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Gaussianity -QUery

Started by utd_anurag September 3, 2004
HI

I have a question:

1). Why do we, in most of the cases, assume a noise to be GAUSSIAN?

2). What are characteristics of Gaussian pulse?

3). what is the difference between "White gaussian Noise (WGN)"
& "Additive White gaussian Noise (AWGN)"?

Thanks



Anurag-

HI

I have a question:

1). Why do we, in most of the cases, assume a noise to be GAUSSIAN? >>> cause in most of the real life sitatuation noise is indeed GAUSSIAN.


2). What are characteristics of Gaussian pulse? 3). what is the difference between "White gaussian Noise (WGN)"
& "Additive White gaussian Noise (AWGN)"?

>>> I Dont know any specific difference between WGN and AWGN ... but
AWGN is opposite to MWGN ( m = multiplicative) where in the signal
through the channel is found by multiplying gaussian noise with the
channel symbols.

Hope this helps

Tarang
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> I have a question:
>
> 1). Why do we, in most of the cases, assume a noise to be GAUSSIAN?
> >>> cause in most of the real life sitatuation noise is indeed GAUSSIAN.

For a formal explanation of your problem, I suggest you read the Central
Limit Theorem in any statistic book. It says in summary that the convolution
of many stochastic processes tend to produce a Gaussian distribution.

>
> 2). What are characteristics of Gaussian pulse? > 3). what is the difference between "White gaussian Noise (WGN)"
> & "Additive White gaussian Noise (AWGN)"?
>
> >>> I Dont know any specific difference between WGN and AWGN ... but
> AWGN is opposite to MWGN ( m = multiplicative) where in the signal
> through the channel is found by multiplying gaussian noise with the
> channel symbols.

I agree with Tarang. White noise defines a flat spectrum, Additive is how it
is incorporated in a Stochastic process. > Hope this helps
>
> Tarang


Gaussian noise is an idealized case. Noise is often
assumed to be Gaussian in order to make the math
easier to find an analytic solution. --- Tarang Dadia <> wrote:

> Anurag-
>
> HI
>
> I have a question:
>
> 1). Why do we, in most of the cases, assume a noise
> to be GAUSSIAN? > >>> cause in most of the real life sitatuation
> noise is indeed GAUSSIAN. > 2). What are characteristics of Gaussian pulse? > 3). what is the difference between "White gaussian
> Noise (WGN)"
> & "Additive White gaussian Noise (AWGN)"?
>
> >>> I Dont know any specific difference between WGN
> and AWGN ... but
> AWGN is opposite to MWGN ( m = multiplicative)
> where in the signal
> through the channel is found by multiplying
> gaussian noise with the
> channel symbols.
>
> Hope this helps
>
> Tarang >
> _____________________________________
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=====
Juan I. Arvelo, Jr., Ph.D.
Johns Hopkins University
11100 Johns Hopkins Rd.
Laurel, MD 20723
240.228.4293

__________________________________________________



Hello,
Continuing with this discussion , can somebody pls let
me know how does noise affect in a practical scenario
( how is it concluded to be multiplicative if this is
the case).
In a simulation environment , every aspect of a
reciever like a matched filter or a equalizer depends
on AWGN scenario . How is a multiplicative noise
simulated and how is a matched filter or a equalizer
created for such a environment ?
Pls do reply.
Rgds

--- "Juan I. Arvelo, Jr., Ph.D."
<> wrote:

> Gaussian noise is an idealized case. Noise is often
> assumed to be Gaussian in order to make the math
> easier to find an analytic solution. > --- Tarang Dadia <> wrote:
>
> > Anurag-
> >
> > HI
> >
> > I have a question:
> >
> > 1). Why do we, in most of the cases, assume a
> noise
> > to be GAUSSIAN?
> >
> >
> > >>> cause in most of the real life sitatuation
> > noise is indeed GAUSSIAN.
> >
> >
> > 2). What are characteristics of Gaussian pulse?
> >
> >
> > 3). what is the difference between "White gaussian
> > Noise (WGN)"
> > & "Additive White gaussian Noise (AWGN)"?
> >
> > >>> I Dont know any specific difference between
> WGN
> > and AWGN ... but
> > AWGN is opposite to MWGN ( m = multiplicative)
> > where in the signal
> > through the channel is found by multiplying
> > gaussian noise with the
> > channel symbols.
> >
> > Hope this helps
> >
> > Tarang
> >
> >
> >
> >
> >
> >
> > _____________________________________
> > Note: If you do a simple "reply" with your email
> > client, only the
> > author of this message will receive your answer.
> > You need to do a
> > "reply all" if you want your answer to be
> > distributed to the entire
> > group.
> >
> > _____________________________________
> > About this discussion group:
> >
> > To Join:
> >
> > To Post:
> >
> > To Leave:
> >
> > Archives: http://www.yahoogroups.com/group/matlab
> >
> > More DSP-Related Groups:
> > http://www.dsprelated.com/groups.php3
> >
> >
> >
> >
> >
> >
> > ________________________________
> > Yahoo! Groups Links
> >
> > To
> >
> >
>
> =====
> Juan I. Arvelo, Jr., Ph.D.
> Johns Hopkins University
> 11100 Johns Hopkins Rd.
> Laurel, MD 20723
> 240.228.4293
>
> __________________________________________________
>

__________________________________


Just completing the excellent explanations:

>2). What are characteristics of Gaussian pulse?

A gaussian function is defined as:
f(x) = e^((x^2)/2sigma^2)

sigma = standard deviation
sigma^2 = variance

Consequently, you have a function centered arond zero,
simmetric. Sigma is an important parameter in the
graph.
The area under the curve is:
Integ(-inf,+inf){f(x)dx} = 1/sqrt(2pi.sigma^2)

Considering a normal distribution, which turns the
majority of the work in many cases pretty simple:
P(x) = (1/sqrt(2pi.sigma^2)).f(x)

We get a gaussian function normalized to unit area.

The convolution of a gaussian function is another
gaussian, the only function which has this property.

Hope it helps.

--- "Juan I. Arvelo, Jr., Ph.D."
<> escreveu:
> Gaussian noise is an idealized case. Noise is often
> assumed to be Gaussian in order to make the math
> easier to find an analytic solution. > --- Tarang Dadia <> wrote:
>
> > Anurag-
> >
> > HI
> >
> > I have a question:
> >

> > 1). Why do we, in most of the cases, assume a
> noise
> > to be GAUSSIAN?
> >
> >
> > >>> cause in most of the real life sitatuation
> > noise is indeed GAUSSIAN.
> >
> >
> >
> >
> >
> > 3). what is the difference between "White gaussian
> > Noise (WGN)"
> > & "Additive White gaussian Noise (AWGN)"?
> >
> > >>> I Dont know any specific difference between
> WGN
> > and AWGN ... but
> > AWGN is opposite to MWGN ( m = multiplicative)
> > where in the signal
> > through the channel is found by multiplying
> > gaussian noise with the
> > channel symbols.
> >
> > Hope this helps
> >
> > Tarang
> >
> >
> >
> >
> >
> >
> > _____________________________________
> > Note: If you do a simple "reply" with your email
> > client, only the
> > author of this message will receive your answer.
> > You need to do a
> > "reply all" if you want your answer to be
> > distributed to the entire
> > group.
> >
> > _____________________________________
> > About this discussion group:
> >
> > To Join:
> >
> > To Post:
> >
> > To Leave:
> >
> > Archives: http://www.yahoogroups.com/group/matlab
> >
> > More DSP-Related Groups:
> > http://www.dsprelated.com/groups.php3
> >
> >
> >
> >
> >
> >
> > ________________________________
> > Yahoo! Groups Links
> >
> > To
> >
> >
>
> =====
> Juan I. Arvelo, Jr., Ph.D.
> Johns Hopkins University
> 11100 Johns Hopkins Rd.
> Laurel, MD 20723
> 240.228.4293
>
> __________________________________________________
> >
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> group.
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> _____________________________________
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> Yahoo! Groups Links >
>

=====
-----------------------------------
Aurio Gonlez Tenio
Mestre em Engenharia Elrica - Telecomunicaes
Faculdade de Engenharia Elrica e de Computao - FEEC
Universidade Estadual de Campinas - UNICAMP
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