# Re: confused about white noise definition

Randy Yates wrote:
Les Cargill <lcargill@xxxxxxxxxx> writes:

Randy Yates wrote:
karl bezzoto <karl.bezzoto@xxxxxxxxxxxxxx> writes:

Hello,
Per definition a white noise signal has a zero mean value.
Really? By whos definition? Neither of two definitions I have found
require the mean to be zero. I examine this question in
some detail here:

http://www.digitalsignallabs.com/white.pdf

Can't you say : " If white noise has a nonzero mean, then
white noise is a signal" ( has nonzero information-content ) ,

Hi Les,

First of all, note that I reversed my conclusion in the Brown definition
(constant PSD) of this paper to conclude such a definition does imply a
zero mean.

I saw that. *Kewl*. I always wondered that.

What I think you're hinting at is the concept of randomness. How random
is "random"? Obviously a plain DC value isn't random at all. But what
about a DC value with some noise on it? Is that a little random? A lot
random? COMPLETELY (purely) random?

Well, think CDMA. If there exists a transform T such that a ..
"variable" DC offset may be decoded from something that is otherwise
indistinguishable from noise ( we're assuming the transform is
secret ), then it's not purely random. Obviously, the sequences
in CDMA are *pseudo*random.

I believe the answer lies in the autocorrelation function (which of
course is uniquely defined by the PSD as well). If the process is
_purely_ random, then there is absolutely no correlation
sample-to-sample. That's what makes it white.

Yes, that was very nice.

Papoulis' definition is somewhat odd since he decided to utilize
not the autocorrelation function but the autocovariance function,
in which case the mean doesn't matter.

His is generative, and may or may not be useful as a description. :)

Perhaps I'm saying the same thing over and over... or hopefully this
helps.

--
Les Cargill
.

## Relevant Pages

• Re: Auto-correlation of white noise
... The answer depends on what properties you think white noise ... function is an impulse. ... equivalent to the requirement that the autocorrelation function ... that the mean be zero. ...
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• Re: Is White Noise Necessarily Zero-Mean?
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• Re: Is White Noise Necessarily Zero-Mean?
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• Re: Is White Noise Necessarily Zero-Mean?
... Can we conclude that Zhas zero mean? ... The intuitive reason that comes to ... process is white noise if the values xand xare uncorrelated ... R is the correlation matrix. ...
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• Re: confused about white noise definition
... Per definition a white noise signal has a zero mean value. ... (constant PSD) ... not the autocorrelation function but the autocovariance function, ...
(comp.dsp)