B. P. Lathi and Roger Green

A comprehensive introductory treatment of signals and linear systems suitable for juniors and seniors. This 2E contains much of the content of *Linear Systems and Signals*, 3e by the same authors, with added chapters on analog and digital filters and digital signal processing, plus additional
applications to communications and controls. Unlike LS&S3e, 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.

**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

**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

**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

**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

**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

**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

**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

**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

**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

**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

**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

**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

**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

**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

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**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.