1 Overview of signals and systems 1.0 introduction 1.1 Basic definitions and classification of signals 1.1.1 Concepts 1.1.2 Description of signals 1.1.3 Classification of signals 1.1.4 Representation and plotting of signals with MATLAB 1.2 Basic operations of signals 1.2.1 Operations "+", "-" and "x" of signals 1.2.2 Signal transformations in the time domain 1.3 Elementary signals 1.3.1 The continuous-time unit step function 1.3.2 The continuous-time unit impulse function 1.3.3 Properties of the CT unit impulse function 1.3.4 The discrete-time unit step and impulse sequences 1.4 Basic definitions and classification of systems 1.4.1 Introduction to systems 1.4.2 Classifications of systems 1.5 Framework of analytical methods 1.5.1 Analytical methods for LTI systems 1.5.2 Key issues to study 1.5.3 Framework of all chapters 1.6 Summary 2 Time-domain analysis of I.TIC systems 2.0 Introduction 2.1 Representation of the LTIC system 2.1.1 Analytical description based on mathematical models 2.1.2 Description based on the block diagram 2.2 Classical solution of the differential equation 2.2.1 Classical solution of the direct method 2.2.2 Initial value of the system 2.2.3 Zero-input response and zero-state response 2.2.4 Response calculation with MATLAB 2.3 The impulse response and step response 2.3.1 CT impulse response 2.3.2 CT step response 2.3.3 Solution by MATLAB 2.4 Convolution integral 2.4.1 Signal decomposition in the time domain 2.4.2 Definition of the convolution integral 2.4.3 Graphical method for evaluating the convolution integral 2.4.4 Properties of the convolution integral 2.4.5 Comprehensive application instances 2.4.6 Convolution computation with MATLAB 2.5 Summary 3 Time-domain analysis of LTID systems 3.0 Introduction 3.1 Representation of an LTID system 3.1.1 Analytical description based on mathematical models 3.1.2 Description based on the block diagram 3.1.3 General form of the difference equation 3.2 Classical solution of the difference equation 3.2.1 Classical solution of the direct method 3.2.2 Zero-input response and zero-state response 3.2.3 Response calculation with MATLAB 3.3 Impulse response and step response 3.3.1 Basic discrete-time sequence 3.3.2 Unit impulse response and step response of an LTID system 3.3.3 Calculation with MATLAB 3.4 Convolution sum 3.4.1 Representation of sequences using Dirac delta functions 3.4.2 Convolution sum 3.4.3 Graphical method for evaluating the convotution sum 3.4.4 The carry-less multiplication method 3.4.5 Properties of the convolution sum 3.4.6 Convolution calcutation with MATLAB 3.4.7 Application of the convolution sum 3.5 Summary 4 Frequency-domain analysis of LTIC systems 4.0 Introduction 4.1 CTFS of periodic signals 4.1.1 Trigonometric CTFS 4.1.2 Symmetry of waveform and harmonic characteristics 4.1.3 Exponential Fourier series 4.1.4 Parsevai's power theorem 4.2 Fourier spectrum of periodic signals 4.2.1 Definition of the Fourier spectrum 4.2.2 Characteristics of the spectrum of periodic signals 4.2.3 Application of the Fourier series 4.3 Continuous-time Fourier transforms 4.3.1 Definition of CTFT 4.3.2 CTFT pairs for elementary CT signals 4.3.3 Properties of CTFT 4.3.4 Fourier transforms of real-valued even and odd functions 4.3.5 Parseval's energy theorem 4.3.6 CTFT of periodic functions 4.4 LTIC systems analysis using CTFT and CTFS 4.4.1 Response of the LTIC system to the complex exponential function 4.4.2 Response of the LTIC system to an arbitrary signal 4.4.3 The Fourier transfer function of an LTIC system 4.4.4 Steps of calculating the response with CTFT 4.4.5 Steps of calculating the response with CTFS 4.4.6 Response computation with MATLAB 4.5 Applications of transmission and filtering 4.5.1 The undistorted transmission system 4.5.2 Frequency characteristics of an ideal low-pass filter 4.5.3 Impulse and step response of an ideal low-pass filter 4.5.4 Conditions of physically realizable systems 4.5.5 Nonideal low-pass filter 4.5.6 Application of the amplitude modulation system 4.6 Sampling theorem 4.6.1 Model of ideal impulse-train sampling 4.6.2 CTFT of the sampled signal 4.6.3 Sampling theorem 4.6.4 Reconstruction of a band-limited signal from its samples 4.6.5 Sampling with MATLAB 4.7 Summary 5 Laplace transform and complex frequency-domain analysis 5.0 Introduction 5.1 Analytical development 5.1.1 From CTFT to the bilateral laplace transform 5.1.2 Region of convergence 5.1.3 Unilateral Laplace transform 5.1.4 Relationship between CTFT and the Laplace transform 5.2 Basic pairs and properties of the Laplace transform 5.2.1 Laplace transform pairs for several elementary CT signals 5.2.2 Properties of the Laplace transform 5.3 Inverse Laplace transformation 5.3.1 Characteristic roots of the Laplace transform 5.3.2 Real-valued and first-order poles 5.3.3 Complex-valued and first-order poles 5.3.4 Real-valued and repeated poles 5.3.5 Calculation with MATLAB 5.4 Application of the Laplace transform in circuit analysis 5.4.1 S-domain models of circuit 5.4.2 Analysis in the S-domain of the circuit system 5.5 Application of solutions of differential equations 5.5.1 Analysis of computing zero-input and zero-state response 5.5.2 Analysis of computing the overall response 5.6 Laplace transfer function 5.6.1 Definition of the Laplace transfer function 5.6.2 Characteristic equation, zeros and poles 5.6.3 Nature of the shape of impulse response for different poles 5.6.4 Stability conditions in the S-plane 5.6.5 Laplace transfer function with the frequency response function 5.6.6 Calculation with MATLAB 5.7 Signal-flow graph and LTIC system simulation 5.7.1 Block diagram representation 5.7.2 Model of basic components of LTIC systems n 5.7.3 The signal-flow graph of LTIC systems 5.7.4 Mason's rule 5.7.5 Simulation of the LTIC system 5.8 Summary 6 The Z-transform and Z-domain analysis 6.0 Introduction 6.1 Analytical development 6.1.1 From the Laplace transform to the Z-transform 6.1.2 Region of convergence 6.1.3 Unilateral Z-transform 6.2 Basic pairs and properties of the Z-transform 6.2.1 Z-transform pairs for several elementary DT signals 6.2.2 Properties of the Z-transform 6.3 inverse Z-transform 6.3.1 Power series method 6.3.2 Characteristic roots of the Z-transform 6.3.3 Real-valued and first-order poles 6.3.4 Complex-valued and first-order poles 6.3.5 Real-valued and repeated poles 6.3.6 Calculation with MATLAB 6.4 Relationship between the Laplace and Z-transforms 6.4.1 Mapping relation between S-plane and Z-plane 6.4.2 Conversion from Z-transform to Laplace transform 6.4.3 Conversion from the Laplace transform to the Z-transform 6.5 Solution of difference equations with the Z-transform 6.5.1 Analysis of corn puting zero-input and zero-state response 6.5.2 Analysis of computing overall response 6.6 Z-transfer function of LTID systems 6.6.1 Definition of the Z-transfer function 6.6.2 Characteristic equation, zeros and poles 6.6.3 Nature of the shape of the impulse response for different poles 6.6.4 Stability analysis in the Z-domain 6.7 Signal flow graph and LTID system simulation 6.7.1 Block diagram representation 6.7.2 Model of basic components of LTID systems 6.7.3 Signal flow graph of LTID systems 6.7.4 Simulation of LTID systems 6.8 Characteristics of frequency response 6.8.1 Response of LTID systems to the complex exponential sequence 6.8.2 Response of LTID systems to the sinusoidal sequence 6.8.3 Definition of frequency response of LTID systems 6.8.4 Calculation with MATLAB 6.9 Summary 7 State-space analysis of systems 7.0 Introduction 7.1 Basic concepts of the state space 7.1.1 State variables of systems 7.1.2 State equations of continuous-time and discrete-time systems 7.1.3 Output equations of continuous-time and discrete-time systems 7.2 State-space description of CT systems 7.2.1 State-space description for electrical circuit systems 7.2.2 State-space description from differential equations 7.2.3 State-space description from the system diagram and the flow graph 7.2.4 State-space description with MATLAB 7.3 State-space description of DT systems 7.3.1 State-space description from difference equations 7.3.2 State-space description from system diagrams and flow graphs 7.4 Solution of state-space equations of LTIC systems 7.4.1 Laplace transform solution of state equations 7.4.2 Laplace transform solution of output equations 7.4.3 Calculation with MATLAB 7.5 Solution of state-space equations of LTID systems 7.5.1 Z-transform solution of state equations 7.5.2 Z-transform solution of output equations 7.5.3 Calculation with MATLAB 7.6 Stability analysis from the transfer function matrix 7.6.1 Stability condition 7.6.2 Calculation with MATLAB 7.7 Summary 8 Applications of system analysis 8.0 Introduction 8.1 Application of the Fourier transform in communication systems 8.1.1 Doubie-sideband suppressed-carrier amplitude modulation (DSB-SC-AM) 8.1.2 Amplitude modulation (AM) 8.1.3 Pulse-amplitude modulation (PAM) 8.2 Fast Fourier transform 8.2.1 Discrete-time Fourier series (DTFS) 8.2.2 Discrete-time Fourier transform (DTFT) 8.2.3 Discrete Fourier transform (DFI) 8.2.4 Relationship between Fourier transforms 8.2.5 Fast Fourier transform (FFT) 8.3 Application of the Laplace transform in control systems 8.3.1 Diagram of the closed-loop feedback system 8.3.2 Analysis of an automatic position control system 8.4 Digital filters 8.4.1 Filter classification 8.4.2 FIR and IIR filters 8.4.3 IIR filter design using the impu|se-invariance method 8.4.4 IIR filter design using bilinear transformation 8.4.5 FIR filter design using the windowing method 8.5 ControUability and observabitity of linear systems 8.5.1 Controllability of linear systems 8.5.2 Observability of linear systems 8.5.3 Calculation with MATLAB 8.6 Applications of the Katman filter 8.6.1 Basic principles of the Kalman filter 8.6.2 Temperature prediction simulation with MATLAB 8.7 Applications of convolution in image processing 8.8 Summary References Index