# Table of Contents

## Table of Contents

**CHAPTER 1 SIGNALS, SEQUENCES and SYSTEMS**

Preview

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 DISCRETE-TIME SYSTEMS and Z TRANSFORMS**

Preview

Properties of Linear Discrete-Time Systems

Nth-Order DE Model for Discrete**–**Time Systems

Zero-Input Solution of a Difference Equation

Zero-State Solution of a Difference Equation

Complete Solution of a First-Order Difference Equation

Linear Convolution

Sinusoidal Steady-State Response

Basic Concepts of z Transforms

Z Transform Pairs

Properties and Relations of Z Transforms

The Evaluation of Inverse Transforms

Inverse z Transforms from the Definition

Inverse z Transforms by Long Division

Inverse z 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 z Transforms Using the m-functions **residue** or **residuez**

Inverse z Transforms by Partial Fraction Expansion, Multiple Poles

Solution of Linear Difference Equations by Z Transforms

Problems

Definitions, Techniques, And Connections

m-Functions Used

Annotated Bibliography

Answers

Table 2.1 Bilateral z–transform pairs

Table 2.2 Bilateral z–transform properties and relations

Table 2.3 Unilateral z–transform properties and relations

**CHAPTER 3 MODELS and IMPORTANT RESULTS**

Time Domain

Linear Difference Equations, Unit Impulse Response

z 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 z 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 DISCRETE-TIME SYSTEMS**

Preview

Review

Sinusoidal Steady-state response

Sampling Theorem

Frequency Response

Frequency Response Characristics

Periodicity

Symmetry

Time and frequency

Decibels

Frequency Response Plots

Rectangular Plots

Polar and Nyquist Plots

Logarithmic, or Bode, Plots

Graphical Estimation of Frequency Response

** **Discrete-Time Filter Characteristics

Ideal Filters

Some Practical Considerations

A Final Note on Linear Phase Nonrecursive Filters

Problems

Definitions, Techniques, And Connections

m-Functions Used

Annotated Bibliography

Answers

**CHAPTER 5 FOURIER TRANSFORMS and DISCRETE-TIME SYSTEMS**

Preview

Discrete-Time Fourier Transforms (DTFT)

Periodic Sequences, Complex Exponentials, and More

Discrete Fourier Series (DFS)

The Discrete Fourier Transform (DFT)

Some Important Relationships

DFTs and the Discrete-Time Fourier Transform** **

** **Relationships Among Record Length, Frequency Resolution, and Sampling Frequency

Properties of the DFT

Linearity

Circular Shift

Symmetry

Alternate Inversion Formula

Duality

Computer Evaluation of DFTs and Inverse DFTs

Another Look at Convolution

Periodic convolution

Circular Convolution

Zero Padding

Frequency Convolution

Modulation

Problems

Definitions, Techniques, And Connections

m-Functions Used

Annotated Bibliography

Answers

**CHAPTER 6 LINKAGES AND APPLICATIONS**

Preview

From One Model to Another

Digital Filter Design by Pole-Zero Placement

Typical Design Specifications (graphical)

Some Design Examples

Applications:

Fast Fourier Transform

Correlation

Designing a Digital Oscillator

A Moving Average Filter

Design of a Multiple-Notch Filter

Frequency Response of a Digital Differentiator

Spectrum Analysis

Block Filtering

DFT Approximation of the CT Fourier Transform

Problems

Definitions, Techniques, And Connections

m-Functions Used

Annotated Bibliography

Answers