Elementary Signals
Signals Described in Math Form.1-1
The Unit Step Function ...1-2
The Unit Ramp Function ...1-10
The Delta Function 1-12
Sampling Property of the Delta Function1-12
Sifting Property of the Delta Function.1-13
Higher Order Delta Functions...1-15
Summary...1-19
Exercises...1-20
Solutions to Exercises 1-21
Chapter 2
The Laplace Transformation
Definition of the Laplace Transformation. 2-1
Properties of the Laplace Transform..2-2
The Laplace Transform of Common Functions of Time .2-12
The Laplace Transform of Common Waveforms..2-23
Summary...2-29
Exercises...2-34
Solutions to Exercises 2-37
Chapter 3
The Inverse Laplace Transformation
The Inverse Laplace Transform Integral3-1
Partial Fraction Expansion ...3-1
Case where is Improper Rational Function ( )... 3-13
Alternate Method of Partial Fraction Expansion... 3-15
Summary.. 3-18
Exercises ..3-20
Solutions to Exercises3-22
Chapter 4
Circuit Analysis with Laplace Transforms
Circuit Transformation from Time to Complex Frequency... 4-1
Complex Impedance ...4-8
Complex Admittance 4-10
Transfer Functions .4-13
Summary ..4-16
Exercises ..4-18
Solutions to Exercises4-21
Chapter 5
State Variables and State Equations
Expressing Differential Equations in State Equation Form...5-1
Solution of Single State Equations..5-7
The State Transition Matrix .5-9
Computation of the State Transition Matrix...5-11
Eigenvectors 5-18
Circuit Analysis with State Variables 5-22
Relationship between State Equations and Laplace Transform...5-28
Summary ..5-35
Exercises ..5-39
Solutions to Exercises5-41
Chapter 6
The Impulse Response and Convolution
The Impulse Response in Time Domain...6-1
Even and Odd Functions of Time..6-5
Convolution...6-7
Graphical Evaluation of the Convolution Integral ..6-8
Circuit Analysis with the Convolution Integral.. 6-18
Summary . 6-20