Signals and Systems

Citation

Oppenheim, A. V., Willsky, A. S., & Nawab, S. H. (1996). Signals and Systems (2nd ed.). Pearson.

Chapter Summary

The second edition has eleven chapters and an appendix on partial-fraction expansion, followed by a bibliography, answers and an index. According to the table of contents, every chapter begins with an introduction and ends with a summary. Pearson describes the book for undergraduate courses in signals and systems: continuous-time and discrete-time concepts and methods are developed in parallel, with the similarities and differences highlighted, and introductory treatments of applications in filtering, communication, sampling, discrete-time processing of continuous-time signals and feedback. It is described as relatively self-contained and assumes no prior experience with system analysis, convolution, Fourier analysis, or Laplace and z-transforms.

Chapter 1: Signals and Systems

Continuous-time and discrete-time signals, transformations of the independent variable, exponential and sinusoidal signals, the unit impulse and unit step functions, continuous-time and discrete-time systems, and basic system properties.

Chapter 2: Linear Time-Invariant Systems

The convolution sum for discrete-time LTI systems and the convolution integral for continuous-time LTI systems, properties of LTI systems, causal LTI systems described by differential and difference equations, and singularity functions.

Chapter 3: Fourier Series Representation of Periodic Signals

A historical perspective, then the response of LTI systems to complex exponentials. Fourier series are developed for continuous-time and discrete-time periodic signals, with convergence and properties, and applied to LTI systems, filtering, and examples of continuous-time filters (differential equations) and discrete-time filters (difference equations).

Chapters 4–5: The Continuous-Time Fourier Transform; The Discrete-Time Fourier Transform

The two chapters follow the same plan: representing aperiodic signals, extending the transform to periodic signals, properties including the convolution and multiplication properties, and tables of properties and transform pairs. Chapter 4 ends with systems characterized by linear constant-coefficient differential equations, and Chapter 5 adds duality and ends with systems characterized by difference equations.

Chapter 6: Time- and Frequency Characterization of Signals and Systems

The magnitude-phase representation of the Fourier transform and of the frequency response of LTI systems, time-domain properties of ideal frequency-selective filters, and time- and frequency-domain aspects of nonideal filters. It also covers first- and second-order continuous-time and discrete-time systems, and works through examples of analysis.

Chapter 7: Sampling

The sampling theorem, reconstruction of a signal from its samples using interpolation, the effect of undersampling (aliasing), discrete-time processing of continuous-time signals and sampling of discrete-time signals.

Chapter 8: Communication Systems

Complex exponential and sinusoidal amplitude modulation, demodulation and frequency-division multiplexing, single-sideband modulation, amplitude modulation with a pulse-train carrier, pulse-amplitude modulation, sinusoidal frequency modulation and discrete-time modulation.

Chapters 9–10: The Laplace Transform; The Z-Transform

Parallel chapters: the transform and its region of convergence, the inverse transform, geometric evaluation of the Fourier transform from the pole-zero plot, properties and common pairs, analysis and characterization of LTI systems, system function algebra and block diagram representations, and the unilateral version of each transform.

Chapter 11: Linear Feedback Systems

Linear feedback systems, some applications and consequences of feedback, root-locus analysis, the Nyquist stability criterion, and gain and phase margins.

Key Concepts

Chapters 1–2: Signals, Systems and Convolution

• Parallel continuous-time and discrete-time treatment: the book's stated organising idea.
• Convolution sum and convolution integral: the discrete-time and continuous-time forms of convolution for LTI systems.
• Singularity functions: introduced in Chapter 2 alongside the unit impulse and step of Chapter 1.

Chapters 3–6: Fourier Analysis and Filtering

• Response of LTI systems to complex exponentials: the topic that precedes the Fourier series in Chapter 3.
• Convolution and multiplication properties: central properties of the Fourier transforms of Chapters 4 and 5.
• Magnitude-phase representation: how Chapter 6 characterises frequency response and filters.

Chapters 7–8: Sampling and Modulation

• Sampling theorem and aliasing: representing a continuous-time signal by its samples, and the effect of undersampling.
• Amplitude and frequency modulation: the communication examples of Chapter 8.

Chapters 9–11: Transforms and Feedback

• Region of convergence: part of the definition of the Laplace and z-transforms.
• Pole-zero plot: used to evaluate the Fourier transform geometrically.
• Root locus, Nyquist criterion, gain and phase margins: the stability tools of the feedback chapter.

Critical Analysis

Strengths

• A unified, parallel structure. Continuous-time and discrete-time signals and systems are developed side by side, as in Chapters 4 and 5 and Chapters 9 and 10, whose headings closely parallel each other. Pearson highlights this parallel development as the book's approach.
• Applications of the basic methods. Filtering (Chapters 3 and 6), sampling (Chapter 7), communication (Chapter 8) and feedback (Chapter 11) show the transforms in use.
• Few prerequisites in the subject itself. Pearson says the text assumes no earlier experience with system analysis, convolution, Fourier analysis, or Laplace and z-transforms, and the contents begin with signals and basic system properties.
• Review aids. Every chapter has an introduction and a summary, and the book supplies tables of Fourier properties and transform pairs, a partial-fraction appendix, a bibliography and answers.

Limitations

• Date. The second edition is from 1996 (copyright 1997). The contents list no computer-based or numerical work.
• Order of topics. Four chapters (3 to 6) on Fourier methods come before sampling, and the Laplace and z-transforms do not appear until Chapters 9 and 10, so a course that needs them early for control must reorder.
• Feedback is introductory. The feedback chapter has five sections; it is a bridge to control, not a control course.
• Edition details. Pearson lists the hardcover as a 1996 publication and notes a 1997 copyright.

Where It Fits in the Course

Oppenheim and Willsky is the full-length text on this list for the standard signals and systems course. Sadiku's Signals and Systems: A Primer with MATLAB is described as a compact, example-driven treatment using MATLAB throughout, and Downey's Think DSP teaches through Python code, with sound as the main example. Either can be a gentler first contact before Oppenheim and Willsky, or a computational companion alongside it.

Nise's Control Systems Engineering and Åström and Murray's Feedback Systems continue into control, and Craig's Introduction to Robotics: Mechanics and Control is a robotics text further along the list.

How to Use This Book

The book is for undergraduates meeting signals and systems for the first time; Pearson says no prior experience with system analysis, convolution, Fourier analysis, or Laplace and z-transforms is assumed. A practical plan:

• Core: Chapters 1 to 7, 9 and 10, in order. Chapters 4 and 5 are best read together, as are Chapters 9 and 10.
• Selective: Chapter 8 (communication systems) for students heading to communications, and Chapter 11 as a bridge to a dedicated control course.
• Chapter 3: read the response of LTI systems to complex exponentials before the series themselves.
• Practice: use the answers to check problems, and compare the continuous-time and discrete-time versions of each result.