Do you know that there is one-to-one correspondence between frequency and time domain images of a function? Some people say that white noise has white noise in frequency domain. However, we know that white noise has a frequency spectrum of constant "1". It is not a Guassian. The sum of all sines in freq domain is a Unit response! Why do they use all these complex random generators to produce a single pulse? Don't they believe that one followed by all zeroes is the most unpredictable sequence on the planet?
Unit pulse for White noise
Started by ●November 2, 2011
Reply by ●November 2, 20112011-11-02
On Wed, 02 Nov 2011 22:36:27 +0200, valtih1978 wrote:> Do you know that there is one-to-one correspondence between frequency > and time domain images of a function? Some people say that white noise > has white noise in frequency domain. However, we know that white noise > has a frequency spectrum of constant "1". It is not a Guassian. The sum > of all sines in freq domain is a Unit response! > > Why do they use all these complex random generators to produce a single > pulse? Don't they believe that one followed by all zeroes is the most > unpredictable sequence on the planet?So, this is either a troll or you are speaking way past your knowledge base. I'll give you the benefit of the doubt: The _Fourier transform_ of a unit pulse is everywhere 1 (or at least constant and real, depending on how you define your Fourier transform gains). The _power spectrum_ of white noise is everywhere constant, and real by the definition of the way that power spectra are calculated. But that's about where the similarity ends. The transform of a unit pulse is the transform of the signal itself. The transform of white noise is the transform of the expected value of the signal's autocorrelation function. If you take the Fourier transform of some sample white noise signal, then the expected value of the signal's magnitude is one, but you can't say anything about it's phase -- and in general you can expect that the phase will be completely random as a consequence of the signal's white Gaussian nature. The phase of a unit pulse, however, is quite well defined -- it is everywhere 0. -- www.wescottdesign.com
Reply by ●November 2, 20112011-11-02
On Nov 2, 4:36�pm, valtih1978 <d...@not.email.me> wrote:> Do you know that there is one-to-one correspondence between frequency > and time domain images of a function? Some people say that white noise > has white noise in frequency domain. However, we know that white noise > has a frequency spectrum of constant "1". It is not a Guassian. The sum > of all sines in freq domain is a Unit response! > > Why do they use all these complex random generators to produce a single > pulse? Don't they believe that one followed by all zeroes is the most > unpredictable sequence on the planet?You are describing an energy signal. White noise in practice is more concerned with a power signal. In other words, a single pulse into a speaker will not exactly sound like white noise. So how do you build a continuous power white noise signal? That is a little bit tougher.
Reply by ●November 4, 20112011-11-04
On Wed, 02 Nov 2011 17:18:30 -0500, Tim Wescott <tim@seemywebsite.com> wrote:>On Wed, 02 Nov 2011 22:36:27 +0200, valtih1978 wrote: > >> Do you know that there is one-to-one correspondence between frequency >> and time domain images of a function? Some people say that white noise >> has white noise in frequency domain. However, we know that white noise >> has a frequency spectrum of constant "1". It is not a Guassian. The sum >> of all sines in freq domain is a Unit response! >> >> Why do they use all these complex random generators to produce a single >> pulse? Don't they believe that one followed by all zeroes is the most >> unpredictable sequence on the planet? > >So, this is either a troll or you are speaking way past your knowledge >base. I'll give you the benefit of the doubt:[Snipped by Lyons] Hi Tim, My complements to you for having such a high tolerance-threshold for thses types of posts. [-Rick-]
Reply by ●November 25, 20112011-11-25
Reply by ●November 25, 20112011-11-25
On 11/25/2011 9:36 AM, valtih1978 wrote:> Why understanding the difference between white spectrum and white noise > is a bad idea?Understanding the difference is a good idea. Tim tried to explain it to you. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●November 25, 20112011-11-25
On 25 Nov, 15:36, valtih1978 <d...@not.email.me> wrote:> Why understanding the difference between white spectrum and white noise > is a bad idea?As with Tim, I'll also give the benefit of the doubts, as I suspect you might not be a native English speaker: *Understanding* the relation is a very good idea. Throwing words and terms together at random into almost-meaningful sentences is not. A I said, I don't think English is your first language and your posts don't make perfect sense. That might be beacuse of your lack of knowledge about the subject, or because of your wanting skills in writing English. Or both. Rune
Reply by ●November 25, 20112011-11-25
> *Understanding* the relation is a very good idea. Throwing words and terms together at random into almost-meaningful sentences is not. Absolutely meaningful sentences can come only from somebody who understands everything. There is no need to post any questions in this case. I draw the contradictions that I see for others could point me out, which premises are wrong. This is done with care rather than "at random".
Reply by ●November 25, 20112011-11-25
On 25 Nov, 17:30, valtih1978 <d...@not.email.me> wrote:> �> *Understanding* the relation is a very good idea. > Throwing words and terms together at random into > almost-meaningful sentences is not. > > Absolutely meaningful sentences can come only from somebody who > understands everything. There is no need to post any questions in this > case. > > I draw the contradictions that I see for others could point me out, > which premises are wrong. This is done with care rather than "at random".If so, then Tim was spot on: You are talking about stuff you don't understand. Rune
Reply by ●November 25, 20112011-11-25
On 11/25/11 9:36 AM, valtih1978 wrote:> Why understanding the difference between white spectrum and white noise > is a bad idea?can you tell us what the difference is? i can tell you that, from the point-of-view of audio, white noise sounds line one thing and a dirac impulse sounds like another. so why are their spectrums *ostensibly* the same flat line? the answer is that the power spectrum of white noise does not (and can not) have phase information. the phase information is random (which changes for each statistical "sample" of the noise), just as the white noise is. the Fourier spectrum of a dirac impulse *does* have well-defined phase information which is zero-phase everywhere. but this skips over the subtleties of the different classes of the two signals. white noise (if you were to bandlimit it to some finite bandwidth) is an infinite energy and finite power signal. so how you define its spectrum must necessarily be different than how you define the spectrum of a finite energy signal which is what an impulse (if you also limit the height and width of the nascent impulse). finite energy signals happen sorta once. they go "blap" and then they're done. infinite energy, finite power signals go on and on and on. so they cannot be compared directly. in addition (as i parenthetically noted above) both white noise and dirac impulses are mathematical idealizations of signals that are physically nonexistent. white noise, having infinite bandwidth, actually has infinite power, not finite power. dirac impulses have zero width and infinite height, real mathematicians refuse to recognize the dirac delta function as a "function" in the strict mathematical sense of the word. so valtih, if you can understand those three different classes of what is different (moving from the most immediate practical difference on to the most esoteric fine points), then you might have some idea of what it is that you are pondering. best, -- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."
