offset, and hence a slight DC offset in the 
autocorrelation?

> 
> but that's using *circular* autocorrelation (that's how the edge
> effects are dealt with, by wrapping it around.



-- 
Oli

robert bristow-johnson wrote:
> Oli Filth wrote:
> > Andre said the following on 04/09/2006 15:54:
> >
> > > You may consider using maximum length sequences instead.
> >
> >
> > Maximum length sequences don't have zero autocorrelation anywhere.
>
> they can be biased upward a little so that they are zero everywhere
> except the zero lag and lags that are an integer multiple of the
> period.

another thing that i forgot to point out is that the MLS is hardly a
random number since the sequence is all -1 and +1 (plus the small bias
mentioned above).  if you look at the p.d.f. function, it hardly looks
random having two dirac deltas at +/- 1.

Oli Filth wrote:
> Andre said the following on 04/09/2006 15:54:
>
> > You may consider using maximum length sequences instead.
>
>
> Maximum length sequences don't have zero autocorrelation anywhere.

they can be biased upward a little so that they are zero everywhere
except the zero lag and lags that are an integer multiple of the
period.

but that's using *circular* autocorrelation (that's how the edge
effects are dealt with, by wrapping it around.

if the OP wants to take a look at the math surrounding the MLS, there's
a little primer (or tutorial, i dunno which), at
http://www.dspguru.com/info/tutor/mls.htm .


Vladimir Vassilevsky wrote:
>
> Any sequence of random numbers can be considered as a white noise.

so a sequence of random numbers we call "pink noise" can be considered
as a white noise?

> > due to chance, the autocorrelation is not exactly 0.
>
> Certainly. It will never be 0.

a pseudo-random number sequence can conceivably be constructed to do
that.  perhaps there is an old Bell Systems Journal that spells out
how.  i wouldn't be so certain as you, Vladimir.

r b-j

jeroen_trip wrote:
> Hi all,
> 
> I'm trying to simulate a small sample, say 15 numbers, of white noise. But
> due to chance, the autocorrelation is not exactly 0. Of course the standard
> deviation is also not exacty 1 but I can fix that. Is there transformation
> to get rid of the unwanted autocorrelation??

Randomness is a tricky concept. If you could devised an RNG that always 
produces zero autocorrelation instead of random variation, you would 
know it was far from random.

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