Computer Explorations in Signals and Systems

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.

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

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Computer Explorations in Signals and Systems Using MATLAB

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Table of Contents

Supplemental Materials