Computer Explorations in Signals and Systems Using MATLAB

by John Buck, Michael Daniel, Andrew Singer

Overview

A comprehensive set of computer exercises of varying levels of difficulty covering the fundamentals of signals and systems. The exercises require the reader to compare answers they compute in MATLAB ® with results and predictions made based on their understanding of material. KEY TOPICS: Chapter covered include Signals and Systems; Linear Time-Invariant Systems; Fourier Series Representation of Periodic Signals; The Continuous-Time Fourier Transform; The Discrete-Time Fourier Transform; Time and Frequency Analysis of Signals and Systems; Sampling; Communications Systems; The Laplace Transform; The z-Transform; Feedback Systems. MARKET: For readers interested in signals and linear systems.

Product Details

ISBN-13:	9780130421555
Publisher:	Pearson Education
Publication date:	09/24/2001
Series:	Prentice Hall Signal Processing Series
Edition description:	2ND
Pages:	224
Product dimensions:	8.40(w) x 10.90(h) x 0.60(d)

Read an Excerpt

This book provides computer exercises for an undergraduate course on signals and linear systems. Such a course or sequence of courses forms an important part of most engineering curricula. This book was primarily designed as a companion to the second edition of Signals and Systems by Oppenheim and Willsky with Nawab. While the sequence of chapter topics and the notation of this book match that of Signals and Systems, this book of exercises is self-contained and the coverage of fundamental theory and applications is sufficiently broad to make it an ideal companion to any introductory signals and systems text or course.

We believe that assignments of computer exercises in parallel with traditional written problems can help readers to develop a stronger intuition and a deeper understanding of signals and linear systems. To this end, the exercises require the readers to compare the answers they compute in MATLAB^® with results and predictions made based on their analytic understanding of the material. The second edition has been updated to MATLAB 6, Release 12. We believe this approach actively challenges and involves the reader, providing more benefit than a passive computer demonstration. Wherever possible, the exercises have been divided into Basic, Intermediate, and Advanced Problems. In working the problems, the reader progresses from fundamental theory to real applications such as speech processing, financial market analysis and designing mechanical or communication systems. Basic Problems provide detailed instructions for readers, guiding them through the issues explored, but still requiring a justification of their results. Intermediate Problemsexamine more sophisticated concepts, and demand more initiative from the readers in their use of MATLAB. Finally, Advanced Problems challenge the readers' understanding of the more subtle or complicated issues, often requiring open-ended work, writing functions, or processing real data. Some of the Advanced Problems in this category are appropriate for advanced undergraduate coursework on signals and systems.

Care has been taken to ensure that all the exercises in this book can be completed within MATLAB 6. To assist readers, a list of MATLAB functions used in the text can be found in the index, which notes the exercise or page number in which they are explained. Throughout this book, MATLAB functions, commands, and variables will be indicated by

typewriter font. The S symbol following the title of an exercise indicates that the exercise requires the Symbolic Math Toolbox.

A number of exercises refer to functions or data files the reader will need. These are in the Computer Explorations Toolbox, which is available from the MathWorks, Inc. via the World Wide Web.

Table of Contents

1. Signals and Systems.

Tutorial: Basic MATLAB Functions for Representing Signals. Discrete-Time Sinusoidal Signals. Transformations of the Time Index for Discrete-Time Signals. Properties of Discrete-Time Systems. Implementing a First-Order Difference Equation. Continuous-Time Complex Exponential Signals. Transformations of the Time Index for Continuous-Time Signals. Energy and Power for Continuous-Time Signals.

2. Linear Time-Invariant Systems.

Tutorial: conv. Tutorial: filter. Tutorial: lsim with Differential Equations. Properties of Discrete-Time LTI Systems. Linearity and Time-Invariance. Noncausal Finite Impulse Response Filters. Discrete-Time Convolution. Numerical Approximations of Continuous-Time Convolution. The Pulse Response of Continuous-Time LTI Systems. Echo Cancellation via Inverse Filtering.

3. Fourier Series Representation of Periodic Signals.

Tutorial: Computing the Discrete-Time Fourier Series with fft. Tutorial: freqz. Tutorial: lsim with System Functions. Eigenfunctions of Discrete-Time LTI Systems. Synthesizing Signals with the Discrete-Time Fourier Series. Properties of the Continuous-Time Fourier Series. Energy Relations in the Continuous-Time Fourier Series. First-Order Recursive Discrete-Time Filters. Frequency Response of a Continuous-Time System. Computing the Discrete-Time Fourier Series. Synthesizing Continuous-Time Signals with the Fourier Series. The Fourier Representation of Square and Triangle Waves. Continuous-Time Filtering.

4. The Continuous-Time Fourier Transform.

Tutorial: freqs. Numerical Approximation to the Continuous-Time Fourier Transform. Properties of the Continuous-Time Fourier Transform. Time- and Frequency-Domain Characterizations of Systems. Impulse Responses of Differential Equations by Partial Fraction Expansion. Amplitude Modulation and the Continuous-Time Fourier Transform. Symbolic Computation of the Continuous-Time Fourier Transform.

5. The Discrete-Time Fourier Transform.

Computing Samples of the DTFT. Telephone Touch-Tone. Discrete-Time All-Pass Systems. Frequency Sampling: DTFT-Based Filter Design. System Identification. Partial Faction Expansion for Discrete-Time Systems.

6. Time and Frequency Analysis of Signals and Systems.

A Second-Order Shock Absorber. Image Processing with One-Dimensional Filters. Filter Design by Transformation. Phase Effects for Lowpass Filters. Frequency Division Multiple-Access. Linear Prediction on the Stock Market.

7. Sampling.

Aliasing due to Undersampling. Signal Reconstruction from Samples. Upsampling and Downsampling. Bandpass Sampling. Half-Sample Delay. Discrete-Time Differentiation.

8. Communications Systems.

The Hilbert Transform and Single-Sideband AM. Vector Analysis of Amplitude Modulation with Carrier. Amplitude Demodulation and Receiver Synchronization. Intersymbol Interference in PAM Systems. Frequency Modulation.

9. The Laplace Transform.

Tutorial: Making Continuous-Time Pole-Zero Diagrams. Pole Locations for Second-Order Systems. Butterworth Filters. Surface Plots of Laplace Transforms. Implementing Noncausal Continuous-Time Filters.

10. The z-Transform.

Tutorial: Making Discrete-Time Pole-Zero Diagrams. Geometric Interpretation of the Discrete-Time Frequency Response. Quantization Effects in Discrete-Time Filter Structures. Designing Discrete-Time Filters with Euler Approximations. Discrete-Time Butterworth Filter Design Using the Bilinear Transformation.

11. Feedback Systems.

Feedback Stabilization: Stick Balancing. Stabilization of Unstable Systems. Using Feedback to Increase the Bandwidth of an Amplifier.

Bibliography.


Index.

Preface

This book provides computer exercises for an undergraduate course on signals and linear systems. Such a course or sequence of courses forms an important part of most engineering curricula. This book was primarily designed as a companion to the second edition of Signals and Systems by Oppenheim and Willsky with Nawab. While the sequence of chapter topics and the notation of this book match that of Signals and Systems, this book of exercises is self-contained and the coverage of fundamental theory and applications is sufficiently broad to make it an ideal companion to any introductory signals and systems text or course.

We believe that assignments of computer exercises in parallel with traditional written problems can help readers to develop a stronger intuition and a deeper understanding of signals and linear systems. To this end, the exercises require the readers to compare the answers they compute in MATLAB^® with results and predictions made based on their analytic understanding of the material. The second edition has been updated to MATLAB 6, Release 12. We believe this approach actively challenges and involves the reader, providing more benefit than a passive computer demonstration. Wherever possible, the exercises have been divided into Basic, Intermediate, and Advanced Problems. In working the problems, the reader progresses from fundamental theory to real applications such as speech processing, financial market analysis and designing mechanical or communication systems. Basic Problems provide detailed instructions for readers, guiding them through the issues explored, but still requiring a justification of their results. Intermediate Problems examine more sophisticated concepts, and demand more initiative from the readers in their use of MATLAB. Finally, Advanced Problems challenge the readers' understanding of the more subtle or complicated issues, often requiring open-ended work, writing functions, or processing real data. Some of the Advanced Problems in this category are appropriate for advanced undergraduate coursework on signals and systems.

Care has been taken to ensure that all the exercises in this book can be completed within MATLAB 6. To assist readers, a list of MATLAB functions used in the text can be found in the index, which notes the exercise or page number in which they are explained. Throughout this book, MATLAB functions, commands, and variables will be indicated by

typewriter font. The S symbol following the title of an exercise indicates that the exercise requires the Symbolic Math Toolbox.

A number of exercises refer to functions or data files the reader will need. These are in the Computer Explorations Toolbox, which is available from the MathWorks, Inc. via the World Wide Web.