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Wierner Filter implementation in Modelling Application

Started by aarthis May 15, 2007
Hi,

If anyone has followed the book: " Adaptive Filters Theory and
Applications" by B.Ferhang-Boroujeny as a text book for Adaptive Filters
course, please let me know. I am trying to solve some problems to
understand the concepts behind white noise. Could anyone please answer
these questions or refer some link as resources:

1. What does white noise with zero mean and unit variance mean? 
2. If we call a white noise as u(n), then what is its Z transform U(z)? 
3. What is its Autocorrelation and how is it calculated?
4. Why do we always assume this kind of input for many of the problems?

Thanks,
Aarthi




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On 16 May, 01:50, "aarthis" <aarthi.s...@gmail.com> wrote:
> Hi, > > If anyone has followed the book: " Adaptive Filters Theory and > Applications" by B.Ferhang-Boroujeny as a text book for Adaptive Filters > course, please let me know. I am trying to solve some problems to > understand the concepts behind white noise. Could anyone please answer > these questions or refer some link as resources:
Lots of people here can answer them. Few, if any, will. These are very basic questions which are fundamental to DSP, and not particular to your textbook. In fact, those questions seem like homework to me, so I will do my best *not* to answer them...
> 1. What does white noise with zero mean and unit variance mean?
The terms "mean" and "variance" are basic concepts from statistics, nad I assume you know what they are. The concepts apply straight forward to signals as well. The term "white" is used to describe *noise*. A different type of noise is "colored" (or, more specifically, "pink") noise. These terms can be traced back all the way to ol'e sir Isaac himself. Because of his famous optical experiment where he found that white light...? The answer will lead you to a characteristic property with white noise that *might* be the answer to question 2.
> 2. If we call a white noise as u(n), then what is its Z transform U(z)?
I don't know exactly what is meant here, but if you want a formula, you need to find the characteristic formula for white noise in part 1).
> 3. What is its Autocorrelation and how is it calculated?
Answer 1) and 2) and the answer to this is self-evident by the time you get here.
> 4. Why do we always assume this kind of input for many of the problems?
Ah, this is the deep one. The key here is to contemplate the alternatives to *not* making assumptions as the above. [ And yes, I *do* have way too much time on my hands. We are in port 12 hrs early for crew change, and I am on night shift with staying awake as my only task for the night. ] Rune
aarthis wrote:
> Hi, > > If anyone has followed the book: " Adaptive Filters Theory and > Applications" by B.Ferhang-Boroujeny as a text book for Adaptive Filters > course, please let me know. I am trying to solve some problems to > understand the concepts behind white noise. Could anyone please answer > these questions or refer some link as resources: > > 1. What does white noise with zero mean and unit variance mean? > 2. If we call a white noise as u(n), then what is its Z transform U(z)? > 3. What is its Autocorrelation and how is it calculated? > 4. Why do we always assume this kind of input for many of the problems? > > Thanks, > Aarthi > >
Ye cannae take the z-transform of white noise Captain! It's a random signal with only a probability of where the next sample is. You can specifiy it's variance and mean only if it is Guassian. Autocorrelation is an impulse at delay zero.(look it up) Assumption - well it makes the problems tractable but we don't always. There are many papers on non-Guassian signals and noise but what do you gain by the complexity?... Not a lot I would say. Wang King

Rune Allnor wrote:


>>If anyone has followed the book: " Adaptive Filters Theory and >>Applications" by B.Ferhang-Boroujeny as a text book for Adaptive Filters >>course, please let me know. I am trying to solve some problems to >>understand the concepts behind white noise. Could anyone please answer >>these questions or refer some link as resources: > > > Lots of people here can answer them. Few, if any, will. These are > very > basic questions which are fundamental to DSP, and not particular > to your textbook. In fact, those questions seem like homework to me, > so I will do my best *not* to answer them...
Yea, this is a case of studiotism.
> >>1. What does white noise with zero mean and unit variance mean?
It means the only one thing: it is too early for someone to think about the adaptive filters. He needs to start with the "ABC" book on math. VLV
> You can specifiy it's variance and mean only if it is Guassian.
Are you sure about that ?!? While it is true that if the noise is white and Gaussian, the mean and variance suffices to describe the process, it does not lead to the fact that the mean and variance for any non-Gaussian white noise is undefined.