Computer Explorations in Signals and Systems Using MATLAB

by Buck, John R.; Daniel, Michael M.; Singer, Andrew C.

• ISBN13: 9780130421555
• ISBN10: 0130421553
• Edition: 2nd
• Format: Paperback
• Copyright: 2001-09-24
• Publisher: Pearson

Summary

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.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.For readers interested in signals and linear systems.

Table of Contents

Preface	xi
Signals and Systems	1	(18)
Tutorial: Basic MATLAB Functions for Representing Signals	2	(5)
Discrete-Time Sinusoidal Signals	7	(1)
Transformations of the Time Index for Discrete-Time Signals	8	(2)
Properties of Discrete-Time Systems	10	(1)
Implementing a First-Order Difference Equation	11	(1)
Continuous-Time Complex Exponential Signals (S)	12	(2)
Transformations of the Time Index for Continuous-Time Signals (S)	14	(2)
Energy and Power for Continuous-Time Signals (S)	16	(3)
Linear Time-Invariant Systems	19	(28)
Tutorial: conv	20	(2)
Tutorial: filter	22	(4)
Tutorial: Isim with Differential Equations	26	(3)
Properties of Discrete-Time LTI Systems	29	(4)
Linearity and Time-Invariance	33	(1)
Noncausal Finite Impulse Response Filters	34	(2)
Discrete-Time Convolution	36	(2)
Numerical Approximations of Continuous-Time Convolution	38	(3)
The Pulse Response of Continuous-Time LTI Systems	41	(3)
Echo Cancellation via Inverse Filtering	44	(3)
Fourier Series Representation of Periodic Signals	47	(24)
Tutorial: Computing the Discrete-Time Fourier Series with fft	47	(4)
Tutorial: freqz	51	(1)
Tutorial: Isim with System Functions	52	(1)
Eigenfunctions of Discrete-Time LTI Systems	53	(2)
Synthesizing Signals with the Discrete-Time Fourier Series	55	(2)
Properties of the Continous-Time Fourier Series	57	(1)
Energy Relations in the Continuous-Time Fourier Series	58	(1)
First-Order Recursive Discrete-Time Filters	59	(1)
Frequency Response of a Continuous-Time System	60	(2)
Computing the Discrete-Time Fourier Series	62	(2)
Synthesizing Continuous-Time Signals with the Fourier Series (S)	64	(2)
The Fourier Representation of Square and Triangle Waves (S)	66	(3)
Continuous-Time Filtering (S)	69	(2)
The Continuous-Time Fourier Transform	71	(18)
Tutorial: freqs	71	(3)
Numerical Approximation to the Continuous-Time Fourier Transform	74	(1)
Properties of the Continuous-Time Fourier Transform	74	(5)
Time- and Frequency-Domain Characterizations of Systems	79	(2)
Impulse Responses of Differential Eqations by Partial Fraction Expansion	81	(2)
Amplitude Modulation and the Continuous-Time Fourier Transform	83	(2)
Symbolic Computation of the Continuous-Time Fourier Transform (S)	85	(4)
The Discrete-Time Fourier Transform	89	(16)
Computing Samples of the DTFT	90	(3)
Telephone Touch-Tone	93	(3)
Discrete-Time All-Pass Systems	96	(1)
Frequency Sampling: DTFT-Based Filter Design	97	(2)
System Identification	99	(2)
Partial Fraction Expansion for Discrete-Time Systems	101	(4)
Time and Frequency Analysis of Signals and Systems	105	(20)
A Second-Order Shock Absorber	106	(4)
Image Processing with One-Dimensional Filters	110	(4)
Filter Design by Transformation	114	(3)
Phase Effects for Lowpass Filters	117	(1)
Frequency Division Multiple-Access	118	(3)
Linear Prediction on the Stock Market	121	(4)
Sampling	125	(18)
Aliasing due to Undersampling	126	(2)
Signal Reconstruction from Samples	128	(3)
Upsampling and Downsampling	131	(3)
Bandpass Sampling	134	(2)
Half-Sample Delay	136	(2)
Discrete-Time Differentiation	138	(5)
Communications Systems	143	(16)
The Hilbert Transform and Single-Sideband AM	144	(3)
Vector Analysis of Amplitude Modulation with Carrier	147	(2)
Amplitude Demodulation and Receiver Synchronization	149	(3)
Intersymbol Interference in PAM Systems	152	(4)
Frequency Modulation	156	(3)
The Laplace Transform	159	(14)
Tutorial: Making Continuous-Time Pole-Zero Diagrams	159	(3)
Pole Locations for Second-Order Systems	162	(2)
Butterworth Filters	164	(1)
Surface Plots of Laplace Transforms	165	(3)
Implementing Noncausal Continuous-Time Filters	168	(5)
The z-Transform	173	(18)
Tutorial: Making Discrete-Time Pole-Zero Diagrams	174	(2)
Geometric Interpretation of the Discrete-Time Frequency Response	176	(3)
Quantization Effects in Discrete-Time Filter Structures	179	(4)
Designing Discrete-Time Filters with Euler Approximations	183	(3)
Discrete-Time Butterworth Filter Design Using the Bilinear Transformation	186	(5)
Feedback Systems	191	(10)
Feedback Stabilization: Stick Balancing	191	(3)
Stabilization of Unstable Systems	194	(3)
Using Feedback to Increase the Bandwidth of an Amplifier	197	(4)
Bibliography	201	(2)
Index	203

Excerpts

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 ofSignals and Systemsby Oppenheim and Willsky with Nawab. While the sequence of chapter topics and the notation of this book match that ofSignals 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. TheSsymbol 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.