Signals and Systems, 2nd edition

Published by Pearson (August 6, 1996) © 1997

  • Alan V Oppenheim
  • Alan S. Willsky Massachusetts Institute of Technology
  • S Hamid Nawab
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  • A print edition

Title overview

For undergraduate-level courses in Signals and Systems.

This comprehensive exploration of signals and systems develops continuous-time and discrete-time concepts/methods in parallel -- highlighting the similarities and differences -- and features introductory treatments of the applications of these basic methods in such areas as filtering, communication, sampling, discrete-time processing of continuous-time signals, and feedback. Relatively self-contained, the text assumes no prior experience with system analysis, convolution, Fourier analysis, or Laplace and z-transforms.

Table of contents

NOTE: Each chapter begins with an Introduction and concludes with a Summary.

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.
  • Basic System Properties.

2. Linear Time-Invariant Systems

  • Discrete-Time LTI Systems: The Convolution Sum.
  • Continuous-Time LTI Systems: The Convolution Integral.
  • Properties of Linear Time-Invariant Systems.
  • Causal LTI Systems Described by Differential and Difference Equations.
  • Singularity Functions.

3. Fourier Series Representation of Periodic Signals

  • A Historical Perspective.
  • The Response of LTI Systems to Complex Exponentials.
  • Fourier Series Representation of Continuous-Time Periodic Signals.
  • Convergence of the Fourier Series.
  • Properties of Continuous-Time Fourier Series.
  • Fourier Series Representation of Discrete-Time Periodic Signals.
  • Properties of Discrete-Time Fourier Series.
  • Fourier Series and LTI Systems.
  • Filtering.
  • Examples of Continuous-Time Filters Described by Differential Equations.
  • Examples of Discrete-Time Filters Described by Difference Equations.

4. The Continuous-Time Fourier Transform

  • Representation of Aperiodic Signals: The Continuous-Time Fourier Transform.
  • The Fourier Transform for Periodic Signals.
  • Properties of the Continuous-Time Fourier Transform.
  • The Convolution Property.
  • The Multiplication Property.
  • Tables of Fourier Properties and Basic Fourier Transform Pairs.
  • Systems Characterized by Linear Constant-Coefficient Differential Equations

5. The Discrete-Time Fourier Transform.

  • Representation of Aperiodic Signals: The Discrete-Time Fourier Transform.
  • The Fourier Transform for Periodic Signals.
  • Properties of the Discrete-Time Fourier Transform.
  • The Convolution Property.
  • The Multiplication Property.
  • Tables of Fourier Transform Properties and Basic Fourier Transform Pairs.
  • Duality.
  • Systems Characterized by Linear Constant-Coefficient Difference Equations.

6. Time- and Frequency Characterization of Signals and Systems

  • The Magnitude-Phase Representation of the Fourier Transform.
  • The Magnitude-Phase Representation of the Frequency Response of LTI Systems.
  • Time-Domain Properties of Ideal Frequency-Selective Filters.
  • Time- Domain and Frequency-Domain Aspects of Nonideal Filters.
  • First-Order and Second-Order Continuous-Time Systems.
  • First-Order and Second-Order Discrete-Time Systems.
  • Examples of Time- and Frequency-Domain Analysis of Systems.

7. Sampling

  • Representation of a Continuous-Time Signal by Its Samples: The Sampling Theorem.
  • Reconstruction of a Signal from Its Samples Using Interpolation.
  • The Effect of Undersampling: Aliasing.
  • Discrete-Time Processing of Continuous-Time Signals.
  • Sampling of Discrete-Time Signals.

8. Communication Systems

  • Complex Exponential and Sinusoidal Amplitude Modulation.
  • Demodulation for Sinusoidal AM. Frequency-Division Multiplexing.
  • Single-Sideband Sinusoidal Amplitude Modulation.
  • Amplitude Modulation with a Pulse-Train Carrier.
  • Pulse-Amplitude Modulation.
  • Sinusoidal Frequency Modulation.
  • Discrete-Time Modulation.

9. The Laplace Transform

  • The Laplace Transform.
  • The Region of Convergence for Laplace Transforms.
  • The Inverse Laplace Transform.
  • Geometric Evaluation of the Fourier Transform from the Pole-Zero Plot.
  • Properties of the Laplace Transform.
  • Some Laplace Transform Pairs.
  • Analysis and Characterization of LTI Systems Using the Laplace Transform.
  • System Function Algebra and Block Diagram Representations.
  • The Unilateral Laplace Transform.

10. The Z-Transform

  • The z-Transform.
  • The Region of Convergence for the z-Transform.
  • The Inverse z-Transform.
  • Geometric Evaluation of the Fourier Transform from the Pole-Zero Plot.
  • Properties of the z-Transform.
  • Some Common z-Transform Pairs.
  • Analysis and Characterization of LTI Systems Using z-Transforms.
  • System Function Algebra and Block Diagram Representations.
  • The Unilateral z-Transforms.

11. Linear Feedback Systems

  • Linear Feedback Systems.
  • Some Applications and Consequences of Feedback.
  • Root-Locus Analysis of Linear Feedback Systems.
  • The Nyquist Stability Criterion.
  • Gain and Phase Margins.

Appendix: Partial-Fraction Expansion

Bibliography

Answers

Index

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