Signal processing for communications

Taking a novel, less classical approach to the subject, the authors have written this book with the conviction that signal processing should be fun. Their treatment is less focused on the mathematics and more on the conceptual aspects, allowing students to think about the subject at a higher conceptual level, thus building the foundations for more advanced topics and helping students solve real-world problems. The last chapter pulls together the individual topics into an in-depth look at the development of an end-to-end communication system. Richly illustrated with examples and exercises in each chapter, the book offers a fresh approach to the teaching of signal processing to upper-level undergraduates.

Preface	p. vii
Chapter 1 What Is Digital Signal Processing?	p. 1
1.1 Some History and Philosophy	p. 2
1.1.1 Digital Signal Processing under the Pyramids	p. 2
1.1.2 The Hellenic Shift to Analog Processing	p. 4
1.1.3 "Gentlemen: calculemus!"	p. 5
1.2 Discrete Time	p. 7
1.3 Discrete Amplitude	p. 10
1.4 Communication Systems	p. 12
1.5 How to Read this Book	p. 17
Further Reading	p. 18
Chapter 2 Discrete-Time Signals	p. 19
2.1 Basic Definitions	p. 19
2.1.1 The Discrete-Time Abstraction	p. 21
2.1.2 Basic Signals	p. 23
2.1.3 Digital Frequency	p. 25
2.1.4 Elementary Operators	p. 26
2.1.5 The Reproducing Formula	p. 27
2.1.6 Energy and Power	p. 27
2.2 Classes of Discrete-Time Signals	p. 28
2.2.1 Finite-Length Signals	p. 29
2.2.2 Infinite-Length Signals	p. 30
Examples	p. 33
Further Reading	p. 36
Exercises	p. 36
Chapter 3 Signals and Hilbert Spaces	p. 37
3.1 Euclidean Geometry: a Review	p. 38
3.2 From Vector Spaces to Hilbert Spaces	p. 41
3.2.1 The Recipe for Hilbert Space	p. 42
3.2.2 Examples of Hilbert Spaces	p. 45
3.2.3 Inner Products and Distances	p. 46
3.3 Subspaces, Bases, Projections	p. 47
3.3.1 Definitions	p. 48
3.3.2 Properties of Orthonormal Bases	p. 49
3.3.3 Examples of Bases	p. 51
3.4 Signal Spaces Revisited	p. 53
3.4.1 Finite-Length Signals	p. 53
3.4.2 Periodic Signals	p. 53
3.4.3 Infinite Sequences	p. 54
Further Reading	p. 55
Exercises	p. 55
Chapter 4 Fourier Analysis	p. 59
4.1 Preliminaries	p. 60
4.1.1 Complex Exponentials	p. 61
4.1.2 Complex Oscillations? Negative Frequencies?	p. 61
4.2 The DFT (Discrete Fourier Transform)	p. 63
4.2.1 Matrix Form	p. 64
4.2.2 Explicit Form	p. 64
4.2.3 Physical Interpretation	p. 67
4.3 The DFS (Discrete Fourier Series)	p. 71
4.4 The DTFT (Discrete-Time Fourier Transform)	p. 72
4.4.1 The DTFT as the Limit of a DFS	p. 75
4.4.2 The DTFT as a Formal Change of Basis	p. 77
4.5 Relationships between Transforms	p. 81
4.6 Fourier Transform Properties	p. 83
4.6.1 DTFT Properties	p. 83
4.6.2 DFS Properties	p. 85
4.6.3 DFT Properties	p. 86
4.7 Fourier Analysis in Practice	p. 90
4.7.1 Plotting Spectral Data	p. 91
4.7.2 Computing the Transform: the FFT	p. 93
4.7.3 Cosmetics: Zero-Padding	p. 94
4.7.4 Spectral Analysis	p. 95
4.8 Time-Frequency Analysis	p. 98
4.8.1 The Spectrogram	p. 98
4.8.2 The Uncertainty Principle	p. 100
4.9 Digital Frequency vs. Real Frequency	p. 101
Examples	p. 102
Further Reading	p. 105
Exercises	p. 106
Chapter 5 Discrete-Time Filters	p. 109
5.1 Linear Time-Invariant Systems	p. 109
5.2 Filtering in the Time Domain	p. 111
5.2.1 The Convolution Operator	p. 111
5.2.2 Properties of the Impulse Response	p. 113
5.3 Filtering by Example - Time Domain	p. 115
5.3.1 FIR Filtering	p. 115
5.3.2 IIR Filtering	p. 117
5.4 Filtering in the Frequency Domain	p. 121
5.4.1 LTI "Eigenfunctions"	p. 121
5.4.2 The Convolution and Modulation Theorems	p. 122
5.4.3 Properties of the Frequency Response	p. 123
5.5 Filtering by Example - Frequency Domain	p. 126
5.6 Ideal Filters	p. 129
5.7 Realizable Filters	p. 133
5.7.1 Constant-Coefficient Difference Equations	p. 134
5.7.2 The Algorithmic Nature of CCDEs	p. 135
5.7.3 Filter Analysis and Design	p. 136
Examples	p. 136
Further Reading	p. 143
Exercises	p. 143
Chapter 6 The Z-Transform	p. 147
6.1 Filter Analysis	p. 148
6.1.1 Solving CCDEs	p. 148
6.1.2 Causality	p. 149
6.1.3 Region of Convergence	p. 150
6.1.4 ROC and System Stability	p. 152
6.1.5 ROC of Rational Transfer Functions and Filter Stability	p. 152
6.2 The Pole-Zero Plot	p. 152
6.2.1 Pole-Zero Patterns	p. 153
6.2.2 Pole-Zero Cancellation	p. 154
6.2.3 Sketching the Transfer Function from the Pole-Zero Plot	p. 155
6.3 Filtering by Example - Z-Transform	p. 156
Examples	p. 157
Further Reading	p. 159
Exercises	p. 159
Chapter 7 Filter Design	p. 165
7.1 Design Fundamentals	p. 165
7.1.1 FIR versus IIR	p. 166
7.1.2 Filter Specifications and Tradeoffs	p. 168
7.2 FIR Filter Design	p. 171
7.2.1 FIR Filter Design by Windowing	p. 171
7.2.2 Minimax FIR Filter Design	p. 179
7.3 IIR Filter Design	p. 190
7.3.1 All-Time Classics	p. 191
7.4 Filter Structures	p. 195
7.4.1 FIR Filter Structures	p. 196
7.4.2 IIR Filter Structures	p. 197
7.4.3 Some Remarks on Numerical Stability	p. 200
7.5 Filtering and Signal Classes	p. 200
7.5.1 Filtering of Finite-Length Signals	p. 200
7.5.2 Filtering of Periodic Sequences	p. 201
Examples	p. 204
Further Reading	p. 208
Exercises	p. 208
Chapter 8 Stochastic Signal Processing	p. 217
8.1 Random Variables	p. 217
8.2 Random Vectors	p. 219
8.3 Random Processes	p. 221
8.4 Spectral Representation of Stationary Random Processes	p. 223
8.4.1 Power Spectral Density	p. 224
8.4.2 PSD of a Stationary Process	p. 225
8.4.3 White Noise	p. 227
8.5 Stochastic Signal Processing	p. 227
Examples	p. 229
Further Reading	p. 232
Exercises	p. 233
Chapter 9 Interpolation and Sampling	p. 235
9.1 Preliminaries and Notation	p. 236
9.2 Continuous-Time Signals	p. 237
9.3 Bandlimited Signals	p. 239
9.4 Interpolation	p. 240
9.4.1 Local Interpolation	p. 241
9.4.2 Polynomial Interpolation	p. 243
9.4.3 Sinc Interpolation	p. 245
9.5 The Sampling Theorem	p. 247
9.6 Aliasing	p. 250
9.6.1 Non-Bandlimited Signals	p. 250
9.6.2 Aliasing: Intuition	p. 251
9.6.3 Aliasing: Proof	p. 253
9.6.4 Aliasing: Examples	p. 255
9.7 Discrete-Time Processing of Analog Signals	p. 260
9.7.1 A Digital Differentiator	p. 260
9.7.2 Fractional Delays	p. 261
Examples	p. 262
Appendix	p. 266
Further Reading	p. 268
Exercises	p. 269
Chapter 10 A/D and D/A Conversions	p. 275
10.1 Quantization	p. 275
10.1.1 Uniform Scalar Quantization	p. 278
10.1.2 Advanced Quantizers	p. 282
10.2 A/D Conversion	p. 283
10.3 D/A Conversion	p. 286
Examples	p. 287
Further Reading	p. 290
Exercises	p. 290
Chapter 11 Multirate Signal Processing	p. 293
11.1 Downsampling	p. 294
11.1.1 Properties of the Downsampling Operator	p. 294
11.1.2 Frequency-Domain Representation	p. 295
11.1.3 Examples	p. 297
11.1.4 Downsampling and Filtering	p. 302
11.2 Upsampling	p. 304
11.2.1 Upsampling and Interpolation	p. 306
11.3 Rational Sampling Rate Changes	p. 310
11.4 Oversampling	p. 311
11.4.1 Oversampled A/D Conversion	p. 311
11.4.2 Oversampled D/A Conversion	p. 314
Examples	p. 319
Further Reading	p. 322
Exercises	p. 322
Chapter 12 Design of a Digital Communication System	p. 327
12.1 The Communication Channel	p. 328
12.1.1 The AM Radio Channel	p. 329
12.1.2 The Telephone Channel	p. 330
12.2 Modem Design: The Transmitter	p. 331
12.2.1 Digital Modulation and the Bandwidth Constraint	p. 331
12.2.2 Signaling Alphabets and the Power Constraint	p. 339
12.3 Modem Design: the Receiver	p. 347
12.3.1 Hilbert Demodulation	p. 348
12.3.2 The Effects of the Channel	p. 350
12.4 Adaptive Synchronization	p. 353
12.4.1 Carrier Recovery	p. 353
12.4.2 Timing Recovery	p. 356
Further Reading	p. 365
Exercises	p. 365
Index	p. 367

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