 |
|
List Archives >
Mathcad List Archive >
Archive by date >
This Month By Date >
This Month By Topic
RE: [mathcad] Modeling White Noise
| RE: [mathcad] Modeling White Noise |
|
Author: Neil Harris
Posted: Thu, 3 Apr 2008 18:23:38 +0100
|
Bill,
Firstly, one never measures for an infinite length of time (!), so there
are fluctuations in "real-world" measurements.
Secondly, if you use the IFFT function, the noise (time-domain) will be
real-only.
Finally, if you want a band-limited noise, use the required power
spectrum for the square of the amplitude; for example
Butterworth, nth order low pass
|H(f)|^2 = fc^2n/(fc^2n + f^2n)
Butterworth, nth order high pass
|H(f)|^2 = f^2n/(fc^2n + f^2n)
I hope this helps a bit?
Neil
From: Bill E Dumke "mailto:Bill.Dumke"
Sent: 03 April 2008 14:37
To: "mathcad"
Subject: RE: [mathcad] Modeling White Noise
Neil,
This is very confusing to me. I was searching around for info on white
noise and discovered this paper:
http://www.home.agilent.com/upload/cmc_upload/All/Exp65.pdf
The paper confirms what you have said. Only the phase is random.
I am in a debate with a PhD friend of mine, and he claims "Noise is a
random process but in conductors (including resistors) it is an
one-dimensional random process".
I created a Mathcad document to match the procedure given in the Agilent
document. And true enough, the vector N is one dimensional. (Since the
white noise vector contains only real numbers, it would seem to me that
adding white noise to a carrier would only affect the amplitude of the
carrier, not the phase.)
Because of this he claims that since white noise is orthogonal to phase
noise, white noise will not affect the signal to noise performance of an
FM receiver. (But that is not what I know about FM receivers. FM is
limited by noise figure just as AM and SSB receivers are limited by
noise figure, the only difference being that FM gives better signal to
noise ratio at the output of the FM demodulator for high input signal to
noise ratios. And I seem to remember that it gives worse performance
below the limiting threshold.)
So I am confused.
Also I wonder why the "bandlimited White" noise shown at the bottom of
the page doesn't show any amplitude variation across the spectrum.
Every time I have looked at the noise coming from a filter with a
spectrum analyzer or power meter it varies in amplitude as well.
Trying to understand this,
Bill
Bill Dumke, RF Engineer
Nsight Telservices dba Cellcom
450 Security Blvd
Green Bay, WI 54313
Office: 920 617-7311
e-mail: "bill.dumke"
From: Neil Harris "mailto:N.Harris"
Sent: Thursday, April 03, 2008 7:37 AM
To: "mathcad"
Subject: RE: [mathcad] Modeling White Noise
Bill,
The definition of white noise is that it has a (long-term) power
spectrum of unity - i.e. the same as an impulse. It is only the phase
response that differs between the two.
In the time domain, the noise signal is "random" due to its random
phase.
Neil
From: Bill Dumke "mailto:billd"
Sent: 03 April 2008 12:49
To: "mathcad"
Subject: Re: [mathcad] Modeling White Noise
Thanks Neil,
But doesn't the amplitude vary randomly in amplitude as well?
Bill
Neil Harris wrote:
> Bill,
>
> The simplest way is to generate a pair of vectors of length 2^N/2 + 1;
> one has the required amplitude response, and the other is a random
phase
> generated by using the function phi := 2*pi*rnd(1).
>
> These are combined into a complex vector amplitude * exp(1j x phi)
>
> The required noise is the simply the inverse FFT of this complex
vector.
>
> Noise = IFF(complex vector)
>
> Apply appropriate scaling to get the right amplitude.
>
> Regards,
> Neil
>
>
> From: Bill E Dumke "mailto:Bill.Dumke"
> Sent: 02 April 2008 16:14
> To: "mathcad"
> Subject: [mathcad] Modeling White Noise
>
> I need a model for bandwidth limited white noise. I have Mathcad 14
but
> would prefer to use Mathcad 11 for this.
>
> Thanks, Bill
>
> Bill Dumke, RF Engineer
> Nsight Telservices dba Cellcom
> 450 Security Blvd
> Green Bay, WI 54313
>
> Office: 920 617-7311
> e-mail: "bill.dumke"
>
> Contributions: "mathcad"
> Hosted by: Adept Scientific http://www.adeptscience.com
> List Archive: http://lists.adeptscience.co.uk/
> Would you like this to come to a different email address?
> Simply leave the mailing list (see below) and re-join by sending a
> blank email from the new address to:
> "mailto:join-mathcad" or
> You are currently subscribed to mathcad as: "n.harris"
> To unsubscribe send a blank email to
> "leave-52344-494237H"
>
> Contributions: "mathcad"
> Hosted by: Adept Scientific http://www.adeptscience.com
> List Archive: http://lists.adeptscience.co.uk/
> Would you like this to come to a different email address?
> Simply leave the mailing list (see below) and re-join by sending a
> blank email from the new address to:
> "mailto:join-mathcad" or
> You are currently subscribed to mathcad as: "billd"
> To unsubscribe send a blank email to
"leave-52400-494029G"
>
>
>
>
>
|
[View Complete Thread]
Previous by date: RE: [mathcad] Modeling White Noise, Bill E Dumke
Next by date: Re: [mathcad] Modeling White Noise, Eden Mei
Previous thread: [mathcad] 3d graphs for random functions, =?iso-8859-2?Q?Damian_Ga=B3=EAziowski?=
Next thread: [mathcad] Modeling White Noise, Bill E Dumke
|
|
|
RSS Feeds
Functions
