Random Signals for Engineers Using MATLAB and Mathcad: Text

Front Cover
Springer Science & Business Media, Sep 8, 2000 - Computers - 374 pages
This introduction to random variables and signals is intended to provide engineering students with the analytical and computational tools for processing random signals using linear systems. It presents the underlying theory as well as examples and applications using computational aids throughout, in particular, computer-based symbolic computation programs are used for performing the analytical manipulations and the numerical calculations. Intended for a one-semester course for advanced undergraduates or beginning graduate students, the book covers such topics as: set theory and an introduction to probability; random variables, distributions, and processes; deterministic signals, spectral properties, and transformations; and filtering, and detection theory. The large number of worked examples together with the programming aids provided on the CD make the book eminently suited for self study as well as classroom use.
 

Contents

Introduction to Sets and Probability
7
12 Introduction to Sets
8
13 Operations on Sets
9
14 Combined Operations on Sets
12
15 Notion of Probability
15
16 Relative Frequency and Probability
18
17 Conditional Probability
23
18 Total Probability
25
Problems for Chapter 4
186
Introduction to Random Processes
191
51 Methods of Generation of Random Processes
192
52 IID Random Variables
197
53 Distribution Functions for a Random Process
204
54 Properties of Expectation Operators
214
55 Properties of the Correlation Functions
228
56 Numerical Computation of the Correlation Function
232

19 Independence
29
110 Summary
31
Problems for Chapter 1
32
OneDimensional Random Variables
37
22 Random Variables
43
23 Distribution Functions
44
24 Density Functions
48
25 Continuous Density Functions
51
26 Conditional Distribution and Density Functions
59
27 Generation of Random Numbers
69
28 Summary
74
Problems for Chapter 2
76
Operations on Random Numbers
81
32 Moments and Functions
87
33 Moment Generating Functions
96
34 Transformation of Random Variables
104
35 Random Variables with Prescribed Distributions
116
36 Summary
123
Problems for Chapter 3
124
TwoDimensional Random Variables
128
41 Joint Distribution and Density Functions
133
42 Conditional Density Functions
140
43 Expectation and Joint Moments
147
44 Transformations and Joint Characteristic Functions
154
45 Independence
165
46 Sum of Independent Random Variables
170
47 Generation of Correlated Gaussian Random Sequences
176
48 Summary
184
57 Summary
238
Problems for Chapter 5
239
Introduction to Transformations
244
62 Transformation by Integration
255
63 Transformation by Differentiation
259
64 Linear Systems
263
65 Power Spectrum Functions
269
66 Transforms of Linear Systems
277
67 Calculation of Power Density Spectrum
289
68 Summary
295
Problems for Chapter 6
297
Introduction to Applications
302
71 Matched Filtering
303
72 Mean Square Filtering
312
73 Detection Theory
319
74 Radar Systems
335
75 Noise in Control Systems
353
Problems for Chapter 7
358
Appendix A
363
A2 Singularity Functions
365
A3 LinearTimeInvariant Systems
366
A4 Correlation Functions
367
Appendix B
369
B3 Mathcad
372
B4 Contents of the CDROM
374
References
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