Signals, Systems and Inference
For upper-level undergraduate courses in deterministic and stochastic signals and system engineering
An Integrative Approach to Signals, Systems and Inference
Signals, Systems and Inference is a comprehensive text that builds on introductory courses in time- and frequency-domain analysis of signals and systems, and in probability. Directed primarily to upper-level undergraduates and beginning graduate students in engineering and applied science branches, this new textbook pioneers a novel course of study. Instead of the usual leap from broad introductory subjects to highly specialized advanced subjects, this engaging and inclusive text creates a study track for a transitional course. Properties and representations of deterministic signals and systems are reviewed and elaborated on, including group delay and the structure and behavior of state-space models.
The text also introduces and interprets correlation functions and power spectral densities for describing and processing random signals. Application contexts include pulse amplitude modulation, observer-based feedback control, optimum linear filters for minimum mean-square-error estimation, and matched filtering for signal detection. Model-based approaches to inference are emphasized, in particular for state estimation, signal estimation, and signal detection. The text explores ideas, methods and tools common to numerous fields involving signals, systems and inference: signal processing, control, communication, time-series analysis, financial engineering, biomedicine, and many others. Signals, Systems, and Inference is a long-awaited and flexible text that can be used for a rigorous course in a broad range of engineering and applied science curricula.
Why Read This Book
You will learn a unified view of deterministic and stochastic signal analysis that connects classical DSP topics (filters, FFT, spectral analysis) with statistical inference and modern algorithms (wavelets, adaptive filtering). The book emphasizes intuition and practical methods, so you can move smoothly from theory to real-world audio, communications, and radar signal‑processing problems.
Who Will Benefit
Upper-level undergraduate or beginning graduate students in electrical engineering, signal processing engineers, and practitioners seeking a coherent bridge between classical DSP and statistical inference for audio, communications, and radar applications.
Level: Advanced — Prerequisites: Single-variable calculus, basic differential equations, linear algebra, introductory signals & systems (time- and frequency-domain concepts), and elementary probability; familiarity with MATLAB or Python is helpful but not required.
Key Takeaways
- Unify time-domain and frequency-domain methods with probabilistic models to analyze deterministic and random signals.
- Apply FFT-based and direct algorithms for digital filter design, spectral analysis, and fast convolution.
- Design and evaluate optimal linear estimators and detectors (Wiener filters, matched filters, basic detection/estimation frameworks).
- Implement adaptive filters and wavelet-based transforms for nonstationary signals such as speech and audio.
- Analyze and synthesize systems for communications and radar tasks using statistical signal-processing tools.
- Translate theoretical results into practical algorithms and experiment with numerical examples (MATLAB/Python).
Topics Covered
- Introduction and overview: signals, systems, and the role of inference
- Review of linear time-invariant systems and Fourier analysis
- Sampling, the discrete-time Fourier transform, and the FFT
- Deterministic digital filter design and implementation
- Spectral analysis: periodograms, windowing, and parametric methods
- Random signals and stochastic processes: stationary processes and power spectra
- Linear estimation: Wiener filtering and mean-square error analysis
- Detection and hypothesis testing for signals in noise
- Adaptive filtering and LMS-family algorithms
- State-space methods and Kalman filtering
- Wavelets and time-frequency representations
- Applications: audio/speech processing, communications, and radar signal processing
- Numerical methods, examples, and laboratory-style problems
Languages, Platforms & Tools
How It Compares
Compared with Oppenheim & Willsky's Signals and Systems (classic LTI focus), this text integrates stochastic modeling and inference more explicitly; for deeper statistical theory, Steven M. Kay's Fundamentals of Statistical Signal Processing provides a more focused, advanced treatment.
