# Laplace transform of white noise, o/p spectral density

Discussion in 'Homework Help' started by dvishu, Jul 30, 2013.

1. ### dvishu Thread Starter New Member

Jul 30, 2013
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HI,
1) Is there is any problem in asking the 'Laplace transform of white noise'? If no, what is it? if yes, why?

2)If a white noise is passed through a system with transfer function H(jω), what will be the output and output spectral desity?

Thank you

2. ### WBahn Moderator

Mar 31, 2012
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Since these are homwork questions, we won't just tell you the answers. We expect you to make some attempt at it. Use your best reasoning to try to say something that is applicable to the questions. That will give us a point to work from in order to guide you to an acceptable answer.

Start be telling us what you know about "white noise".

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3. ### dvishu Thread Starter New Member

Jul 30, 2013
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Actually i posted it in the wrong place. this wasnt an homework thing Im working professional and came across this type of questions while preparing for Masters. But ill prefer to get the aswers here itself w/o posting it elsewhere in the site.
White noise is a randon natured signal which contains all the possible frequencies.
LT you can say as a superset of Fourier transform in which all the frequencies are noted in terms of single frequency sinusoidal components with only difference that unlike FT the real part is also considered in LT(hope that xplntn is true)
Spectraal density is the power(or whatever else like amplitude we are considering) per unit frequency

4. ### dvishu Thread Starter New Member

Jul 30, 2013
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Also please do mention, in which area i should post, when i am posting it for the next time
Thank You

5. ### WBahn Moderator

Mar 31, 2012
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Posting here is fine, or in the General Electronics Chat forum.

So if white noise contains all frequencies, (and without giving preference to one frequency over another), then what would your guess be about the power spectral density of white does as a function of frequency.

Hint, if the answer to the above isn't true, we call it pink noise instead of white noise.

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6. ### dvishu Thread Starter New Member

Jul 30, 2013
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sinse it contains all the frequencies the PSD will be constant throughout.
Does it means LT will be a constant then? But then how can it be, as the inverse LT of a constant is an impulse?

7. ### WBahn Moderator

Mar 31, 2012
18,085
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There are several qualitative ways to look at it.

It takes an impulse to excite all of the frequencies in a system response.

Just as an impulse in the freqquency domain transforms to a single frequency over all time in the time domain, an impulse in the time domain mapse to all frequencies all frequencies in the frequency domain, and all frequencies in the frequency domain maps to a single time in the time domain.

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8. ### dvishu Thread Starter New Member

Jul 30, 2013
5
0
That much i had got. I mean the two basic point i knew was
1)
• white noise contains all frequency, literally. By 'literally' what i meant is that if you cut the signal into infinitesimally small parts and check its frequency and continues this experiment infinite number of times, we will get all the frequencies(positive ones only which has physical meaning)
• A impulse also contains all frequencies. But here the case is like if you add infinite number of sine/cosine wave(in time domain) each containing separate and all frequencies from 0 to infinity, you will get an impulse.

So my question again is
-Does these to points sufficient enuf to say the transform of both of them is a constant in frequeny domain?
-if so, it will become a many to one mapping and then how it can become a function yet alone an invertible one!?
-Or is a white noise is the real-face of a proper impulse? i.e, does passing an impulse though a speaker and passing a white noise are one & the same?