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3 | (22) |
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1.1 Types of Random Signals |
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3 | (8) |
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1.2 Characteristics of Signals |
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11 | (1) |
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1.3 Time Domain and Frequency Domain Descriptions of Periodic Signals |
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12 | (7) |
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1.4 Building a Better Mousetrap: Complex Exponentials |
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19 | (3) |
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1.5 Problems and Exercises |
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22 | (3) |
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2 Spectral Representation of Deterministic Signals: Fourier Series and Transforms |
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25 | (32) |
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2.1 Complex Fourier Series for Periodic Signals |
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25 | (10) |
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2.2 Approximation of Periodic Signals by Finite Fourier Sums |
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35 | (6) |
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2.3 Aperiodic Signals and Fourier Transforms |
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41 | (3) |
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2.4 Basic Properties of Fourier Transform |
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44 | (3) |
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2.5 Fourier Transforms of Some Non-integrable Signals: Dirac's Delta-Impulse |
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47 | (4) |
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2.6 Discrete and Fast Fourier Transforms |
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51 | (2) |
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2.7 Problems and Exercises |
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53 | (4) |
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3 Uncertainty Principle and Wavelet Transforms |
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57 | (34) |
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3.1 Time-Frequency Localization and the Uncertainty Principle |
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57 | (3) |
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3.2 Windowed Fourier Transform |
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60 | (5) |
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3.3 Continuous Wavelet Transforms |
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65 | (13) |
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3.4 Haar Wavelets and Multiresolution Analysis |
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78 | (6) |
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3.5 Continuous Daubechies' Wavelets |
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84 | (5) |
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89 | (2) |
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4 Random Quantities and Random Vectors |
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91 | (60) |
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4.1 Discrete, Continuous, and Singular Random Quantities |
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91 | (22) |
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4.2 Expectations and Moments of Random Quantities |
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113 | (4) |
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4.3 Random Vectors, Conditional Probabilities, Statistical Independence, and Correlations |
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117 | (12) |
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4.4 The Least Squares Fit, Linear Regression |
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129 | (4) |
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4.5 The Law of Large Numbers and the Stability of Fluctuations Law |
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133 | (3) |
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4.6 Estimators of Parameters and Their Accuracy: Confidence Intervals |
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136 | (8) |
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4.7 Problems and Exercises |
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144 | (7) |
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151 | (24) |
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5.1 Stationarity and Autocovariance Functions |
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151 | (15) |
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5.2 Estimating the Mean and the Autocovariance Function, Ergodic Signals |
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166 | (4) |
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5.3 Problems and Exercises |
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170 | (5) |
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6 Power Spectra of Stationary Signals |
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175 | (18) |
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6.1 Mean Power of a Stationary Signal |
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175 | (2) |
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6.2 Power Spectrum and Autocovariance Function |
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177 | (7) |
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6.3 Power Spectra of Interpolated Digital Signals |
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184 | (5) |
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6.4 Problems and Exercises |
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189 | (4) |
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7 Transmission of Stationary Signals Through Linear Systems |
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193 | (24) |
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193 | (9) |
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7.2 Frequency Domain Analysis and System's Bandwidth |
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202 | (4) |
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7.3 Digital Signal, Discrete Time Sampling |
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206 | (6) |
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7.4 Problems and Exercises |
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212 | (5) |
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8 Optimization of Signal-to-Noise Ratio in Linear Systems |
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217 | (12) |
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8.1 Parametric Optimization for a Fixed Filter Structure |
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217 | (4) |
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8.2 Filter Structure Matched to Input Signal |
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221 | (3) |
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224 | (3) |
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8.4 Problems and Exercises |
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227 | (2) |
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9 Gaussian Signals, Covariance Matrices, and Sample Path Properties |
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229 | (18) |
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9.1 Linear Transformations of Random Vectors |
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229 | (3) |
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9.2 Gaussian Random Vectors |
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232 | (5) |
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9.3 Gaussian Stationary Signals |
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237 | (2) |
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9.4 Sample Path Properties of General and Gaussian Stationary Signals |
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239 | (6) |
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9.5 Problems and Exercises |
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245 | (2) |
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10 Spectral Representation of Discrete-Time Stationary Signals and Their Computer Simulations |
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247 | (32) |
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10.1 Spectral Representation |
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247 | (2) |
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10.2 Autocovariance as a Positive-Definite Sequence |
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249 | (2) |
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10.3 Cumulative Power Spectrum of Discrete-Time Stationary Signal |
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251 | (3) |
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10.4 Stochastic Integration with Respect to Signals with Uncorrelated Increments |
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254 | (5) |
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10.5 Spectral Representation of Stationary Signals |
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259 | (4) |
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10.6 Computer Algorithms: Complex-Valued Case |
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263 | (6) |
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10.7 Computer Algorithms: Real-Valued Case |
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269 | (6) |
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10.8 Problems and Exercises |
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275 | (4) |
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11 Prediction Theory for Stationary Random Signals |
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279 | (12) |
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11.1 The Wold Decomposition Theorem and Optimal Predictors |
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279 | (3) |
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11.2 Application of the Spectral Representation to the Solution of the Prediction Problem |
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282 | (5) |
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11.3 Examples of Linear Prediction for Stationary Time Series |
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287 | (2) |
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11.4 Problems and Exercises |
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289 | (2) |
Solutions to Selected Problems and Exercises |
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291 | (32) |
Bibliographical Comments |
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323 | (4) |
Index |
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327 | |