Signal Analysis and Estimation
This work introduces the analysis (using Fourier techniques) of continuous and discrete deterministic signals along with both estimation and spectral analysis of random signals. It is divided into two sections. Chapters 1-5 are devoted to the analysis of continuous and discrete deterministic signals, while Chapters 6-9 cover the properties, spectral analysis, and estimation of random signals. In addition, in order to assist readers, examples are liberally included throughout every chapter.
Why Read This Book
You should read this book if you want a focused, mathematically grounded introduction to Fourier-based signal analysis and basic spectral/estimation techniques with plentiful worked examples. It gives you the core theory needed to understand power spectra, correlation functions, and elementary estimators without wading through overly abstract treatments.
Who Will Benefit
Advanced undergraduates, graduate students, and practicing engineers who need a concise introduction to Fourier methods and elementary spectral estimation for analysis and design tasks.
Level: Intermediate — Prerequisites: Calculus (including complex exponentials and integrals), basic signals-and-systems concepts (linear time-invariant systems, convolution), and elementary probability/statistics.
Key Takeaways
- Understand Fourier series and transforms for continuous and discrete deterministic signals and how to apply them to analysis problems.
- Apply sampling and discrete-time transform concepts to move between continuous and discrete representations.
- Compute and interpret autocorrelation and power spectral density for random processes.
- Implement basic nonparametric spectral estimation methods (periodogram-style approaches) and understand their biases and variances.
- Formulate and apply linear estimation concepts (e.g., mean-square estimation, basic Wiener filtering) to practical problems.
Topics Covered
- 1. Mathematical Preliminaries and Signal Representations
- 2. Fourier Series and Fourier Transform for Continuous Signals
- 3. Sampling Theorem and Continuous-to-Discrete Conversion
- 4. Discrete-Time Signals and the Discrete-Time Fourier Transform
- 5. Deterministic Signal Analysis and Applications
- 6. Random Processes: Definitions and Statistical Properties
- 7. Correlation Functions and Power Spectral Density
- 8. Spectral Estimation Methods and Practical Considerations
- 9. Linear Estimation and Elementary Filtering Techniques
- Appendix: Worked Examples and Mathematical Tables
Languages, Platforms & Tools
How It Compares
More concise and example-focused than Oppenheim & Willsky's Signals and Systems for deterministic analysis, and far more introductory than Steven M. Kay's modern spectral-estimation/estimation-theory texts which cover estimation in much greater depth.
