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Low pass filtration of white noise

Started by Unknown March 18, 2007
Hello,

The scenario:

A white noise signal. (Uniformly distributed between 0 and 1)
A square pulse signal in the time domain. The first zero of the sinc
function in the amplitude spectrum is at 50 Hz.

The result of the convolution of the two above signals is a gaussian
distributed signal.

How can I predict that?

Thank you!

nothxx@gmail.com wrote:
> Hello, > > The scenario: > > A white noise signal. (Uniformly distributed between 0 and 1) > A square pulse signal in the time domain. The first zero of the sinc > function in the amplitude spectrum is at 50 Hz. > > The result of the convolution of the two above signals is a gaussian > distributed signal.
How much will you bet?
> How can I predict that?
If you know it, why predict it? Is this homework? Jerry -- Engineering is the art of making what you want from things you can get. ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
nothxx@gmail.com wrote on Sunday 18 Mar 2007 10:17:

> Hello, > > The scenario: > > A white noise signal. (Uniformly distributed between 0 and 1) > A square pulse signal in the time domain. The first zero of the sinc > function in the amplitude spectrum is at 50 Hz. > > The result of the convolution of the two above signals is a gaussian > distributed signal. > > How can I predict that?
Central limit theorem? -- Oli
On Mar 18, 1:19 pm, Jerry Avins <j...@ieee.org> wrote:
> not...@gmail.com wrote: > > Hello, > > > The scenario: > > > A white noise signal. (Uniformly distributed between 0 and 1) > > A square pulse signal in the time domain. The first zero of the sinc > > function in the amplitude spectrum is at 50 Hz. > > > The result of the convolution of the two above signals is a gaussian > > distributed signal. > > How much will you bet? > > > How can I predict that? > > If you know it, why predict it? Is this homework? > > Jerry > -- > Engineering is the art of making what you want from things you can get. > =AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=
=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF= =AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF I can do a lot of practical things but I would also like to know the theory. I won't settle with observing a result. I would like to be able to explain it. This is not homework, but even if it was does it really matter for you? R=2EA Alters: Wide Band Systems and Gaussianity, IEEE Transactions on Information Theory, IT-21, November 1975, pp 679-82 states that if the "duration" of the impulse response of the filter is greater than the "duration" of the autocorrelation of the input then the pdf will tend towards the gaussian distribution independent of the pdf of the input signal. So is that the way to do it or can it be expressed in another way?
On 18 Mar, 11:17, not...@gmail.com wrote:
> Hello, > > The scenario: > > A white noise signal. (Uniformly distributed between 0 and 1)
Does this qualify as white noise? I always thought that the noise had to be Gaussian to be white... Rune
On 18 Mar, 13:51, run...@gmail.com wrote:

> This is not homework, but even if it was does it really matter for > you?
Yes. The people here are very helpful with solving problems people come across. However, people here consistently do *not* give away homework for free. The reason is very simple: You could become a colleague one day. I, for one, would not like to work along side someody who have the formal certificates but not the skills and knowledge requered for the job. Rune
Rune Allnor wrote on Sunday 18 Mar 2007 15:12:

> On 18 Mar, 11:17, not...@gmail.com wrote: >> Hello, >> >> The scenario: >> >> A white noise signal. (Uniformly distributed between 0 and 1) > > Does this qualify as white noise? I always thought that > the noise had to be Gaussian to be white...
"White" refers to the PSD, or equivalently, the autocorrelation function of the signal. "Gaussian" refers to the amplitude distribution (i,e. it describes p(x)). The two often occur together (as in AWGN), but are in fact completely independent characteristics. -- Oli
On Mar 18, 4:15 pm, "Rune Allnor" <all...@tele.ntnu.no> wrote:
> On 18 Mar, 13:51, run...@gmail.com wrote: > > > This is not homework, but even if it was does it really matter for > > you? > > Yes. The people here are very helpful with solving problems > people come across. However, people here consistently do > *not* give away homework for free. The reason is very simple: > You could become a colleague one day. I, for one, would not > like to work along side someody who have the formal certificates > but not the skills and knowledge requered for the job. > > Rune
Good point. I'm interested in understanding this. I'm not looking for a full description but rather a hint or a reference. I only have a 30 year only article for reference. Nothing newer if it exists. White noise is when a signals autocorrelation is a delta function. So white noise signals amplitudes can be distributed in many ways. As far as I know
runech@gmail.com writes:
> [...] > This is not homework, but even if it was does it really matter for > you?
I can't speak for the others, but, yes, it does matter to me. -- % Randy Yates % "How's life on earth? %% Fuquay-Varina, NC % ... What is it worth?" %%% 919-577-9882 % 'Mission (A World Record)', %%%% <yates@ieee.org> % *A New World Record*, ELO http://home.earthlink.net/~yatescr
runech@gmail.com writes:

> On Mar 18, 4:15 pm, "Rune Allnor" <all...@tele.ntnu.no> wrote: >> On 18 Mar, 13:51, run...@gmail.com wrote: >> >> > This is not homework, but even if it was does it really matter for >> > you? >> >> Yes. The people here are very helpful with solving problems >> people come across. However, people here consistently do >> *not* give away homework for free. The reason is very simple: >> You could become a colleague one day. I, for one, would not >> like to work along side someody who have the formal certificates >> but not the skills and knowledge requered for the job. >> >> Rune > > Good point. I'm interested in understanding this. I'm not looking for > a full description but rather a hint or a reference. I only have a 30 > year only article for reference. Nothing newer if it exists.
Consider what happens when you sum N, independent, uniform RV's together. Take the limit as N approaches infinity. Here are a few of my standard references. @book{papoulis, title = "Probability, Random Variables, and Stochastic Processes", author = "{Athanasios~Papoulis}", publisher = "WCB/McGraw-Hill", edition = "Third", year = "1991"} @book{garcia, title = "Probability and Random Processes for Electrical Engineering", author = "{Alberto~Leon-Garcia}", publisher = "Addison-Wesley", year = "1989"} @BOOK{viniotis, title = "{Probability and Random Processes for Electrical Engineers}", author = "{Yannis~Viniotis}", publisher = "WCB McGraw-Hill", year = "1998"} --RY -- % Randy Yates % "With time with what you've learned, %% Fuquay-Varina, NC % they'll kiss the ground you walk %%% 919-577-9882 % upon." %%%% <yates@ieee.org> % '21st Century Man', *Time*, ELO http://home.earthlink.net/~yatescr