A First Course in Electrical and Computer
Engineering By: Louis Scharf
Table of Contents
Dedication of "A First Course in Electrical and
Computer Engineering". . . . . . . . 1
Preface to "A First Course in Electrical and Computer
Engineering". . . . . . . . . . . . . . . . . . . 3
1 Complex Numbers
1.1 Complex Numbers: Introduction . . . . 9
1.2 Complex Numbers: Geometry of Complex Numbers . . . . .
10
1.3 Complex Numbers: Algebra of Complex Numbers . . . . . .
. . . . 16
1.4 Complex Numbers: Roots of Quadratic Equations . . . . .
. . . . 25
1.5 Complex Numbers: Representing Complex Numbers in a
Vector Space . . . . . . . . . 31
1.6 Complex Numbers: An Electric Field Computation . . . . .
. . . 36
1.7 Complex Numbers: Numerical Experiment (Quadratic Roots) .
. . . . . . . . . . . . . . . . . 39
2 The Functions e^x and e^j
2.1 The Functions e^x and e^j: Introduction . . . . . . . .
. . . . . . . 43
2.2 The Functions e^x and e^j: The Function e^x . . . . . .
. . . . 44
2.3 The Functions e^x and e^j: The Function
e^jand the Unit Circle . . . . . . . . . . . . . . . . . . .
. .. . . . . . . . . . . . . 49
2.4 The Functions e^x and e^j: The Euler and
De Moivre Identities . . . . . . . . . . . . . . . 54
2.5 The Functions e^x and e^j: Roots of Unity
and Related Topics . . . . . . . . . . . . . . . . . 57
2.6 The Functions e^x and e^j: Second-Order
Dierential and Dierence Equations . . . . . . . . . . . . .
. . . . . . . . 61
2.7 The Functions e^x and e^j: Numerical Experiment
(Approximating e^j) . . . . . 65
3 Phasors
3.1 Phasors: Introduction . . . . . . . . . . . . . . 69
3.2 Phasors: Phasor Representation of Signals . . . . . . .
. . . . . . . . 70
3.3 Phasors: Beating between Tones . . . 80
3.4 Phasors: Multiphase Power . . . . . . . . 83
3.5 Phasors: Lissajous Figures . . . . . . . . . 86
3.6 Phasors: Sinusoidal Steady State and the Series
RLC Circuit . . . . . . . . . . . . . . . . . . . 89
3.7 Phasors: Light Scattering by a Slit . 99
3.8 Phasors: Numerical Experiment (Interference
Patterns) . . . . . . . . . . . . . .. . . . . . . . . . . .
106
4 Linear Algebra
4.1 Linear Algebra: Introduction . . . . . . . . . . . . . .
. .. . . . . . . . . . . . 109
4.2 Linear Algebra: Vectors . . . . . . . . . . . 112
4.3 Linear Algebra: Inner Product and Euclidean
Norm . . . . . . . 117
4.4 Linear Algebra: Direction Cosines . . . . . . . . . . ..
. . . . . . . . . . . 120
4.5 Linear Algebra: Projections . . . . . . . 127
4.6 Linear Algebra: Other Norms . . . . . 133
4.7 Linear Algebra: Matrices . . . . . . . . . 137
4.8 Linear Algebra: Solving Linear Systems of
Equations . . . 146
4.9 Linear Algebra: Circuit Analysis . . 155
4.10 Linear Algebra: Numerical Experiment (Circuit
Design) . . . . . . . . . . . . . . . . . . . . . . . 161
5 Vector Graphics
5.1 Vector Graphics: Introduction . . . . 163
5.2 Vector Graphics: Two-Dimensional Image
Representation . . . . . . . . . . . . . . . . . . . . 166
5.3 Vector Graphics: Two-Dimensional Image
Transformations . . . . . . . . . . . . . . . . . . . 172
5.4 Vector Graphics: Composition of Transformations
. . . . . . . . 174
5.5 Vector Graphics: Homogeneous Coordinates .. . . . . . .
. . . . . 176
5.6 Vector Graphics: Three-Dimensional Homogeneous
Coordinates . . . . .. . . . . . . . . . . . 180
5.7 Vector Graphics: Projections . . . . . . . . . . . . . .
. .. . . . . . . . . . . . 188
5.8 Vector Graphics: Numerical Experiment (Star
Field) . . . . . . . 195
6 Filtering
6.1 Filtering: Introduction . . . . . . . . . . . . 203
6.2 Filtering: Simple Averages . . . . . . . . 209
6.3 Filtering: Weighted Averages . . . . . . . . . . . . . .
. .. . . . . . . . . . . . 216
6.4 Filtering: Moving Averages . . . . . . . . . . . . . . .
. . .. . . . . . . . . . . . 218
6.5 Filtering: Exponential Averages and Recursive
Filters . . . . . . 221
6.6 Filtering: Test Sequences . . . . . . . . . 223
6.7 Filtering: Numerical Experiment (Frequency
Response of First-Order Filter) . . . . 230
v
7 Binary Codes
7.1 Binary Codes: Introduction . . . . . . . 233
7.2 Binary Codes: The Communication Paradigm . . . . . . . .
. . . . 235
7.3 Binary Codes: From Symbols to Binary Codes . . . . . . .
. . . . . 238
7.4 Binary Codes: Human Codes for Source Coding
. . . . . . . . . . 246
7.5 Binary Codes: Hamming Codes for Channel
Coding . . . . . . 254
7.6 Binary Codes: Numerical Experiment (Hu-
man Codes) . . . . . . . . . . . . . . . . . . . . . . . 263
8 An Introduction to MATLAB
8.1 An Introduction to MATLAB: Introduction . . . . . . . .
. . . . . 265
8.2 An Introduction to MATLAB: Running MATLAB
(Macintosh) . . . . . . . . . . . . . . . . . 266
8.3 An Introduction to MATLAB: Running MATLAB
(PC) . . 268
8.4 An Introduction to MATLAB: Interactive
Mode . . . . . . . 269
8.5 An Introduction to MATLAB: Variables . . . . . . . . . .
. . . . . . 270
8.6 An Introduction to MATLAB: Complex Variables
. . . . . . . . 271
8.7 An Introduction to MATLAB: Vectors and
Matrices . . . . 273
8.8 An Introduction to MATLAB: The Colon . . . . . . . . . .
. . . . . 278
8.9 An Introduction to MATLAB: Graphics . . . . .. . . . . .
. . . . . . 279
8.10 An Introduction to MATLAB: Editing Files
and Creating Functions (Macintosh) . . . . . . . . . . . . .
. . . . . . . . 283
8.11 An Introduction to MATLAB: Editing Files
and Creating Functions (PC) . . . . . . 286
8.12 An Introduction to MATLAB: Loops and
Control . . . . . 288
9 The Edix Editor . . 293
10 Useful Mathematical Identities . . . . . . 295
Index . . . . . . . . . . . . . . . . . 298
Attributions . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . .
