Circuits, Signals, and Systems
These twenty lectures have been developed and refined by Professor Siebert during the more than two decades he has been teaching introductory Signals and Systems courses at MIT. The lectures are designed to pursue a variety of goals in parallel: to familiarize students with the properties of a fundamental set of analytical tools; to show how these tools can be applied to help understand many important concepts and devices in modern communication and control engineering practice; to explore some of the mathematical issues behind the powers and limitations of these tools; and to begin the development of the vocabulary and grammar, common images and metaphors, of a general language of signal and system theory.
Although broadly organized as a series of lectures, many more topics and examples (as well as a large set of unusual problems and laboratory exercises) are included in the book than would be presented orally. Extensive use is made throughout of knowledge acquired in early courses in elementary electrical and electronic circuits and differential equations.
Contents: Review of the "classical" formulation and solution of dynamic equations for simple electrical circuits; The unilateral Laplace transform and its applications; System functions; Poles and zeros; Interconnected systems and feedback; The dynamics of feedback systems; Discrete-time signals and linear difference equations; The unilateral Z-transform and its applications; The unit-sample response and discrete-time convolution; Convolutional representations of continuous-time systems; Impulses and the superposition integral; Frequency-domain methods for general LTI systems; Fourier series; Fourier transforms and Fourier's theorem; Sampling in time and frequency; Filters, real and ideal; Duration, rise-time and bandwidth relationships: The uncertainty principle; Bandpass operations and analog communication systems; Fourier transforms in discrete-time systems; Random Signals; Modern communication systems.
Circuits, Signals, and Systems is included in The MIT Press Series in Electrical Engineering and Computer Science, copublished with McGraw-Hill.
Why Read This Book
You should read this book if you want a concise, lecture-driven grounding in the mathematical tools that underpin modern DSP, communications, and control — you will learn how transforms, linear systems, and sampling theory connect to practical problems like filter design, spectral analysis, and signal modulation. Siebert’s classroom-tested explanations emphasize intuition and physical insight, so you’ll come away able to reason about algorithm choices and system behavior even before coding simulations.
Who Will Benefit
Intermediate engineers, graduate students, and practicing practitioners who know basic calculus and circuits and want a clear, mathematically grounded introduction to signals and systems that supports work in DSP, communications, radar, and audio processing.
Level: Intermediate — Prerequisites: Single-variable calculus, basic differential equations, elementary circuit theory (voltage/current laws, passive components), and some exposure to complex numbers and linear algebra.
Key Takeaways
- Understand and apply the Fourier, Laplace, and sampling theorems to analyze continuous- and discrete-time signals and systems.
- Analyze linear time-invariant (LTI) systems using impulse response, convolution, and frequency response to predict system behavior.
- Design and reason about basic analog and digital filter concepts (frequency-selective behavior, stability, causality) relevant to DSP implementations.
- Perform spectral analysis of signals and relate time-domain operations to frequency-domain effects used in communications and radar.
- Translate physical circuits and systems into mathematical models (transfer functions, poles/zeros) to guide algorithm and hardware choices.
- Build the theoretical foundation needed to learn FFT-based algorithms, adaptive filtering, and statistical signal-processing techniques.
Topics Covered
- 1. Introduction: Signals, Systems, and Modeling
- 2. Time-Domain Analysis and Convolution for LTI Systems
- 3. Fourier Series and the Continuous-Time Fourier Transform
- 4. The Laplace Transform and System Functions
- 5. Sampling Theorem and Continuous-to-Discrete Conversion
- 6. Discrete-Time Signals and the Z-Transform
- 7. Frequency Response, Bode Plots, and Filter Concepts
- 8. Network and Circuit Realizations of Signal-Processing Elements
- 9. Spectral Analysis and Power Spectra
- 10. Modulation, Communication System Concepts, and Bandpass Signals
- 11. Introductory Treatment of Noise and Statistical Considerations
- 12. Applications: Audio/Speech, Radar, and Communication Examples
- 13. Mathematical Issues: Convergence, Stability, and Approximation
- 14. Wrap-up: Common Images, Metaphors, and Problem-Solving Strategies
Languages, Platforms & Tools
How It Compares
Covers the same foundational territory as Oppenheim & Willsky's Signals and Systems but in a more lecture-oriented, physically intuitive style; complements Proakis' Digital Signal Processing by providing stronger continuous-time and circuit-based perspective.
