Why Read This Book

You should read this book if you need a deep, mathematically sound foundation in how signals and linear systems behave in both continuous and discrete time — knowledge that underpins filter design, sampling, and control in embedded systems. It teaches the analysis tools you will repeatedly use when designing firmware that interfaces with sensors/actuators, implementing DSP on microcontrollers/FPGAs, or reasoning about sampling and aliasing.

Who Will Benefit

Upper-level undergraduates, graduate students, and embedded engineers who implement or analyze signal processing, filtering, and control algorithms on microcontrollers, DSPs, or FPGAs.

Level: Advanced — Prerequisites: Single-variable calculus, ordinary differential equations, basic linear algebra, and familiarity with basic circuit or systems vocabulary (signals, convolution).

Key Takeaways

• Analyze continuous- and discrete-time linear time-invariant (LTI) systems using convolution and impulse responses.
• Compute and interpret Fourier series/transform representations for signal frequency content and filtering behavior.
• Apply Laplace and Z-transforms to solve differential/difference equations and assess system stability and causality.
• Use sampling theory to design and reason about ADC/DAC systems, aliasing, and reconstruction.
• Model systems in state-space form and analyze system properties such as controllability, observability, and stability.
• Design and evaluate basic analog and discrete-time filters and understand their frequency responses.

Topics Covered

1. Introduction to Signals and Systems
2. Time-Domain Analysis of Continuous-Time Signals
3. Time-Domain Analysis of Continuous-Time LTI Systems
4. Fourier Series and Continuous-Time Fourier Transform
5. Laplace Transform and Continuous-Time System Analysis
6. Sampling and Reconstruction of Continuous-Time Signals
7. Discrete-Time Signals and Systems
8. The Z-Transform and Discrete-Time System Analysis
9. Discrete-Time Fourier Transform and Frequency Analysis
10. State-Space Analysis of Linear Systems
11. Stability, Causality, and System Properties
12. Applications: Filtering, Modulation, and System Realization

Languages, Platforms & Tools

How It Compares

More mathematically rigorous and general than many applied DSP texts (e.g., Proakis); compared to Oppenheim & Schafer's Discrete-Time Signal Processing, this book covers both continuous- and discrete-time theory in a unified way rather than focusing primarily on discrete-time DSP.