Contents
1.1 Second-Order Characterization of Stochastic Processes
1.3 Almost-Cyclostationary Processes
1.4 Some Properties of Cumulants
Chapter 2: Generalized Almost-Cyclostationary Processes
2.2 Characterization of GACS Stochastic Processes
2.3 Linear Time-Variant Filtering of GACS Processes
2.4 Estimation of the Cyclic Cross-Correlation Function
2.5 Sampling of GACS Processes
2.6 Discrete-Time Estimator of the Cyclic Cross-Correlation Function
Chapter 3: Complements and Proofs on Generalized Almost-Cyclostationary Processes
3.1 Proofs for Section 2.2.2 “Second-Order Wide-Sense Statistical Characterization”
3.2 Proofs for Section 2.2.3 “Second-Order Spectral Characterization”
3.3 Proofs for Section 2.3 “Linear Time-Variant Filtering of GACS Processes”
3.4 Proofs for Section 2.4.1 “The Cyclic Cross-Correlogram”
3.5 Proofs for Section 2.4.2 “Mean-Square Consistency of the Cyclic Cross-Correlogram”
3.6 Proofs for Section 2.4.3 “Asymptotic Normality of the Cyclic Cross-Correlogram”
3.8 Proofs for Section 2.5 “Sampling of GACS Processes”
3.9 Proofs for Section 2.6.1 “Discrete-Time Cyclic Cross-Correlogram”
3.10 Proofs for Section 2.6.2 “Asymptotic Results as N→ ∞”
3.11 Proofs for Section 2.6.3 “Asymptotic Results as N→ ∞ and Ts → 0′′
3.12 Proofs for Section 2.6.4 “Concluding Remarks”
3.13 Discrete-Time and Hybrid Conjugate Covariance
Chapter 4: Spectrally Correlated Processes
4.2 Characterization of SC Stochastic Processes
4.3 Linear Time-Variant Filtering of SC Processes
4.4 The Bifrequency Cross-Periodogram
4.5 Measurement of Spectral Correlation –Unknown Support Curves
4.6 The Frequency-Smoothed Cross-Periodogram
4.7 Measurement of Spectral Correlation –Known Support Curves
4.8 Discrete-Time SC Processes
4.10 Multirate Processing of Discrete-Time Jointly SC Processes
4.11 Discrete-Time Estimators of the Spectral Cross-Correlation Density
4.13 Spectral Analysis with Nonuniform Frequency Spacing
Chapter 5: Complements and Proofs on Spectrally Correlated Processes
5.1 Proofs for Section 4.2 “Characterization of SC Stochastic Processes”
5.2 Proofs for Section 4.4 “The Bifrequency Cross-Periodogram”
5.3 Proofs for Section 4.5 “Measurement of Spectral Correlation –Unknown Support Curves”
5.4 Proofs for Section 4.6 “The Frequency-Smoothed Cross-Periodogram”
5.5 Proofs for Section 4.7.1 “Mean-Square Consistency of the Frequency-Smoothed Cross-Periodogram”
5.6 Proofs for Section 4.7.2 “Asymptotic Normality of the Frequency-Smoothed Cross-Periodogram”
5.9 Proofs for Section 4.8 “Discrete-Time SC Processes”
5.10 Proofs for Section 4.9 “Sampling of SC Processes”
5.11 Proofs for Section 4.10 “Multirate Processing of Discrete-Time Jointly SC Processes”
Chapter 6: Functional Approach for Signal Analysis
6.3 Almost-Periodically Time-Variant Model
6.4 Nonstationarity Classification in the Functional Approach
6.5 Proofs of FOT Counterparts of Some Results on ACS and GACS Signals
Chapter 7: Applications to Mobile Communications and Radar/Sonar
7.1 Physical Model for the Wireless Channel
7.3 Constant Relative Radial Speed
7.4 Constant Relative Radial Acceleration
7.5 Transmitted Signal: Narrow-Band Condition
7.7 Spectral Analysis of Doppler-Stretched Signals –Constant Radial Speed
7.8 Spectral Analysis of Doppler-Stretched Signals –Constant Relative Radial Acceleration
7.9 Other Models of Time-Varying Delays
Chapter 8: Bibliographic Notes
8.3 Generalizations of Cyclostationarity
8.4 Other Nonstationary Signals
8.5 Functional Approach and Generalized Harmonic Analysis
8.6 Linear Time-Variant Processing
8.8 Complex Random Variables, Signals, and Systems