dc.contributor.author |
Berber, Stevan |
en |
dc.date.accessioned |
2016-07-05T00:11:51Z |
en |
dc.date.issued |
2015-11 |
en |
dc.identifier.citation |
Nov 2015. Department of Electrical and Computer Engineering, University of Auckland, Auckland |
en |
dc.identifier.uri |
http://hdl.handle.net/2292/29313 |
en |
dc.description.abstract |
There are, maybe, the largest number of random variables and stochastic processes in nature, which are described in science and engineering, that have Gaussian continuous distribution and density function. However, the theoretical analysis and application of these processes, in particular when the random variable is both discrete and truncated, is not completed. For the sake of completeness, this Report presents a brief review of Gaussian continuous density functions, both un-truncated and truncated, which are well described in existing literature. Then the discrete density function is derived and expressed in terms of Dirac’s delta functions and related mean and variance are derived and analyzed. The necessity of having truncated discrete density function, from the application point of view in communication systems, for example, is explained and related density and distribution functions are derived. For these functions, the mean and variance are expressed as functions of the length of the defined truncation interval and compared with related moments of the continuous truncated density function. The important advancement is achieved by deriving the truncated discrete density functions and expressing them in terms of Dirac’s delta and unit step functions. In this way it becomes possible to solve integrals which contain these density and distribution functions. |
en |
dc.publisher |
Department of Electrical and Computer Engineering, University of Auckland |
en |
dc.relation.ispartofseries |
Faculty of Engineering Report |
en |
dc.rights |
Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher. |
en |
dc.rights.uri |
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm |
en |
dc.title |
Comprehensive Analysis of Gaussian Discrete Truncated Random Variables |
en |
dc.type |
Report |
en |
dc.description.version |
VoR - Version of Record |
en |
dc.rights.holder |
Copyright:
Department of Electrical and Computer Engineering, University of Auckland |
en |
pubs.place-of-publication |
Auckland |
en |
dc.rights.accessrights |
http://purl.org/eprint/accessRights/OpenAccess |
en |
pubs.subtype |
Technical Report |
en |
pubs.elements-id |
511520 |
en |
dc.relation.isnodouble |
38092 |
* |
pubs.org-id |
Engineering |
en |
pubs.org-id |
Department of Electrical, Computer and Software Engineering |
en |
pubs.number |
694 |
en |
pubs.record-created-at-source-date |
2015-12-06 |
en |