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