Signals and Systems

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(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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