Contents

Preface                                                                                                                                                                              

1          FUNDAMENTAL CONCEPTS                                                                                                                                   

1.1    Continuous-Time Signals

1.2    Discrete-Time Signals

1.3    Systems

1.4    Examples of Systems  

1.5    Basic System Properties  

Problems  

2          TIME-DOMAIN MODELS OF SYSTEMS                                                                                                                

2.1    Input/Output Representation of Discrete-Time Systems

2.2    Convolution of Discrete-Time Signals

2.3    Difference Equation Models

2.4    Differential Equation Models

2.5    Solution of Differential Equations

2.6    Convolution Representation of Continuous-Time Systems

            Problems

3          THE FOURIER SERIES AND FOURIER TRANSFORM                                                                                   

3.1    Representation of Signals in Terms of Frequency Components  

3.2    Trigonometric Fourier Series

3.3    Complex Exponential Series

3.4    Fourier Transform

3.5    Spectral Content of Common Signals

3.6    Properties of the Fourier Transform  

3.7    Generalized Fourier Transform  

3.8    Application to Signal Modulation and Demodulation

Problems  

4          FOURIER ANALYSIS OF DISCRETE-TIME SIGNALS

4.1      Discrete-Time Fourier Transform

4.2      Discrete Fourier Transform

4.3      DFT of Truncated Signals

4.4      FFT Algorithm

4.5      Application to Data Analysis

 Problems

5          FOURIER ANALYSIS OF SYSTEMS                                                                                                                        

5.1    Fourier Analysis of Continuous-Time Systems

5.2    Response to Periodic and Nonperiodic Inputs  

5.3    Analysis of Ideal Filters  

5.4    Sampling  

5.5    Fourier Analysis of Discrete-Time Systems

5.6    Application to Lowpass Digital Filtering

Problems  

6          THE LAPLACE TRANSFORM AND THE TRANSFER FUNCTION REPRESENTATION                       

6.1    Laplace Transform of a Signal  

6.2    Properties of the Laplace Transform  

6.3    Computation of the Inverse Laplace Transform  

6.4    Transform of the Input/Output Differential Equation  

6.5    Transform of the Input/Output Convolution Integral

6.6    Direct Construction of the Transfer Function

Problems  

7          THE z-TRANSFORM AND DISCRETE-TIME SYSTEMS

7.1   z-Transform of a Discrete-Time Signal  

7.2   Properties of the z-Transform  

7.3   Computation of the Inverse z-Transform  

7.4   Transfer Function Representation  

7.5    System Analysis Using the Transfer Function Representation

             Problems

8          ANALYSIS OF CONTINUOUS-TIME SYSTEMS USING THE TRANSFER FUNCTION REPRESENTATION          

8.1    Stability and the Impulse Response  

8.2    Routh–Hurwitz Stability Test  

8.3    Analysis of the Step Response  

8.4    Response to Sinusoids and Arbitrary Inputs  

8.5    Frequency Response Function  

8.6    Causal Filters  

Problems  

9          APPLICATION TO CONTROL                                                                                                                                   

9.1   Introduction to Control  

9.2   Tracking Control  

9.3   Root Locus  

9.4   Application to Control System Design  

           Problems

10        DESIGN OF DIGITAL FILTERS AND CONTROLLERS                                                                                     

10.1   Discretization  

10.2   Design of IIR Filters  

10.3   Design of IIR Filters Using MATLAB  

10.4   Design of FIR Filters  

10.5   Design of Digital Controllers  

Problems  

APPENDIX  BRIEF REVIEW OF COMPLEX VARIABLES                                                                             

BIBLIOGRAPHY