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Discussion Groups | Comp.DSP | Integral of White noise

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Integral of White noise - junas125 - 2005-11-22 13:54:00

What happens when you integrate white noise over time? Can anyone give a
mathematical representation of this thing?


Re: Integral of White noise - Real_McCoy - 2005-11-22 14:09:00

"junas125" <j...@yahoo.com> wrote in message
news:N...@giganews.com...
> What happens when you integrate white noise over time? Can anyone give a
> mathematical representation of this thing?
>
>
I believe this is known as a random walk but I am not sure. In engineering
terms it is just coloured noise of a sort.
It's not good to try since and slight dc and it saturates the integrator.

McC


Re: Integral of White noise - Real_McCoy - 2005-11-22 14:11:00

"junas125" <j...@yahoo.com> wrote in message
news:N...@giganews.com...
> What happens when you integrate white noise over time? Can anyone give a
> mathematical representation of this thing?
>
>

It's spectrum is defined as

S(w) = sigma^2/w^2

where sigma is the sd of the white noise and w is freq in rads/s.

McC


Re: Integral of White noise - robert bristow-johnson - 2005-11-22 14:14:00

in article N...@giganews.com, junas125 at
j...@yahoo.com wrote on 11/22/2005 13:54:

> What happens when you integrate white noise over time? Can anyone give a
> mathematical representation of this thing?

it's called "Brownian motion".  i'm gonna sidestep doing any real work with
the "mathematical representation of this thing" and recommend Google.

-- 

r b-j                  r...@audioimagination.com

"Imagination is more important than knowledge."


Re: Integral of White noise - Jerry Avins - 2005-11-22 17:42:00

junas125 wrote:
> What happens when you integrate white noise over time? Can anyone give a
> mathematical representation of this thing?

Integrate any signal with a flat spectrum and the result is a spectrum 
that tilts down at 20 dB/decade as frequency increases. You can also say 
that the spectrum tilts up at 20 dB/decade as frequency decreases, which 
implies infinite gain at DC.

The noise you ask about is called "brown noise", after the statistics of 
Brownian motion. http://www.ptpart.co.uk/colors.htm

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


Re: Integral of White noise - Tim Wescott - 2005-11-22 20:05:00

junas125 wrote:

> What happens when you integrate white noise over time? Can anyone give a
> mathematical representation of this thing?
> 
> 
While you're googling look for "Wiener Process".

White noise is stationary, meaning that knowing what time you're looking 
at it doesn't tell you anything about the noise.

Integrated Gaussian white noise has a Gaussian distribution who's 
standard deviation goes up with time as the integration period is 
increased, hence "random walk".

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com