Table of Contents

CHAPTER 1 SIGNALS, SEQUENCES and SYSTEMS

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Signals, Sequences, and Systems

Continuous-Time Signals

Discrete-Time Signals or Sequences

Conversion Between Continuous-Time and Discrete-Time Signals

The Sampling Theorem

A Road Map

Table 1.1 Domains for Continuous- and Discrete-Time Systems

Table 1.2 Models for Continuous- and Discrete-Time Systems

Table 1.3 Operations for Linear Systems

Problems

Definitions, Techniques, And Connections

m-Functions Used

Annotated Bibliography

Answers

CHAPTER 2 LINEAR CONTINUOUS-TIME SYSTEMS and LAPLACE TRANSFORMS

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Properties of Linear Continuous-Time Systems

Nth-Order DE Model for Continuous-Time Systems

Zero-Input Solution of a Differential Equation

Zero-State Solution of a Differential Equation

Complete Solution of a First-Order Differential Equation

Unit Impulse Response Model

Linear Convolution

Sinusoidal Steady-State Response

Basic Concepts of Laplace Transforms

Laplace Transform Pairs

Properties and Relations of Laplace Transforms

The Evaluation of Inverse Transforms

Inverse Laplace Transforms by Partial Fraction Expansion (PFE). Distinct Poles, Degree of Numerator Less Than or Equal to Degree of Denominator

Inverse Transform by Partial Fraction Expansion (PFE), Distinct Poles, Degree of Denominator Less Than Degree of Numerator (Website)

Inverse LaplaceTransforms Using the m-function residue

Inverse Laplace Transforms by Partial Fraction Expansion, Multiple Poles

Solution of Linear Differential Equations by Laplace Transforms

Problems

Definitions, Techniques, And Connections

m-Functions Used

Annotated Bibliography

Answers

Table 2.1 Bilateral Laplace transform pairs

Table 2.2 Unilateral Laplace transform properties and relations

CHAPTER 3 MODELS and IMPORTANT RESULTS

Time Domain

Linear Differential Equations, Unit Impulse Response

Laplace Domain

Transfer Functions

Poles and Zeros

Region of Convergence

Linear Convolution

Sinusoidal Steady-State Response

System Diagrams or Structures

Mason Gain Rule

The State-Space or First-Order Model

Solution in the time domain

Solution in the Laplace domain

State Equations from System Diagrams

Stability of:

Linear DE models, UIR models, Transfer Function models, State Equation models

Characteristic Equation and Characteristic Roots, Eigenvalues

Stability and Region of Convergence

Problems

Definitions, Techniques, And Connections

m-Functions Used

Annotated Bibliography

Answers

CHAPTER 4 FREQUENCY RESPONSE of CONTINUOUS-TIME SYSTEMS

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Review

Transfer Function

Stability

Sinusoidal Steady-state response

Frequency Response

Characteristics

Symmetry

Time and frequency

Decibels

Bandwidth

Frequency Response Plots

Rectangular Plots

Polar and Nyquist Plots

Logarithmic, or Bode, Plots

Graphical Estimation of Frequency Response

Asymptotic Approximation

Continuous-Time Filter Characteristics

Ideal Filters

Some Practical Considerations

Definitions, Techniques, And Connections

m-Functions Used

Annotated Bibliography

Answers

CHAPTER 5 CONTINUOUS-TIME FOURIER SERIES and TRANSFORMS

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Fourier Series

Periodic Signals,

Complex Periodic Exponentials, and More

Fourier Series Coefficients and Pairs

Gibbs’ Phenomenon, Frequency Spectrum, Mean Square Error

Transmission of a Periodic Signal Through a Linear System, Power in a Periodic

Signal

Fourier Transform

Definition,

Pairs for Finite Energy Signals

Pairs for Power Signals

Properties of the Fourier Transform

Linearity

Time and Frequency Shift

Symmetry or Duality

Time and Frequency Convolution

Applications of the Fourier Transform

Signal Transmission through a Linear System

Ideal Filters

Sampling Theorem

Cross-Correlation for Energy Signals

Energy Spectral Density

Problems

Definitions, Techniques, And Connections

m-Functions Used

Annotated Bibliography

Answers

CHAPTER 6 LINKAGES AND APPLICATIONS

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From One Model to Another

Introduction –

Analog Filter Design by Pole-Zero Placement

Typical Design Specifications (graphical)

Some Design Examples

Applications

Second-Order Systems

Unit Impulse of a Lowpass Filter

Analysis of Frequency Response Data

Active Circuits for Bandpass and Bandstop Filtering

An Impulse Train Applied to an Electric Circuit

Signal Transmission Through a Linear System

Impulse Response of an Ideal and a Butterworth Filter

Modulation/Demodulation

System Models and Time Response Characteristics

Systems with Piecewise-Constant Inputs (Digital Control)

Problems

Definitions, Techniques, And Connections

m-Functions Used

Annotated Bibliography

Answers