# Wierner Filter implementation in Modelling Application

Started by 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
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

_____________________________________
Do you know a company who employs DSP engineers?
Is it already listed at http://dsprelated.com/employers.php ?
```
```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
> 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...?

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
> 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
>>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

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.

```