1. Signals and Systems.

OntinuousTime and DiscreteTime Signals.

Transformations of the Independent Variable.

Exponential and Sinusoidal Signals.

The Unit Impulse and Unit Step Functions.

ContinuousTime and DiscreteTime Systems.

Basic System Properties.

2. Linear TimeInvariant Systems.

DiscreteTime LTI Systems: The Convolution Sum.

ContinuousTime LTI Systems: The Convolution Integral.

Properties of Linear TimeInvariant Systems.

Causal LTI Systems Described by Differential and Difference Equations.

Singularity Functions.

3. Fourier Series Representation of Periodic Signals.

Historical Perspective.

The Response of LTI Systems to Complex Exponentials.

Fourier Series Representation of ContinuousTime Periodic Signals.

Convergence of the Fourier Series.

Properties of ContinuousTime Fourier Series.

Fourier Series Representation of DiscreteTime Periodic Signals.

Properties of DiscreteTime Fourier Series.

Fourier Series and LTI Systems. Filtering.

Examples of ContinuousTime Filters Described by Differential Equations.

Examples of DiscreteTime Filters Described by Difference Equations.

4. The ContinuousTime Fourier Transform.

Representation of Aperiodic Signals: The ContinuousTime Fourier Transform.

The Fourier Transform for Periodic Signals.

Properties of the ContinuousTime Fourier Transform.

The Convolution Property.

The Multiplication Property.

Tables of Fourier Properties and Basic Fourier Transform Pairs.

Systems Characterized by Linear ConstantCoefficient Differential Equations.

5. The DiscreteTime Fourier Transform.

Representation of Aperiodic Signals: The DiscreteTime Fourier Transform.

The Fourier Transform for Periodic Signals.

Properties of the DiscreteTime Fourier Transform.

The Convolution Property.

The Multiplication Property.

Tables of Fourier Transform Properties and Basic Fourier Transform Pairs.

Duality. Systems Characterized by Linear ConstantCoefficient Difference Equations.

6. Time and Frequency Characterization of Signals and Systems.

The MagnitudePhase Representation of the Fourier Transform.

The MagnitudePhase Representation of the Frequency Response of LTI Systems.

TimeDomain Properties of Ideal FrequencySelective Filters.

Time Domain and FrequencyDomain Aspects of Nonideal Filters.

FirstOrder and SecondOrder ContinuousTime Systems.

FirstOrder and SecondOrder DiscreteTime Systems.

Examples of Time and FrequencyDomain Analysis of Systems.

7. Sampling.

Representation of a ContinuousTime Signal by Its Samples: The Sampling Theorem.

Reconstruction of a Signal from Its Samples Using Interpolation.

The Effect of Undersampling: Aliasing.

DiscreteTime Processing of ContinuousTime Signals.

Sampling of DiscreteTime Signals.

8. Communication Systems.

Complex Exponential and Sinusoidal Amplitude Modulation.

Demodulation for Sinusoidal AM.

FrequencyDivision Multiplexing.

SingleSideband Sinusoidal Amplitude Modulation.

Amplitude Modulation with a PulseTrain Carrier. PulseAmplitude Modulation.

Sinusoidal Frequency Modulation. DiscreteTime 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 PoleZero 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 ZTransform.

The zTransform.

The Region of Convergence for the zTransform.

The Inverse zTransform.

Geometric Evaluation of the Fourier Transform from the PoleZero Plot.

Properties of the zTransform.

Some Common zTransform Pairs.

Analysis and Characterization of LTI Systems Using zTransforms.

System Function Algebra and Block Diagram Representations.

The Unilateral zTransforms.

11. Linear Feedback Systems.

Linear Feedback Systems.

Some Applications and Consequences of Feedback.

RootLocus Analysis of Linear Feedback Systems.

The Nyquist Stability Criterion.

Gain and Phase Margins.
