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C. Sidney Burrus
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Error Analysis of Digital Communications
(m31814)
Author:
Phil Schniter
Maintainers:
Phil Schniter
,
Daniel Williamson
,
Richard Baraniuk
,
C. Sidney Burrus
,
Jared Adler
Keywords:
BER
,
bit error rate
,
conditional probability
,
constellation diagram
,
decision regions
,
erfc
,
eye diagram
,
Gray coding
,
PAM
,
phaseshift keying
,
PSK
,
QAM
,
Q function
,
SER
,
symbol alphabet
,
symbol error rate
Summary:
In this module, we first introduce the eye diagram and constellation diagram as qualitative ways of evaluating the symbol error probability of a digital communication system. We discuss various symbol alphabets, such as QAM, PAM, and PSK, and their associated decision regions. Finally, we derive the symbol error probability for ... Gray coding.
[Expand Summary]
In this module, we first introduce the eye diagram and constellation diagram as qualitative ways of evaluating the symbol error probability of a digital communication system. We discuss various symbol alphabets, such as QAM, PAM, and PSK, and their associated decision regions. Finally, we derive the symbol error probability for PAM and QAM in additive white Gaussian noise, using the Q and erfc functions, and discuss Gray coding.
[Collapse Summary]
Subject:
Mathematics and Statistics
Language:
English
Popularity:
82.61%
Revised:
20090916
Revisions:
3
An Introduction to MATLAB: Loops and Control
(m21392)
Author:
Louis Scharf
Maintainers:
Louis Scharf
,
Daniel Williamson
,
C. Sidney Burrus
,
Richard Baraniuk
Keywords:
electrical engineering
,
engineering
,
MATLAB
Subject:
Mathematics and Statistics
Language:
English
Popularity:
81.52%
Revised:
20090916
Revisions:
5
Convergence and the central Limit Theorem
(m23475)
Author:
Paul E Pfeiffer
Maintainers:
Paul E Pfeiffer
,
Daniel Williamson
,
C. Sidney Burrus
Keywords:
Convergence of sequences of random variables
,
Relationships between types of convergence
,
Weak law of large numbers
Summary:
The central limit theorem (CLT) asserts that the sum of a large class of independent random variables, each with reasonable distributions,is approximately normally distributed. Various versions of this theorem have been studied intensively. On the other hand, certain common forms serve as the basis of an extraordinary amount of ... quite appropriate
[Expand Summary]
The central limit theorem (CLT) asserts that the sum of a large class of independent random variables, each with reasonable distributions,is approximately normally distributed. Various versions of this theorem have been studied intensively. On the other hand, certain common forms serve as the basis of an extraordinary amount of applied work. In the statistics of large samples, the sample average is approximately normal—whether or not the population distribution is normal. In much of the theory of errors of measurement, the observed error is the sum of a large number of independent random quantities which contribute additively to the result. Similarly, in the theory of noise, the noise signal is the sum of a large number of random components, independently produced. In such situations, the assumption of a normal population distribution is frequently quite appropriate
[Collapse Summary]
Subject:
Mathematics and Statistics
Language:
English
Popularity:
81.42%
Revised:
20090918
Revisions:
6
Linear Algebra: Introduction
(m21454)
Author:
Louis Scharf
Maintainers:
Louis Scharf
,
Daniel Williamson
,
C. Sidney Burrus
,
Richard Baraniuk
Keywords:
electrical engineering
,
engineering
,
linear algebra
Subject:
Mathematics and Statistics
Language:
English
Popularity:
81.34%
Revised:
20090916
Revisions:
7
Simple Random Samples and Statistics
(m23496)
Author:
Paul E Pfeiffer
Maintainers:
Paul E Pfeiffer
,
Daniel Williamson
,
C. Sidney Burrus
Keywords:
Matllab techniques
,
Population distribution
,
Population parameters
,
Random sample
,
Sample parameters
,
Sampling process
,
Statistic as estimator
Summary:
The (simple) random sample, is basic to much of classical statistics. Once formulated, we may apply probability theory to exhibit several basic ideas of statistical analysis. A population may be most any collection of individuals or entities. Associated with each member is a quantity or a feature that can be ... population parameters.
[Expand Summary]
The (simple) random sample, is basic to much of classical statistics. Once formulated, we may apply probability theory to exhibit several basic ideas of statistical analysis. A population may be most any collection of individuals or entities. Associated with each member is a quantity or a feature that can be assigned a number. The population distribution is the distribution of that quantity among the members of the population. To obtain information about the population distribution, we select “at random” a subset of the population and observe how the quantity varies over the sample. Hopefully, the distribution in the sample will give a useful approximation to the population distribution. We obtain values of such quantities as the mean and variance in the sample (which are random quantities) and use these as estimators for corresponding population parameters (which are fixed). Probability analysis provides estimates of the variation of the sample parameters about the corresponding population parameters.
[Collapse Summary]
Subject:
Mathematics and Statistics
Language:
English
Popularity:
81.28%
Revised:
20090918
Revisions:
8
Minterms
(m23247)
Author:
Paul E Pfeiffer
Maintainers:
Paul E Pfeiffer
,
Daniel Williamson
,
C. Sidney Burrus
Keywords:
applied probability
,
minterm expansion
,
minterm maps
,
minterms
,
minterm vectors
,
partitions
Summary:
A fundamental problem is to determine the probability of a logical (Boolean) combination of a finite class of events, when the probabilities of certain other combinations are known. If we partition an event F into component events whose probabilities can be determined, then the additivity property implies the probability of ... orderly arrangement.
[Expand Summary]
A fundamental problem is to determine the probability of a logical (Boolean) combination of a finite class of events, when the probabilities of certain other combinations are known. If we partition an event F into component events whose probabilities can be determined, then the additivity property implies the probability of F is the sum of these component probabilities. Frequently, the event F is a Boolean combination of members of a finite class  say {A, B, C} or {A, B, C,D}. For each such finite class, there is a fundamental partition determined by the class. The members of this partition are called minterms. Any Boolean combination of members of the class can be expressed as the disjoint union of a unique subclass of the minterms. If the probability of every minterm in this subclass can be determined, then by additivity the probability of the Boolean combination is determined. An important geometric aid to analysis is the minterm map, which has spaces for minterms in an orderly arrangement.
[Collapse Summary]
Subject:
Mathematics and Statistics
Language:
English
Popularity:
81.25%
Revised:
20090918
Revisions:
8
Adaptive Quantization
(m32074)
Author:
Phil Schniter
Maintainers:
Phil Schniter
,
Daniel Williamson
,
Richard Baraniuk
,
C. Sidney Burrus
,
Jared Adler
Keywords:
adaptive quantization
,
AQB
,
AQF
,
forgetting factor
,
learning period
,
nonstationary
,
uniform quantization
Summary:
Motivated by the practical problem of nonstationary sources, adaptation of the uniform quantizer's stepsize is discussed. In particular, adaptive quantization based on forward estimation (AQF) and backward estimation (AQB) are discussed, in both blockbased and recursive forms.
Subject:
Mathematics and Statistics
Language:
English
Popularity:
80.32%
Revised:
20090922
Revisions:
2
Matlab Procedures for Markov Decision Processes
(m31095)
Author:
Paul E Pfeiffer
Maintainers:
Paul E Pfeiffer
,
Daniel Williamson
,
Richard Baraniuk
,
C. Sidney Burrus
,
Jared Adler
Keywords:
Alpha potential
,
Alphapotential matrix
,
Costs and rewards
,
Decision policy
,
Discounting and potentials
,
Gain patterns
,
Long run averages
,
Markov chain
,
Matlab policy procedures
,
Matlab procedures w discounting
,
Next period gains
,
Policy iteration
,
Recurrence relation
,
State space
Summary:
We first summarize certain essentials in the analysis of homogeneous Markov chains with costs and rewards associated with states, or with transitions between states. Then we consider three cases: a. Gain associated with a state; b. Onestep transition gains; and c. Gains associated with a demand under certain reasonable ... of problems.
[Expand Summary]
We first summarize certain essentials in the analysis of homogeneous Markov chains with costs and rewards associated with states, or with transitions between states. Then we consider three cases: a. Gain associated with a state; b. Onestep transition gains; and c. Gains associated with a demand under certain reasonable conditions. Matlab implementations of the results of analysis provide machine solutions to a variety of problems.
[Collapse Summary]
Subject:
Mathematics and Statistics
Language:
English
Popularity:
79.93%
Revised:
20090918
Revisions:
7
Complex Numbers: Geometry of Complex Numbers
(m21411)
Author:
Louis Scharf
Maintainers:
Louis Scharf
,
Daniel Williamson
,
C. Sidney Burrus
,
Richard Baraniuk
Keywords:
complex numbers
,
electrical engineering
,
engineering
,
geometry
Subject:
Mathematics and Statistics
Language:
English
Popularity:
79.29%
Revised:
20090916
Revisions:
6
Vector Graphics: Projections
(m21493)
Author:
Louis Scharf
Maintainers:
Louis Scharf
,
Daniel Williamson
,
C. Sidney Burrus
,
Richard Baraniuk
Keywords:
electrical engineering
,
engineering
,
vector graphics
Subject:
Mathematics and Statistics
Language:
English
Popularity:
78.65%
Revised:
20090917
Revisions:
6
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