Signal Processing

1. Signals, Spectra, and Samples.- 1.0. Introduction.- 1.1. Signals.- 1.2. Fourier Series.- 1.3. Fourier, Laplace, and Hubert Transforms.- 1.4. Linear Systems and Filters.- 1.5. Sampling.- 1.6. Digital Signals and Discrete Transforms.- 1.7. Matrix and State Variable Methods.- 1.8. Bibliographical Notes.- Exercises.- Appendix 1.A. The Fast Fourier Transforms.- Appendix 1.B. Zeros and Poles.- Appendix 1.C. Proofs of Fourier, Laplace, and z Transforms.- Appendix 1.D. Digital Filter Fundamentals.- 2. Random Samples.- 2.0. Introduction.- 2.1. Probability Space.- 2.2. Probability Assignment.- 2.3. Random Variable.- 2.4. Moments and Characteristic Function.- 2.5. Functions of Random Variables.- 2.6. Multidimensional Random Variable.- 2.7. Conditional Probability: Distribution and Density.- 2.8. Distribution Associated with Gaussian Variables.- 2.9. Bibliographical Notes.- Exercises.- Appendix 2.A. Cauchy-Schwarz Inequality.- 3. Random Signals, Estimation, and Filtering.- 3.0. Introduction.- 3.1. Definition and Description.- 3.2. Correlation and Covariance Functions.- 3.3. Gaussian and Markov Processes.- 3.4. Stationary Random Signals.- 3.5. Spectral Analysis and Sampling.- 3.6. Narrow Band Noise Process.- 3.7. Estimation of Parameters.- 3.8. Estimation Methods.- 3.9. Recursive Estimation.- 3.10. Optimum Linear Filters.- 3.11. Bibliographical Notes.- Exercises.- Appendix 3.A. Spectral Estimation.- Appendix 3.B. Kaiman Filtering.- 4. Detection of Signals.- 4.0. Introduction.- 4.1. Hypothesis Testing.- 4.2. Signals with Known Parameters.- 4.3. Signals with Random Parameters.- 4.4. Signals in Colored Noise.- 4.5. Multiple Signals.- 4.6. Sequential Detection.- 4.7. Nonparametric Methods.- 4.8. Bibliographical Notes.- Exercises.- Appendix 4.A. Two Double-Integral Identities.- Appendix 4.B. Link Calculation for Satellite Communication and Rain Attenuation.