Why Read This Book

You should read this book if you want a compact, mathematically grounded introduction to continuous- and discrete-time signals and linear systems that prepares you to analyze real DSP problems. You will learn core transform techniques (Fourier, Laplace, z-transform), sampling theory, and time‑domain/system analysis that form the foundation for filter design, spectral analysis, and communications work.

Who Will Benefit

Upper-level undergraduates, graduate students, and practicing engineers seeking a clear, theory-focused refresher on signals and linear systems before tackling applied DSP, communications, or control problems.

Level: Intermediate — Prerequisites: Calculus (including integrals and complex-valued functions), basic differential equations, and elementary linear algebra; prior exposure to basic circuit or systems concepts is helpful but not required.

Key Takeaways

• Apply Fourier, Laplace, and z-transforms to analyze continuous- and discrete-time signals and LTI systems
• Compute and interpret convolution, impulse responses, and frequency responses for system analysis
• Use sampling theory to move between continuous- and discrete-time representations without aliasing
• Evaluate system stability, causality, and the significance of poles and zeros in the s- and z-planes
• Perform basic spectral analysis and understand when FFT-based methods are appropriate for numerical work
• Translate time-domain descriptions to frequency-domain insights useful for filter design and communications analysis

Topics Covered

1. 1. Introduction to Signals and Systems
2. 2. Time-Domain Signal Representation and Properties
3. 3. Linear Time-Invariant (LTI) Systems and Convolution
4. 4. Continuous-Time Fourier Series and Transforms
5. 5. Laplace Transform and System Analysis in the s-Domain
6. 6. Sampling Theorem and Reconstruction
7. 7. Discrete-Time Signals and Systems
8. 8. Discrete-Time Fourier Transform (DTFT) and z-Transform
9. 9. Frequency Response, Poles, and Zeros
10. 10. Basic Digital Filter Concepts (FIR/IIR)
11. 11. Spectral Analysis and Practical Considerations (including FFT)
12. 12. State-Space Approaches and System Realizations
13. 13. Stability, Causality, and System Properties

Languages, Platforms & Tools

How It Compares

Carlson's text covers the core signals-and-systems theory in a concise, accessible way; compared with Oppenheim & Willsky it is shorter and more focused on fundamentals rather than extensive DSP algorithm development, and it is less implementation-oriented than Proakis & Manolakis's Digital Signal Processing.