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Computer Explorations in Signals and Systems Using MATLAB.pdf

Contents
1 Signals and Systems 1
1.1 Tutorial: Basic MATLAB Functions for Representing Signals ........ 2
1.2 Discrete-Time Sinusoidal Signals ........................ 7
1.3 Transformations of the Time Index for Discrete-Time Signals ........ 8
1.4 Properties of Discrete-Time Systems ...................... 10
1.5 Implementing a First-Order Difference Equation ............... 11
1.6 Continuous-Time Complex Exponential Signals @ .............. 12
1.7 Transformations of the Time Index for Continuous-Time Signals @ ..... 14
1.8 Energy and Power for Continuous-Time Signals @ .............. 16
2 Linear Time-Invariant Systems 19
2.1 Tutorial: conv .................................. 20
2.2 Tutorial: filter ................................. 22
2.3 Tutorial: lsim with Differential Equations ................... 26
2.4 Properties of Discrete-Time LTI Systems .................... 29
2.5 Linearity and Time-Invariance ......................... 33
2.6 Noncausal Finite Impulse Response Filters ....... .......... 34
2.7 Discrete-Time Convolution ............... .......... 36
2.8 Numerical Approximations of Continuous-Time ......... 38
2.9 The Pulse Response of Continuous-Time LTI Systems ............ 41
2.10 Echo Cancellation via Inverse Filtering .................... 44
3 Fourier Series Representation of Periodic Signals 47
3.1 Tutorial: Computing the Discrete-Time Fourier Series with f ft ....... 47
3.2 Tutorial: freqz .................................. 51
3.3 Tutorial: lsim with System Functions ..................... 52
3.4 Eigenfunctions of Discrete-Time LTI Systems ................. 53
3.5 Synthesizing Signals with the Discrete-Time Fourier Series ......... 55
3.6 Properties of the Continuous-Time Fourier Series ............... 57
3.7 Energy Relations in the Continuous-Time Fourier Series ........... 58
3.8 First-Order Recursive Discrete-Time Filters .................. 59
3.9 Frequency Response of a Continuous-Time System .............. 60
3.10 Computing the Discrete-Time Fourier Series .................. 62 
CONTENTS
3.11 Synthesizing Continuous-Time Signals with the Fourier Series @ ...... 64
3.12 The Fourier Representation of Square and Triangle Waves @ ........ 66
3.13 Continuous-Time Filtering @ .......................... 69
4 The Continuous-Time Fourier Transform 71
4.1 Tutorial: freqs .................................. 71
4.2 Numerical Approximation to the Continuous-Time Fourier Transform ... 74
4.3 Properties of the Continuous-Time Fourier Transform ............ 76
4.4 Time- and Frequency-Domain Characterizations of Systems ......... 79
4.5 Impulse Responses of Differential Equations by Partial Fraction Expansion 81
4.6 Amplitude Modulation and the Continuous-Time Fourier Transform .... 83
4.7 Symbolic Computation of the Continuous-Time Fourier Transform @ ... 86
5 The Discrete-Time Fourier Transform 89
5.1 Computing Samples of the DTFT ....................... 90
5.2 TelephoneTouch-Tone .............................. 93
5.3 Discrete-Time All-Pass Systems ......................... 96
5.4 Frequency Sampling: DTFT-Based Filter Design ............... 97
5.5 System Identification ............................... 99
5.6 Partial Fraction Expansion for Discrete-Time Systems ............ 101
6 Time and Frequency Analysis of Signals and Systems 105
6.1 A Second-Order Shock Absorber ........................ 106
6.2 Image Processing with One-Dimensional Filters ................ 110
6.3 Filter Design by Transformation ........................ 114
6.4 Phase Effects for Lowpass Filters ........................ 117
6.5 Frequency Division Multiple-Access ....................... 118
6.6 Linear Prediction on the Stock Market ..................... 121
7 Sampling 125
7.1 Aliasing due to Undersampling ......................... 126
7.2 Signal Reconstruction from Samples ...................... 128
7.3 Upsampling and Downsampling ......................... 131
7.4 Bandpass Sampling ............................... 134
7.5 Half-Sample Delay ................................ 136
7.6 Discrete-Time Differentiation .......................... 138
8 Communications Systems 143
8.1 The Hilbert Transform and Single-Sideband AM ............... 144
8.2 Vector Analysis of Amplitude Modulation with Carrier ............ 147
8.3 Amplitude Demodulation and Receiver Synchronization ........... 149
8.4 Intersymbol Interference in PAM Systems ................... 152
8.5 Frequency Modulation .............................. 156
9 The Laplace Transform 159
9.1 Tutorial: Making Continuous-Time Pole-Zero Diagrams ........... 159 
CONTENTS
9.2 Pole Locations for Second-Order Systems ................... 162
9.3 Butterworth Filters ................................ 164
9.4 Surface Plots of Laplace Transforms ...................... 165
9.5 Implementing Noncausal Continuous-Time Filters .............. 168
10 The z-Transform 173
10.1 Tutorial: Making Discrete-Time Pole-Zero Diagrams ............. 174
10.2 Geometric Interpretation of the Discrete-Time F'requency Response 176 ..... 10.3 Quantization Effects in Discrete-Time Filter Structures ........... 179
10.4 Designing Discrete-Time Filters with Euler Approximations ......... 183
10.5 Discrete-Time Butterworth Filter Design Using the Bilinear Transformation 186
11 Feedback Systems 191
11.1 Feedback Stabilization: Stick Balancing .................... 191
11.2 Stabilization of Unstable Systems ........................ 194
11.3 Using Feedback to Increase the Bandwidth of an Amplifier .......... 197