Re: confused about white noise definition
- From: Les Cargill <lcargill@xxxxxxxxxx>
- Date: Sat, 15 Aug 2009 23:12:23 -0400
Randy Yates wrote:
Les Cargill <lcargill@xxxxxxxxxx> writes:
Randy Yates wrote:karl bezzoto <karl.bezzoto@xxxxxxxxxxxxxx> writes:Can't you say : " If white noise has a nonzero mean, then
Hello,Really? By whos definition? Neither of two definitions I have found
Per definition a white noise signal has a zero mean value.
require the mean to be zero. I examine this question in
some detail here:
white noise is a signal" ( has nonzero information-content ) ,
leading to a contradiction?
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
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
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