Digital and Kalman Filtering: An Introduction to Discrete-Time Filtering and Optimum Linear Estimation, Second Edition (
The treatment is presented in tutorial form, but readers are assumed to be familiar with basic circuit theory, statistical averages, and elementary matrices. Central topics are developed gradually, including both worked examples and problems with solutions, and this second edition features new material and problems.
Why Read This Book
You will get a compact, tutorial-style bridge between classical digital filter design and optimum linear estimation so you can design practical FIR/IIR filters and apply Wiener and Kalman estimators to real noisy data. The book emphasizes worked examples and problems that make theory immediately applicable to audio, radar, and communications signal-processing tasks.
Who Will Benefit
Advanced undergraduates, graduate students, and practicing engineers who need a concise, application-oriented introduction to discrete-time filtering, Wiener estimation, and Kalman recursive estimation.
Level: Intermediate — Prerequisites: Basic signals and systems concepts, elementary linear algebra (matrices and vectors), probability/statistics (means, autocorrelation), and basic circuit theory; familiarity with MATLAB or similar numerical tools is helpful.
Key Takeaways
- Design FIR and IIR digital filters using windowing, frequency-sampling, and analog-prototype techniques
- Apply FFT-based spectral analysis to characterize signals and evaluate filter performance
- Formulate and implement nonrecursive Wiener (FIR) estimators for MMSE signal estimation
- Derive, implement, and tune the recursive Kalman filter for scalar and vector state-space models
- Analyze stability, numerical issues, and practical realizations of digital filters and estimators
Topics Covered
- Introduction to discrete-time filtering and estimation
- Discrete-time signals and systems — z-transform and frequency response
- FIR filter design: windows, optimal approximations, and realizations
- IIR filter design: analog prototypes, bilinear transform, and stability
- Filter structures, realization forms, and numerical considerations
- Fast algorithms and spectral analysis: FFT, periodograms, and resolution
- Nonrecursive estimation: Wiener filters and MMSE design
- State-space modeling and fundamentals of recursive estimation
- Kalman filter: derivation, implementation, and properties
- Vector Kalman filtering and optimum estimation of multivariate signals
- Adaptive filtering concepts and practical considerations
- Applications: audio/speech, radar, and communications examples; worked problems
- Appendices: mathematical tools, tables, and problem solutions
Languages, Platforms & Tools
How It Compares
More concise and tutorial-oriented than Haykin's Adaptive Filter Theory (which is deeper on adaptive algorithms) and more focused on connecting digital filter design with Kalman estimation than Brown & Hwang's broader Introduction to Random Signals and Kalman Filtering.
