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Preface | p. vii |
What Is Digital Signal Processing? | p. 1 |
Some History and Philosophy | p. 2 |
Digital Signal Processing under the Pyramids | p. 2 |
The Hellenic Shift to Analog Processing | p. 4 |
"Gentlemen: calculemus!" | p. 5 |
Discrete Time | p. 7 |
Discrete Amplitude | p. 10 |
Communication Systems | p. 12 |
How to Read this Book | p. 17 |
Further Reading | p. 18 |
Discrete-Time Signals | p. 19 |
Basic Definitions | p. 19 |
The Discrete-Time Abstraction | p. 21 |
Basic Signals | p. 23 |
Digital Frequency | p. 25 |
Elementary Operators | p. 26 |
The Reproducing Formula | p. 27 |
Energy and Power | p. 27 |
Classes of Discrete-Time Signals | p. 28 |
Finite-Length Signals | p. 29 |
Infinite-Length Signals | p. 30 |
Examples | p. 33 |
Further Reading | p. 36 |
Exercises | p. 36 |
Signals and Hilbert Spaces | p. 37 |
Euclidean Geometry: a Review | p. 38 |
From Vector Spaces to Hilbert Spaces | p. 41 |
The Recipe for Hilbert Space | p. 42 |
Examples of Hilbert Spaces | p. 45 |
Inner Products and Distances | p. 46 |
Subspaces, Bases, Projections | p. 47 |
Definitions | p. 48 |
Properties of Orthonormal Bases | p. 49 |
Examples of Bases | p. 51 |
Signal Spaces Revisited | p. 53 |
Finite-Length Signals | p. 53 |
Periodic Signals | p. 53 |
Infinite Sequences | p. 54 |
Further Reading | p. 55 |
Exercises | p. 55 |
Fourier Analysis | p. 59 |
Preliminaries | p. 60 |
Complex Exponentials | p. 61 |
Complex Oscillations? Negative Frequencies? | p. 61 |
The DFT (Discrete Fourier Transform) | p. 63 |
Matrix Form | p. 64 |
Explicit Form | p. 64 |
Physical Interpretation | p. 67 |
The DFS (Discrete Fourier Series) | p. 71 |
The DTFT (Discrete-Time Fourier Transform) | p. 72 |
The DTFT as the Limit of a DFS | p. 75 |
The DTFT as a Formal Change of Basis | p. 77 |
Relationships between Transforms | p. 81 |
Fourier Transform Properties | p. 83 |
DTFT Properties | p. 83 |
DFS Properties | p. 85 |
DFT Properties | p. 86 |
Fourier Analysis in Practice | p. 90 |
Plotting Spectral Data | p. 91 |
Computing the Transform: the FFT | p. 93 |
Cosmetics: Zero-Padding | p. 94 |
Spectral Analysis | p. 95 |
Time-Frequency Analysis | p. 98 |
The Spectrogram | p. 98 |
The Uncertainty Principle | p. 100 |
Digital Frequency vs. Real Frequency | p. 101 |
Examples | p. 102 |
Further Reading | p. 105 |
Exercises | p. 106 |
Discrete-Time Filters | p. 109 |
Linear Time-Invariant Systems | p. 109 |
Filtering in the Time Domain | p. 111 |
The Convolution Operator | p. 111 |
Properties of the Impulse Response | p. 113 |
Filtering by Example - Time Domain | p. 115 |
FIR Filtering | p. 115 |
IIR Filtering | p. 117 |
Filtering in the Frequency Domain | p. 121 |
LTI "Eigenfunctions" | p. 121 |
The Convolution and Modulation Theorems | p. 122 |
Properties of the Frequency Response | p. 123 |
Filtering by Example - Frequency Domain | p. 126 |
Ideal Filters | p. 129 |
Realizable Filters | p. 133 |
Constant-Coefficient Difference Equations | p. 134 |
The Algorithmic Nature of CCDEs | p. 135 |
Filter Analysis and Design | p. 136 |
Examples | p. 136 |
Further Reading | p. 143 |
Exercises | p. 143 |
The Z-Transform | p. 147 |
Filter Analysis | p. 148 |
Solving CCDEs | p. 148 |
Causality | p. 149 |
Region of Convergence | p. 150 |
ROC and System Stability | p. 152 |
ROC of Rational Transfer Functions and Filter Stability | p. 152 |
The Pole-Zero Plot | p. 152 |
Pole-Zero Patterns | p. 153 |
Pole-Zero Cancellation | p. 154 |
Sketching the Transfer Function from the Pole-Zero Plot | p. 155 |
Filtering by Example - Z-Transform | p. 156 |
Examples | p. 157 |
Further Reading | p. 159 |
Exercises | p. 159 |
Filter Design | p. 165 |
Design Fundamentals | p. 165 |
FIR versus IIR | p. 166 |
Filter Specifications and Tradeoffs | p. 168 |
FIR Filter Design | p. 171 |
FIR Filter Design by Windowing | p. 171 |
Minimax FIR Filter Design | p. 179 |
IIR Filter Design | p. 190 |
All-Time Classics | p. 191 |
Filter Structures | p. 195 |
FIR Filter Structures | p. 196 |
IIR Filter Structures | p. 197 |
Some Remarks on Numerical Stability | p. 200 |
Filtering and Signal Classes | p. 200 |
Filtering of Finite-Length Signals | p. 200 |
Filtering of Periodic Sequences | p. 201 |
Examples | p. 204 |
Further Reading | p. 208 |
Exercises | p. 208 |
Stochastic Signal Processing | p. 217 |
Random Variables | p. 217 |
Random Vectors | p. 219 |
Random Processes | p. 221 |
Spectral Representation of Stationary Random Processes | p. 223 |
Power Spectral Density | p. 224 |
PSD of a Stationary Process | p. 225 |
White Noise | p. 227 |
Stochastic Signal Processing | p. 227 |
Examples | p. 229 |
Further Reading | p. 232 |
Exercises | p. 233 |
Interpolation and Sampling | p. 235 |
Preliminaries and Notation | p. 236 |
Continuous-Time Signals | p. 237 |
Bandlimited Signals | p. 239 |
Interpolation | p. 240 |
Local Interpolation | p. 241 |
Polynomial Interpolation | p. 243 |
Sinc Interpolation | p. 245 |
The Sampling Theorem | p. 247 |
Aliasing | p. 250 |
Non-Bandlimited Signals | p. 250 |
Aliasing: Intuition | p. 251 |
Aliasing: Proof | p. 253 |
Aliasing: Examples | p. 255 |
Discrete-Time Processing of Analog Signals | p. 260 |
A Digital Differentiator | p. 260 |
Fractional Delays | p. 261 |
Examples | p. 262 |
Appendix | p. 266 |
Further Reading | p. 268 |
Exercises | p. 269 |
A/D and D/A Conversions | p. 275 |
Quantization | p. 275 |
Uniform Scalar Quantization | p. 278 |
Advanced Quantizers | p. 282 |
A/D Conversion | p. 283 |
D/A Conversion | p. 286 |
Examples | p. 287 |
Further Reading | p. 290 |
Exercises | p. 290 |
Multirate Signal Processing | p. 293 |
Downsampling | p. 294 |
Properties of the Downsampling Operator | p. 294 |
Frequency-Domain Representation | p. 295 |
Examples | p. 297 |
Downsampling and Filtering | p. 302 |
Upsampling | p. 304 |
Upsampling and Interpolation | p. 306 |
Rational Sampling Rate Changes | p. 310 |
Oversampling | p. 311 |
Oversampled A/D Conversion | p. 311 |
Oversampled D/A Conversion | p. 314 |
Examples | p. 319 |
Further Reading | p. 322 |
Exercises | p. 322 |
Design of a Digital Communication System | p. 327 |
The Communication Channel | p. 328 |
The AM Radio Channel | p. 329 |
The Telephone Channel | p. 330 |
Modem Design: The Transmitter | p. 331 |
Digital Modulation and the Bandwidth Constraint | p. 331 |
Signaling Alphabets and the Power Constraint | p. 339 |
Modem Design: the Receiver | p. 347 |
Hilbert Demodulation | p. 348 |
The Effects of the Channel | p. 350 |
Adaptive Synchronization | p. 353 |
Carrier Recovery | p. 353 |
Timing Recovery | p. 356 |
Further Reading | p. 365 |
Exercises | p. 365 |
Index | p. 367 |
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