HighBeam Research - Newspaper archives and journal articles
Options
Cancel changes
Follow us:
  • Subscription benefits
  • Log in
  • Sign up for a free, 7-day trial
  • Publications
  • Research topics
  • Topics home
  • People
    • Artists and Entertainers
    • Company executives
    • Historical figures
    • Politicians and Government officials
    • World Leaders
  • Issues and Events
    • Health and Medicine
    • Historical Events
    • Religion and Theology
    • Science and Technology
  • Places
  • Organizations
  • A-Z
    • A-G
    • H-O
    • P-T
    • U-Z
    • 0-9
  • Publications home
  • Journals
    • Academic journals
    • Business journals
    • Education journals
    • Math and Engineering journals
    • Medical journals
    • Science and Technology journals
    • Trade journals
  • Magazines
    • Business magazines
    • Computer magazines
    • Education magazines
    • Industry magazines
    • Lifestyle magazines
    • Medical magazines
  • Newspapers
    • International newspapers and newswires
    • Reports, newsletters, and transcripts
    • U.K. newspapers
    • U.S. newspapers and newswires
  • Reference works and books
    • Almanacs
    • Dictionaries and thesauruses
    • Encyclopedias
    • Non-fiction books
  • Subscription benefits
  • Log in
  • PUBLICATIONS HOME
  • Journals
    • Academic journals
    • Business journals
    • Education journals
    • Math and Engineering journals
    • Medical journals
    • Science and Technology journals
    • Trade journals
  • Magazines
    • Business magazines
    • Computer magazines
    • Education magazines
    • Industry magazines
    • Lifestyle magazines
    • Medical magazines
  • Newspapers
    • International newspapers and newswires
    • Reports, newsletters, and transcripts
    • U.K. newspapers
    • U.S. newspapers and newswires
  • Reference works and books
    • Almanacs
    • Dictionaries and thesauruses
    • Encyclopedias
    • Non-fiction books
Home » Publications » Math and Engineering journals » EE-Evaluation Engineering » May 2008 »
  • Save
    This article has been saved!
    You may organize and add notes about this article below.
    This article has been saved!
    View all saved articles
  • Export

    To export this article to Microsoft Word, please log in or subscribe.

    Have an account? Please log in

    Not a subscriber? Sign up today

  • Print
  • Cite

    MLA

    Lecklider, Tom. "The colorful world of noise.(SIGNAL SOURCES)." EE-Evaluation Engineering. NP Communications, LLC. 2008. HighBeam Research. 21 Apr. 2018 <https://www.highbeam.com>.

    Chicago

    Lecklider, Tom. "The colorful world of noise.(SIGNAL SOURCES)." EE-Evaluation Engineering. 2008. HighBeam Research. (April 21, 2018). https://www.highbeam.com/doc/1G1-179195185.html

    APA

    Lecklider, Tom. "The colorful world of noise.(SIGNAL SOURCES)." EE-Evaluation Engineering. NP Communications, LLC. 2008. Retrieved April 21, 2018 from HighBeam Research: https://www.highbeam.com/doc/1G1-179195185.html

    Please use HighBeam citations as a starting point only. Not all required citation information is available for every article, and citation requirements change over time.

The colorful world of noise.(SIGNAL SOURCES)

EE-Evaluation Engineering
EE-Evaluation Engineering

See all results for this publication

Browse back issues of this publication by date

May 1, 2008 | Lecklider, Tom | Copyright
COPYRIGHT 2009 Nelson Publishing. This material is published under license from the publisher through the Gale Group, Farmington Hills, Michigan. All inquiries regarding rights or concerns about this content should be directed to Customer Service.
  • Permalink

    Create a link to this page

    Copy and paste this link tag into your Web page or blog:

    <a href="https://www.highbeam.com/doc/1G1-179195185.html" title="The colorful world of noise.(SIGNAL SOURCES) | HighBeam Research">The colorful world of noise.(SIGNAL SOURCES)</a>

Although much telecom testing involves additive white Gaussian noise (AWGN), white noise does not need to be Gaussian, nor is Gaussian noise necessarily white. White noise is defined by two characteristics: It has a zero mean value, and its autocorrelation is represented by a delta function. In other words, successive values are completely uncorrelated with previous values.

In the frequency domain, such a time-domain function has a constant power spectral density. This means that the spectrum of an ideal white noise source has constant power per cycle regardless of frequency.

Practical white noise sources are flat within some small deviation across a defined frequency band. For example, the Model WGN-1/200 White Noise Generator from dBm is specified as producing -87-dBm/Hz noise density with 0.5-dB flatness from 1 MHz to 200 MHz.

[FIGURE 1 OMITTED]

By definition, successive values of a truly random variable cannot be predetermined. Nevertheless, all of the values that occur within an arbitrarily large set of observations determine a distribution. The Gaussian or normal distribution is perhaps the most common and defined by the probability density function (PDF)

P(x) = [1/[[sigma][square root of (2[pi])]]] = [e.sup.[-(x-[mu])[.sup.2]]/[2[[sigma].sup.2]]] (1)

where [mu] = the mean

[[sigma].sup.2] = the variance

[sigma] = the standard deviation

When [sigma] = 1.0 and [mu] = 0.0, the definition simplifies to the standard form of the normal distribution

N(x) = [1/[square root of (2[pi])]] [e.sup.[-[x.sup.2]]/2] (2)

This equation describes the familiar bell-shaped curve shown in Figure 1. The probability density at the mean is 0.3989, at 1[sigma] larger or smaller = 0.2420, 2[sigma] = 0.0540, and 3[sigma] = 0.004432. Because of the square term in the exponent, the probability density falls off very quickly above 3[sigma] so that at 5[sigma] away from the mean N(x) = 0.000001487.

A large series of observed values can conform to a Gaussian distribution but occur in time in a deterministic, highly ordered manner. The signal would not have a flat spectrum and could not be used for noise testing. It would have a Gaussian distribution but would not be white--successive values would not be statistically independent.

Gaussian white noise has the benefit of a well-understood and compact mathematical description. Even if the actual distribution is not quite Gaussian, the Normal distribution often is assumed to apply because it simplifies further analysis.

The integral of the PDF is the cumulative probability density function (CDF), also shown in Figure 1. It indicates the probability that a value is to the left of any arbitrary point. For example, the probability that a sample within a Gaussian distribution has a value less than +1.0 is about 0.84. Obviously, the probability that a value lies between -5 and +5 is close to 1. …


To read the full text of this article and others like it, subscribe today!



Related articles on HighBeam Research

Monthly Weather Review
The Discrete Brier and Ranked Probability Skill Scores

Monthly Weather Review; January 1, 2007

By Weigel, Andreas P Liniger, Mark A Appenzeller, Christof; 700+ words
ABSTRACT The Brier skill score (BSS) and the ranked probability skill score (RPSS) are widely used measures to describe the quality of categorical probabilistic forecasts. They quantify the extent to which a forecast strategy improves predictions with respect to a (usually climatological) reference…
Psychonomic Bulletin & Review
Effects of Redundant Auditory Stimuli on Reaction Time

Psychonomic Bulletin & Review; February 1, 2007

By Schröter, Hannes Ulrich, Rolf Miller, Jeff; 700+ words
Auditory redundancy gains were assessed in two experiments in which a simple reaction time task was used. In each trial, an auditory stimulus was presented to the left ear, to the right ear, or simultaneously to both ears. The physical difference between auditory stimuli presented to the two ears…
See all related articles »

Publication Finder

Browse back issues from our extensive library of more than 6,500 trusted publications.

Popular publicationson HighBeam Research

The Washington Post
Washington D.C. newspapers
Newsweek
National newspapers
Harper's Magazine
Cultural magazines
The Economist (US)
Political magazines
The Boston Globe (Boston, MA)
Massachusetts newspapers
Visit Cengage Brain
  • Company
  • About us
  • Subscription benefits
  • Group subscriptions
  • Careers
  • Privacy policy
  • Terms and conditions
  • Contact us
  • Help topics
  • FAQ
  • Search tips
  • Using the Research Center
  • Billing questions
  • Rights inquiries
  • Customer Service
  • Cengage Learning Network
  • Questia
  • CengageBrain.com
  • HighBeam Business
  • ed2go
  • MiLadyPro
  •  
HighBeam Research
Follow us:

HighBeam Research is operated by Cengage Learning. © Copyright 2018. All rights reserved.

The HighBeam advertising network includes: womensforum.com GlamFamily