CONTINUOUS AND DISCRETE TIME SIGNALS AND SYSTEMS
CONTENTS PART I INTRODUCTION TO SIGNALS AND SYSTEMS 1 INTRODUCTION TO SIGNALS 1 1 CLASSI?CATION OF SIGNALS 1 2 ELEMENTARY SIGNALS 1 3 SIGNAL OPERATIONS 1 4 SIGNAL IMPLEMENTATION WITH MATLAB 1 5 SUMMARY PROBLEMS 2 INTRODUCTION TO SYSTEMS 2 1 EXAMPLES OF SYSTEMS 2 2 CLASSI?CATION OF SYSTEMS 2 3 INTERCONNECTION OF SYSTEMS 2 4 SUMMARY PART II CONTINUOUS-TIME SIGNALS AND SYSTEMS 3 TIME-DOMAIN ANALYSIS OF LTIC SYSTEMS 3 1 REPRESENTATION OF LTIC SYSTEMS 3 2 REPRESENTATION OF SIGNALS USING DIRAC DELTA FUNCTIONS 3 3 IMPULSE RESPONSE OF A SYSTEM 3 4 CONVOLUTION INTEGRAL 3 5 GRAPHICAL METHOD FOR EVALUATING THE CONVOLUTION INTEGRAL 3 6 PROPERTIES OF THE CONVOLUTION INTEGRAL 3 7 IMPULSE RESPONSE OF LTIC SYSTEMS 3 8 EXPERIMENTS WITH MATLAB 3 9 SUMMARY 4 SIGNAL REPRESENTATION USING FOURIER SERIES 4 1 ORTHOGONAL VECTOR SPACE 4 2 ORTHOGONAL SIGNAL SPACE 4 3 FOURIER BASIS FUNCTIONS 4 4 TRIGONOMETRIC CTFS 4 5 EXPONENTIAL FOURIER SERIES 4 6 PROPERTIES OF EXPONENTIAL CTFS 4 7 EXISTENCE OF FOURIER SERIES 4 8 APPLICATION OF FOURIER SERIES 4 9 SUMMARY 5 CONTINUOUS-TIME FOURIER TRANSFORM 5 1 CTFT FOR APERIODIC SIGNALS 5 2 EXAMPLES OF CTFT 5 3 INVERSE FOURIER TRANSFORM 5 4 FOURIER TRANSFORM OF REAL, EVEN, AND ODD FUNCTIONS 5 5 PROPERTIES OF THE CTFT 5 6 EXISTENCE OF THE CTFT 5 7 CTFT OF PERIODIC FUNCTIONS 5 8 CTFS COEF?CIENTS AS SAMPLES OF CTFT 5 9 LTIC SYSTEMS ANALYSIS USING CTFT 5 10 MATLAB EXERCISES 5 11 SUMMARY 6 LAPLACE TRANSFORM 6 1 ANALYTICAL DEVELOPMENT 6 2 UNILATERAL LAPLACE TRANSFORM 6 3 INVERSE LAPLACE TRANSFORM 6 4 PROPERTIES OF THE LAPLACE TRANSFORM 6 5 SOLUTION OF DIFFERENTIAL EQUATIONS 6 6 CHARACTERISTIC EQUATION, ZEROS, AND POLES 6 7 PROPERTIES OF THE ROC 6 8 STABLE AND CAUSAL LTIC SYSTEMS 6 9 LTIC SYSTEMS ANALYSIS USING LAPLACE TRANSFORM 6 10 BLOCK DIAGRAM REPRESENTATIONS 6 11 SUMMARY 7 CONTINUOUS-TIME ?LTERS 7 1 FILTER CLASSI?CATION 7 2 NON-IDEAL ?LTER CHARACTERISTICS 7 3 DESIGN OF CT LOWPASS ?LTERS 7 4 FREQUENCY TRANSFORMATIONS 7 5 SUMMARY 8 CASE STUDIES FOR CT SYSTEMS 8 1 AMPLITUDE MODULATION OF BASEBAND SIGNALS 8 2 MECHANICAL SPRING DAMPER SYSTEM 8 3 ARMATURE-CONTROLLED DC MOTOR 8 4 IMMUNE SYSTEM IN HUMANS 8 5 SUMMARY PART III DISCRETE-TIME SIGNALS AND SYSTEMS 9 SAMPLING AND QUANTIZATION 9 1 IDEAL IMPULSE-TRAIN SAMPLING 9 2 PRACTICAL APPROACHES TO SAMPLING 9 3 QUANTIZATION 9 4 COMPACT DISKS 9 5 SUMMARY 10 TIME-DOMAIN ANALYSIS OF DISCRETE-TIME SYSTEMS SYSTEMS 10 1 FINITE-DIFFERENCE EQUATION REPRESENTATION OF LTID SYSTEMS 10 2 REPRESENTATION OF SEQUENCES USING DIRAC DELTA FUNCTIONS 10 3 IMPULSE RESPONSE OF A SYSTEM 10 4 CONVOLUTION SUM 10 5 GRAPHICAL METHOD FOR EVALUATING THE CONVOLUTION SUM 10 6 PERIODIC CONVOLUTION 10 7 PROPERTIES OF THE CONVOLUTION SUM 10 8 IMPULSE RESPONSE OF LTID SYSTEMS 10 9 EXPERIMENTS WITH MATLAB 10 10 SUMMARY 11 DISCRETE-TIME FOURIER SERIES AND TRANSFORM 11 1 DISCRETE-TIME FOURIER SERIES 11 2 FOURIER TRANSFORM FOR APERIODIC FUNCTIONS 11 3 EXISTENCE OF THE DTFT 11 4 DTFT OF PERIODIC FUNCTIONS 11 5 PROPERTIES OF THE DTFT AND THE DTFS 11 6 FREQUENCY RESPONSE OF LTID SYSTEMS 11 7 MAGNITUDE AND PHASE SPECTRA 11 8 CONTINUOUS- AND DISCRETE-TIME FOURIER TRANSFORMS 11 9 SUMMARY 12 DISCRETE FOURIER TRANSFORM 12 1 CONTINUOUS TO DISCRETE FOURIER TRANSFORM 12 2 DISCRETE FOURIER TRANSFORM 12 3 SPECTRUM ANALYSIS USING THE DFT 12 4 PROPERTIES OF THE DFT 12 5 CONVOLUTION USING THE DFT 12 6 FAST FOURIER TRANSFORM 12 7 SUMMARY 13 THE Z-TRANSFORM 13 1 ANALYTICAL DEVELOPMENT 13 2 UNILATERAL Z-TRANSFORM 13 3 INVERSE Z-TRANSFORM 13 4 PROPERTIES OF THE Z-TRANSFORM 13 5 SOLUTION OF DIFFERENCE EQUATIONS 13 6 Z-TRANSFER FUNCTION OF LTID SYSTEMS 13 7 RELATIONSHIP BETWEEN LAPLACE AND Z-TRANSFORMS 13 8 STABILTY ANALYSIS IN THE Z-DOMAIN 13 9 FREQUENCY-RESPONSE CALCULATION IN THE Z-DOMAIN 13 10 DTFT AND THE Z-TRANSFORM 13 11 EXPERIMENTS WITH MATLAB 13 12 SUMMARY 14 DIGITAL ?LTERS 14 1 FILTER CLASSI?CATION 14 2 FIR AND IIR ?LTERS 14 3 PHASE OF A DIGITAL ?LTER 14 4 IDEAL VERSUS NON-IDEAL ?LTERS 14 5 FILTER REALIZATION 14 6 FIR ?LTERS 14 7 IIR ?LTERS 14 8 FINITE PRECISION EFFECT 14 9 MATLAB EXAMPLES 14 10 SUMMARY 15 FIR ?LTER DESIGN 15 1 LOWPASS ?LTER DESIGN USING WINDOWING METHOD 15 2 DESIGN OF HIGHPASS ?LTERS USING WINDOWING 15 3 DESIGN OF BANDPASS ?LTERS USING WINDOWING 15 4 DESIGN OF A BANDSTOP ?LTER USING WINDOWING 15 5 OPTIMAL FIR ?LTERS 15 6 MATLAB EXAMPLES 15 7 SUMMARY 16 IIR ?LTER DESIGN 16 1 IIR ?LTER DESIGN PRINCIPLES 16 2 IMPULSE INVARIANCE 16 3 BILINEAR TRANSFORMATION 16 4 DESIGNING HIGHPASS, BANDPASS, AND BANDSTOP IIR ?LTERS 16 5 IIR AND FIR ?LTERS 16 6 SUMMARY 17 APPLICATIONS OF DIGITAL SIGNAL PROCESSING 17 1 SPECTRAL ESTIMATION 17 2 DIGITAL AUDIO 17 3 AUDIO ?LTERING 17 4 DIGITAL AUDIO COMPRESSION 17 5 DIGITAL IMAGES 17 6 IMAGE ?LTERING 17 7 IMAGE COMPRESSION 17 8 SUMMARY