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Signal Processing and Linear Systems

Second Edition

B. P. Lathi and Roger Green

Publication Date - February 2021

ISBN: 9780190299040

1152 pages
8 x 10 inches

In Stock

Retail Price to Students: $199.94

A comprehensive introductory treatment of signals and linear systems suitable for juniors and seniors.


This second edition contains much of the content of Linear Systems and Signals, Third Edition, by the same authors, with added chapters on analog and digital filters and digital signal processing, plus additional applications to communications and controls. Unlike Linear Systems & Signals 3e, in this book the Laplace transform follows Fourier. This book contains enough material on discrete-time systems to be used in a traditional course in Signals and Systems and in an introductory course in Digital Signal Processing.

New to this Edition

  • Updated MATLAB material
  • Improved navigation/titling of examples and drills
  • Approximately half of the problems are new or revised


  • Additional material on digital and analog filters
  • Discrete-time systems that allow this book to be used in Digital Signal Processing courses
  • Separate explanations of continuous-time and discrete-time systems

About the Author(s)

B. P. Lathi is Professor Emeritus of Electrical Engineering at California State University, Sacramento. Dr. Lathi is renowned for his excellent writing, and each of his books has found significant markets in the crowded upper-level electrical engineering segment.

Roger Green is an Associate Professor of Electrical Engineering at North Dakota State University. He has published numerous scholarly articles and given presentations on MATLAB, Signal Processing, and Fourier Analysis as a member of both the IEEE and ASEE. Along with four colleagues, he is the proud owner of a patent for a Vector Calibration System, designed to identify vector mismatch between a plurality of signal paths and frequencies.

Table of Contents

    Chapter B: Background
    B.1 Complex Numbers
    B.2 Sinusoids
    B.3 Sketching Signals
    B.4 Cramer's Rule
    B.5 Partial Fraction Expansion
    B.6 Vectors and Matrices
    B.7 MATLAB: Elementary Operations
    B.8 Appendix: Useful Mathematical Formulas

    Chapter 1: Signals and Systems
    1.1 Size of a Signal
    1.2 Some Useful Signal Operations
    1.3 Classification of Signals
    1.4 Some Useful Signal Models
    1.5 Even and Odd Functions
    1.6 Systems
    1.7 Classification of Systems
    1.8 System Model: Input-Output Description
    1.9 Internal and External Descriptions of a System
    1.10 Internal Description: The State-Space Description
    1.11 MATLAB: Working with Functions
    1.12 Summary

    Chapter 2: Time-Domain Analysis of Continuous-Time Systems
    2.1 Introduction
    2.2 System Response to Internal Conditions: The Zero-Input Response
    2.3 The Unit Impulse Response h(t)
    2.4 System Response to External Input: The Zero-State Response
    2.5 System Stability
    2.6 Intuitive Insights into System Behavior
    2.7 MATLAB: M-Files
    2.8 Appendix: Determining the Impulse Response
    2.9 Summary

    Chapter 3: Signal Representation by Fourier Series
    3.1 Signals as Vectors
    3.2 Signal Comparison: Correlation
    3.3 Signal Representation by an Orthogonal Signal Set
    3.4 Trigonometric Fourier Series
    3.5 Existence and Convergence of the Fourier Series
    3.6 Exponential Fourier Series
    3.7 LTIC System Response to Periodic Inputs
    3.8 Numerical Computation of Dn
    3.9 MATLAB: Fourier Series Applications
    3.10 Summary

    Chapter 4: Continuous-Time Signal Analysis: The Fourier Transform
    4.1 Aperiodic Signal Representation by the Fourier Integral
    4.2 Transforms of Some Useful Functions
    4.3 Some Properties of the Fourier Transform
    4.4 Signal Transmission Through LTIC Systems
    4.5 Ideal and Practical Filters
    4.6 Signal Energy
    4.7 Application to Communications: Amplitude Modulation
    4.8 Angle Modulation
    4.9 Data Truncation: Window Functions
    4.10 MATLAB: Fourier Transform Topics
    4.11 Summary

    Chapter 5: Sampling
    5.1 The Sampling Theorem
    5.2 Signal Reconstruction
    5.3 Analog-to-Digital (A/D) Conversion
    5.4 Dual of Time Sampling: Spectral Sampling
    5.5 Numerical Computation of the Fourier Transform: The Discrete Fourier Transform
    5.6 The Fast Fourier Transform (FFT)
    5.7 MATLAB: The Discrete Fourier Transform
    5.8 Summary

    Chapter 6: Continuous-Time System Analysis Using the Laplace Transform
    6.1 The Laplace Transform
    6.2 Some Properties of the Laplace Transform
    6.3 Solution of Differential and Integro-Differential Equations
    6.3.4 Inverse Systems
    6.4 Analysis of Electrical Networks: The Transformed Network
    6.5 Block Diagrams
    6.6 System Realization
    6.7 Application to Feedback and Controls
    6.8 The Bilateral Laplace Transform
    6.9 Summary

    Chapter 7: Frequency Response and Analog Filters
    7.1 Frequency Response of an LTIC System
    7.2 Bode Plots
    7.3 Control System Design Using Frequency Response
    7.4 Filter Design by Placement of Poles and Zeros of H(s)
    7.5 Butterworth Filters
    7.6 Chebyshev Filters
    7.7 Frequency Transformations
    7.8 Filters to Satisfy Distortionless Transmission Conditions
    7.9 MATLAB: Continuous-Time Filters
    7.10 Summary

    Chapter 8: Discrete-Time Signals and Systems
    8.1 Introduction
    8.2 Useful Signal Operations
    8.3 Some Useful Discrete-Time Signal Models
    8.4 Aliasing and Sampling Rate
    8.5 Examples of Discrete-Time Systems
    8.6 MATLAB: Representing, Manipulating, and Plotting Discrete-Time Signals
    8.7 Summary

    Chapter 9: Time-Domain Analysis of Discrete-Time Systems
    9.1 Classification of Discrete-Time Systems
    9.2 Discrete-Time System Equations
    9.3 System Response to Internal Conditions: The Zero-Input Response
    9.4 The Unit Impulse Response h[n]
    9.5 System Response to External Input: The Zero-State Response
    9.6 System Stability
    9.7 Intuitive Insights into System Behavior
    9.8 MATLAB: Discrete-Time Systems
    9.9 Appendix: Impulse Response for a Special Case
    9.10 Summary

    Chapter 10: Fourier Analysis of Discrete-Time Signals
    10.1 Periodic Signal Representation by Discrete-Time Fourier Series
    10.2 Aperiodic Signal Representation by Fourier Integral
    10.3 Properties of the DTFT
    10.4 DTFT Connection with the CTFT
    10.5 LTI Discrete-Time System Analysis by
    10.6 Signal Processing by the DFT and FFT
    10.7 Generalization of the DTFT to the z-Transform
    10.8 MATLAB: Working with the DTFS and the DTFT
    10.9 Summary

    Chapter 11: Discrete-Time System Analysis Using the z-Transform
    11.1 The z-Transform
    11.2 Some Properties of the z-Transform
    11.3 z-Transform Solution of Linear Difference Equations
    11.4 System Realization
    11.5 Connecting the Laplace and z-Transforms
    11.6 Sampled-Data (Hybrid) Systems
    11.7 The Bilateral z-Transform
    11.8 Summary

    Chapter 12: Frequency Response and Digital Filters
    12.1 Frequency Response of Discrete-Time Systems
    12.2 Frequency Response from Pole-Zero Locations
    12.3 Digital Filters
    12.4 Filter Design Criteria
    12.5 Recursive Filter Design: The Impulse Invariance Method
    12.6 Recursive Filter Design: The Bilinear Transformation Method
    12.7 Nonrecursive Filters
    12.8 Nonrecursive Filter Design
    12.9 MATLAB: Designing High-Order Filters
    12.10 Summary

    Chapter 13: State-Space Analysis
    13.1 Mathematical Preliminaries
    13.2 Introduction to State Space
    13.3 A Systematic Procedure to Determine State Equations
    13.4 Solution of State Equations
    13.5 Linear Transformation of a State Vector
    13.6 Controllability and Observability
    13.7 State-Space Analysis of Discrete-Time Systems
    13.8 MATLAB: Toolboxes and State-Space Analysis
    13.9 Summary