As explained in discussion:
White noise in frequency domain =/= noise spectrum

The spectrum of white noise is obtained in two steps:

1. By Computing the auto-correlation of noise. <= this turns out to look like an impulse due to certain mathematical properties of noise.
2. By Computing FT of result of step 1. <= since the result of step 1 turns out to be like an impulse therefore its FT should be a constant 1. 

"They" whoever they are, do not use complex generators to generate a single pulse (impulse function), they use it to generate a sequence who's autocorrelation will be an impulse function.

As explained in discussion:
White noise in frequency domain =/= noise spectrum

The spectrum of white noise is obtained in two steps:

1. By Computing the auto-correlation of noise. <= this turns out to look like an impulse due to certain mathematical properties of noise.
2. By Computing FT of result of step 1. <= since the result of step 1 turns out to be like an impulse therefore its FT should be a constant 1. 

"They" whoever they are, do not use complex generators to generate a single pulse (impulse function), they use it to generate a sequence who's autocorrelation will be an impulse function.

On Fri, 25 Nov 2011 19:10:04 +0000 (UTC), Rob Gaddi <rgaddi@technologyhighland.invalid> wrote:
> On Fri, 25 Nov 2011 16:36:14 +0200, valtih1978 wrote:
>
>> Why understanding the difference between white spectrum and white noise
>> is a bad idea?
>
> Why is a raven like a writing desk?

They're both examples of poe conductors?



Frank McKenney
-- 
    Fortunately, man was given a sense of humor to help
    compensate for nature's law of gravity.
-- 
Frank McKenney, McKenney Associates
Richmond, Virginia / (804) 320-4887
Munged E-mail: frank uscore mckenney aatt mindspring ddoott com

On 25 Nov, 18:26, robert bristow-johnson <r...@audioimagination.com>
wrote:
> 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. &#4294967295;the phase information is random (which
> changes for each statistical "sample" of the noise), just as the white
> noise is. &#4294967295;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. &#4294967295;white noise (if you were to bandlimit it to some finite
> bandwidth) is an infinite energy and finite power signal. &#4294967295;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. &#4294967295;they go "blap" and then
> they're done. &#4294967295;infinite energy, finite power signals go on and on and
> on. &#4294967295;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. &#4294967295;white noise, having infinite bandwidth,
> actually has infinite power, not finite power. &#4294967295;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.

There is one more subtlety that one needs to be aware of:

When dealing with stochastic signals, one does not deal
wit the DFT of the signal itself, but the DFT of the
*autocorrelation* of the signal. From a mathematical
point of view, this is taken care of by the distinction
between energy and power signals.

The consequence is that phase information is *lost* when
computing the power spectrun (which is a different thing
than the DFT) of stochastic signals.

Again: The phase is *not* 0, it is *lost*.

Simplified, the power spectrum S_xx(w) is compted from
the FT X(w) of the signal x(t) as ('simplified' because
certain technical issues with the DFT has to be addressed
during actual computations)

S_xx(w) = |X(w)|^2 = X(w)*conj(X(w))

X(w) might well have a non-vanishing imaginary component
but S_xx(x) is still real-valued.

Rune

On Fri, 25 Nov 2011 16:36:14 +0200, valtih1978 wrote:

> Why understanding the difference between white spectrum and white noise
> is a bad idea?

Who said it was?  For that matter, who said that white noise doesn't have 
a white power spectral density?

-- 
Tim Wescott
Control system and signal processing consulting
www.wescottdesign.com

On Fri, 25 Nov 2011 19:10:04 +0000 (UTC), Rob Gaddi
<rgaddi@technologyhighland.invalid> wrote:

>On Fri, 25 Nov 2011 16:36:14 +0200, valtih1978 wrote:
>
>> Why understanding the difference between white spectrum and white noise
>> is a bad idea?
>
>Why is a raven like a writing desk?

Because there is a B in both and an N in neither.

>-- 
>Rob Gaddi, Highland Technology -- www.highlandtechnology.com
>Email address domain is currently out of order.  See above to fix.


Eric Jacobsen
Anchor Hill Communications
www.anchorhill.com

On Fri, 25 Nov 2011 16:36:14 +0200, valtih1978 wrote:

> Why understanding the difference between white spectrum and white noise
> is a bad idea?

Why is a raven like a writing desk?

-- 
Rob Gaddi, Highland Technology -- www.highlandtechnology.com
Email address domain is currently out of order.  See above to fix.

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."

On 25 Nov, 17:30, valtih1978 <d...@not.email.me> wrote:
> &#4294967295;> *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