Unit pulse for White noise

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 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?

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 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 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

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.