5
Complements and Proofs on Spectrally Correlated Processes
In this chapter, complements and proofs for the results of Chapter 4 are presented.
Chapter 5: Complements and Proofs on Spectrally Correlated Processes
by Antonio Napolitano
Generalizations of Cyclostationary Signal Processing: Spectral Analysis and Applications
- Cover
- Title Page
- Copyright
- Dedication
- About the Author
- Acknowledgements
- Preface
- List of Abbreviations
- Chapter 1: Background
- Chapter 2: Generalized Almost-Cyclostationary Processes
- 2.1 Introduction
- 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
- 2.7 Numerical Results
- 2.8 Summary
- 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”
- 3.7 Conjugate Covariance
- 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
- 4.1 Introduction
- 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
- 4.9 Sampling of SC Processes
- 4.10 Multirate Processing of Discrete-Time Jointly SC Processes
- 4.11 Discrete-Time Estimators of the Spectral Cross-Correlation Density
- 4.12 Numerical Results
- 4.13 Spectral Analysis with Nonuniform Frequency Spacing
- 4.14 Summary
- 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”
- 5.7 Alternative Bounds
- 5.8 Conjugate Covariance
- 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
- Chapter 7: Applications to Mobile Communications and Radar/Sonar
- 7.1 Physical Model for the Wireless Channel
- 7.2 Constant Velocity Vector
- 7.3 Constant Relative Radial Speed
- 7.4 Constant Relative Radial Acceleration
- 7.5 Transmitted Signal: Narrow-Band Condition
- 7.6 Multipath Doppler Channel
- 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
- 7.10 Proofs
- Chapter 8: Bibliographic Notes
- 8.1 Almost-Periodic Functions
- 8.2 Cyclostationary Signals
- 8.3 Generalizations of Cyclostationarity
- 8.4 Other Nonstationary Signals
- 8.5 Functional Approach and Generalized Harmonic Analysis
- 8.6 Linear Time-Variant Processing
- 8.7 Sampling
- 8.8 Complex Random Variables, Signals, and Systems
- 8.9 Stochastic Processes
- 8.10 Mathematics
- 8.11 Signal Processing and Communications
- References
- Index
-
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