# Signals and Systems, 2nd edition

Published by Pearson (August 6th 1996) - Copyright © 1997

2nd edition

## Overview

This comprehensive exploration of signals and systems develops continuous- time and discrete-time concepts/methods in *parallel* highlighting the similarities and differences and features introductory treatments of the applications of these basic methods in such areas as filtering, communication, sampling, discrete-time processing of continuous-time signals, and feedback. Relatively self-contained, the book assumes no prior experience with system analysis, convolution, Fourier analysis, or Laplace and z-transforms.

**FEATURES:**

**Develops continuous-time and discrete-time concepts in parallel** highlighting the similarities and differences. E.g.:- Ch. 1 on basic signals and system properties, Ch. 2 on linear time-invariant systems, and Ch. 3 on Fourier series representation each develop the continuous-time and discrete-time concepts in parallel.
- Ch. 9 on the Laplace Transform and Ch. 10 on the Z-transform deal with the two domains separately, but often draw parallels between results in the two domains.

- Introduces
**some of the important uses of the basic methods**that are developed e.g., filtering, communication, sampling, discrete-time processing of continuous-time signals, and feedback. **NEW****A companion book**contains**MATLAB-based computer exercises**for each topic.**NEW**Material on Fourier analysis has been reorganized significantly to provide an easier path for the reader to master and appreciate the importance of this topic. Now represented in four chapters, each of which is far more streamlined and focused, introducing a smaller and more cohesive set of topics.**NEW**Frequency-domain filtering is introduced very early in the development to provide a central and concrete illustration of why this topic is important and to provide some intuition with a minimal amount of mathematical preliminaries.**NEW**Relocates coverage of**Sampling**before Communication. * Allows for discussion of important forms of communication, namely those involving discrete or digital signals, in which sampling concepts are intimately involved.**NEW****Chapter-end Problems**- They provide a better balance between exercises developing basic skills and understanding ones that pursue more advanced problem-solving skills. The new edition organizes chapter-end problems into four types of sections which makes it easier for the reader to locate the problems that will best serve their purposes; and provides two types of basic problems, ones with answers (but not solutions); and ones with solutions to provide immediate feedback, while attempting to master the material.

The four types of chapter-end problems are- Basic Problems with Answers.
- Basic Problems.
- Advanced Problems.
- Extension Problems.

## Table of contents

(NOTE: Each chapter begins with an Introduction and concludes with a Summary.)

**1. Signals and Systems.**

Continuous-Time and Discrete-Time Signals. Transformations of the Independent Variable. Exponential and Sinusoidal Signals. The Unit Impulse and Unit Step Functions. Continuous-Time and Discrete-Time Systems. Basic System Properties.

**2. Linear Time-Invariant Systems.**

Discrete-Time LTI Systems: The Convolution Sum. Continuous-Time LTI Systems: The Convolution Integral. Properties of Linear Time-Invariant Systems. Causal LTI Systems Described by Differential and Difference Equations. Singularity Functions.

**3. Fourier Series Representation of Periodic Signals.**

A Historical Perspective. The Response of LTI Systems to Complex Exponentials. Fourier Series Representation of Continuous-Time Periodic Signals. Convergence of the Fourier Series. Properties of Continuous-Time Fourier Series. Fourier Series Representation of Discrete-Time Periodic Signals. Properties of Discrete-Time Fourier Series. Fourier Series and LTI Systems. Filtering. Examples of Continuous-Time Filters Described by Differential Equations. Examples of Discrete-Time Filters Described by Difference Equations.

**4. The Continuous-Time Fourier Transform.**

Representation of Aperiodic Signals: The Continuous-Time Fourier Transform. The Fourier Transform for Periodic Signals. Properties of the Continuous-Time Fourier Transform. The Convolution Property. The Multiplication Property. Tables of Fourier Properties and Basic Fourier Transform Pairs. Systems Characterized by Linear Constant-Coefficient Differential Equations.

**5. The Discrete-Time Fourier Transform.**

Representation of Aperiodic Signals: The Discrete-Time Fourier Transform. The Fourier Transform for Periodic Signals. Properties of the Discrete-Time Fourier Transform. The Convolution Property. The Multiplication Property. Tables of Fourier Transform Properties and Basic Fourier Transform Pairs. Duality. Systems Characterized by Linear Constant-Coefficient Difference Equations.

**6. Time- and Frequency Characterization of Signals and Systems.**

The Magnitude-Phase Representation of the Fourier Transform. The Magnitude-Phase Representation of the Frequency Response of LTI Systems. Time-Domain Properties of Ideal Frequency-Selective Filters. Time- Domain and Frequency-Domain Aspects of Nonideal Filters. First-Order and Second-Order Continuous-Time Systems. First-Order and Second-Order Discrete-Time Systems. Examples of Time- and Frequency-Domain Analysis of Systems.

**7. Sampling.**

Representation of a Continuous-Time Signal by Its Samples: The Sampling Theorem. Reconstruction of a Signal from Its Samples Using Interpolation. The Effect of Undersampling: Aliasing. Discrete-Time Processing of Continuous-Time Signals. Sampling of Discrete-Time Signals.

**8. Communication Systems.**

Complex Exponential and Sinusoidal Amplitude Modulation. Demodulation for Sinusoidal AM. Frequency-Division Multiplexing. Single-Sideband Sinusoidal Amplitude Modulation. Amplitude Modulation with a Pulse-Train Carrier. Pulse-Amplitude Modulation. Sinusoidal Frequency Modulation. Discrete-Time Modulation.

**9. The Laplace Transform.**

The Laplace Transform. The Region of Convergence for Laplace Transforms. The Inverse Laplace Transform. Geometric Evaluation of the Fourier Transform from the Pole-Zero Plot. Properties of the Laplace Transform. Some Laplace Transform Pairs. Analysis and Characterization of LTI Systems Using the Laplace Transform. System Function Algebra and Block Diagram Representations. The Unilateral Laplace Transform.

**10. The Z-Transform.**

The z-Transform. The Region of Convergence for the z-Transform. The Inverse z-Transform. Geometric Evaluation of the Fourier Transform from the Pole-Zero Plot. Properties of the z-Transform. Some Common z-Transform Pairs. Analysis and Characterization of LTI Systems Using z-Transforms. System Function Algebra and Block Diagram Representations. The Unilateral z-Transforms.

**11. Linear Feedback Systems.**

Linear Feedback Systems. Some Applications and Consequences of Feedback. Root-Locus Analysis of Linear Feedback Systems. The Nyquist Stability Criterion. Gain and Phase Margins.

**Appendix: Partial-Fraction Expansion.****Bibliography.****Answers.****Index.**## For teachers

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