COVER -- CONTENTS -- PREFACE -- 1 INTRODUCTION -- 1.1 Modeling -- 1.2 Continuous-Time Physical Systems -- Electric Circuits -- Operational Amplifier Circuits -- Simple Pendulum -- DC Power Supplies -- Analogous Systems -- 1.3 Samplers and Discrete-Time Physical Systems -- Analog-to-Digital Converter -- Numerical Integration -- Picture in a Picture -- Compact Disks -- Sampling in Telephone Systems -- Data-Acquisition System -- 1.4 MATLAB and SIMULINK -- 2 CONTINUOUS-TIME SIGNALS AND SYSTEMS -- 2.1 Transformations of Continuous-Time Signals -- Time Transformations -- Amplitude Transformations -- 2.2 Signal Characteristics -- Even and Odd Signals -- Periodic Signals -- 2.3 Common Signals in Engineering -- 2.4 Singularity Functions -- Unit Step Function -- Unit Impulse Function -- 2.5 Mathematical Functions for Signals -- 2.6 Continuous-Time Systems -- Interconnecting Systems -- Feedback System -- 2.7 Properties of Continuous-Time Systems -- Stability -- Linearity -- Summary -- Problems -- 3 CONTINUOUS-TIME LINEAR TIME-INVARIANT SYSTEMS -- 3.1 Impulse Representation of Continuous-Time Signals -- 3.2 Convolution for Continuous-Time LTI Systems -- 3.3 Properties of Convolution -- 3.4 Properties of Continuous-Time LTI Systems -- Memoryless Systems -- Invertibility -- Causality -- Stability -- Unit Step Response -- 3.5 Differential-Equation Models -- Solution of Differential Equations -- General Case -- Relation to Physical Systems -- 3.6 Terms in the Natural Response -- Stability -- 3.7 System Response for Complex-Exponential Inputs -- Linearity -- Complex Inputs for LTI Systems -- Impulse Response -- 3.8 Block Diagrams -- Direct Form I -- Direct Form II -- nth-Order Realizations -- Practical Considerations -- Summary -- Problems -- 4 FOURIER SERIES -- 4.1 Approximating Periodic Functions -- Periodic Functions -- Approximating Periodic Functions.

4.2 Fourier Series -- Fourier Series -- Fourier Coefficients -- 4.3 Fourier Series and Frequency Spectra -- Frequency Spectra -- 4.4 Properties of Fourier Series -- 4.5 System Analysis -- 4.6 Fourier Series Transformations -- Amplitude Transformations -- Time Transformations -- Summary -- Problems -- 5 THE FOURIER TRANSFORM -- 5.1 Definition of the Fourier Transform -- 5.2 Properties of the Fourier Transform -- Linearity -- Time Scaling -- Time Shifting -- Time Transformation -- Duality -- Convolution -- Frequency Shifting -- Time Differentiation -- Time Integration -- Frequency Differentiation -- Summary -- 5.3 Fourier Transforms of Time Functions -- DC Level -- Unit Step Function -- Switched Cosine -- Pulsed Cosine -- Exponential Pulse -- Fourier Transforms of Periodic Functions -- Summary -- 5.4 Sampling Continuous-Time Signals -- Impulse Sampling -- Shannon's Sampling Theorem -- Practical Sampling -- 5.5 Application of the Fourier Transform -- Frequency Response of Linear Systems -- Frequency Spectra of Signals -- Summary -- 5.6 Energy and Power Density Spectra -- Energy Density Spectrum -- Power Density Spectrum -- Power and Energy Transmission -- Summary -- Summary -- Problems -- 6 APPLICATIONS OF THE FOURIER TRANSFORM -- 6.1 Ideal Filters -- 6.2 Real Filters -- RC Low-Pass Filter -- Butterworth Filter -- Chebyschev and Elliptic Filters -- Bandpass Filters -- Summary -- 6.3 Bandwidth Relationships -- 6.4 Reconstruction of Signals from Sample Data -- Interpolating Function -- Digital-to-Analog Conversion -- 6.5 Sinusoidal Amplitude Modulation -- Frequency-Division Multiplexing -- 6.6 Pulse-Amplitude Modulation -- Time-Division Multiplexing -- Flat-Top PAM -- Summary -- Problems -- 7 THE LAPLACE TRANSFORM -- 7.1 Definitions of Laplace Transforms -- 7.2 Examples -- 7.3 Laplace Transforms of Functions -- 7.4 Laplace Transform Properties.

Real Shifting -- Differentiation -- Integration -- 7.5 Additional Properties -- Multiplication by t -- Initial Value -- Final Value -- Time Transformation -- 7.6 Response of LTI Systems -- Initial Conditions -- Transfer Functions -- Convolution -- Transforms with Complex Poles -- Functions with Repeated Poles -- 7.7 LTI Systems Characteristics -- Causality -- Stability -- Invertibility -- Frequency Response -- 7.8 Bilateral Laplace Transform -- Region of Convergence -- Bilateral Transform from Unilateral Tables -- Inverse Bilateral Laplace Transform -- 7.9 Relationship of the Laplace Transform to the Fourier Transform -- Summary -- Problems -- 8 STATE VARIABLES FOR CONTINUOUS-TIME SYSTEMS -- 8.1 State-Variable Modeling -- 8.2 Simulation Diagrams -- 8.3 Solution of State Equations -- Laplace-Transform Solution -- Convolution Solution -- Infinite Series Solution -- 8.4 Properties of the State-Transition Matrix -- 8.5 Transfer Functions -- Stability -- 8.6 Similarity Transformations -- Transformations -- Properties -- Summary -- Problems -- 9 DISCRETE-TIME SIGNALS AND SYSTEMS -- 9.1 Discrete-Time Signals and Systems -- Unit Step and Unit Impulse Functions -- Equivalent Operations -- 9.2 Transformations of Discrete-Time Signals -- Time Transformations -- Amplitude Transformations -- 9.3 Characteristics of Discrete-Time Signals -- Even and Odd Signals -- Signals Periodic in n -- Signals Periodic in (S](B -- 9.4 Common Discrete-Time Signals -- 9.5 Discrete-Time Systems -- Interconnecting Systems -- 9.6 Properties of Discrete-Time Systems -- Systems with Memory -- Invertibility -- Inverse of a System -- Causality -- Stability -- Time Invariance -- Linearity -- Summary -- Problems -- 10 DISCRETE-TIME LINEAR TIME-INVARIANT SYSTEMS -- 10.1 Impulse Representation of Discrete-Time Signals -- 10.2 Convolution for Discrete-Time Systems -- Properties of Convolution.

10.3 Properties of Discrete-Time LTI Systems -- Memory -- Invertibility -- Causality -- Stability -- Unit Step Response -- 10.4 Difference-Equation Models -- Difference-Equation Models -- Classical Method -- Solution by Iteration -- 10.5 Terms in the Natural Response -- Stability -- 10.6 Block Diagrams -- Two Standard Forms -- 10.7 System Response for Complex-Exponential Inputs -- Linearity -- Complex Inputs for LTI Systems -- Stability -- Sampled Signals -- Impulse Response -- Summary -- Problems -- 11 THE z-TRANSFORM -- 11.1 Definitions of z-Transforms -- 11.2 Examples -- Two z-Transforms -- Digital-Filter Example -- 11.3 z-Transforms of Functions -- Sinusoids -- 11.4 z-Transform Properties -- Real Shifting -- Initial and Final Values -- 11.5 Additional Properties -- Time Scaling -- Convolution in Time -- 11.6 LTI System Applications -- Transfer Functions -- Inverse z-Transform -- Complex Poles -- Causality -- Stability -- Invertibility -- 11.7 Bilateral z-Transform -- Bilateral Transforms -- Regions of Convergence -- Inverse Bilateral Transforms -- Summary -- Problems -- 12 FOURIER TRANSFORMS OF DISCRETE-TIME SIGNALS -- 12.1 Discrete-Time Fourier Transform -- z-Transform -- 12.2 Properties of the Discrete-Time Fourier Transform -- Periodicity -- Linearity -- Time Shift -- Frequency Shift -- Symmetry -- Time Reversal -- Convolution in Time -- Convolution in Frequency -- Multiplication by n -- Parseval's Theorem -- 12.3 Discrete-Time Fourier Transform of Periodic Sequences -- 12.4 Discrete Fourier Transform -- Shorthand Notation for the DFT -- Frequency Resolution of the DFT -- Validity of the DFT -- Summary -- 12.5 Fast Fourier Transform -- Decomposition-in-Time Fast Fourier Transform Algorithm -- Decomposition-in-Frequency Fast Fourier Transform -- Summary -- 12.6 Applications of the Discrete Fourier Transform -- Calculation of Fourier Transforms.

Convolution -- Filtering -- Correlation -- Energy Spectral Density Estimation -- Summary -- 12.7 The Discrete Cosine Transform -- Summary -- Problems -- 13 STATE VARIABLES FOR DISCRETE-TIME SYSTEMS -- 13.1 State-Variable Modeling -- 13.2 Simulation Diagrams -- 13.3 Solution of State Equations -- Recursive Solution -- z-Transform Solution -- 13.4 Properties of the State Transition Matrix -- 13.5 Transfer Functions -- Stability -- 13.6 Similarity Transformations -- Properties -- Summary -- Problems -- APPENDICES -- A. Integrals and Trigonometric Identities -- Integrals -- Trigonometric Identities -- B. Leibnitz's and L'H�opital's Rules -- Leibnitz's Rule -- L'H�opital's Rule -- C. Summation Formulas for Geometric Series -- D. Complex Numbers and Euler's Relation -- Complex-Number Arithmetic -- Euler's Relation -- Conversion Between Forms -- E. Solution of Differential Equations -- Complementary Function -- Particular Solution -- General Solution -- Repeated Roots -- F. Partial-Fraction Expansions -- G. Review of Matrices -- Algebra of Matrices -- Other Relationships -- H. Answers to Selected Problems -- I. Signals and Systems References -- INDEX -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- L -- M -- N -- O -- P -- R -- S -- T -- U -- V -- W -- Z.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2018. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.