Michael Corinthios

Corinthios, M: Signals, Systems, Transforms, and Digital Sig

Name: Corinthios, M: Signals, Systems, Transforms, and Digital Sig
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ISBN: 978-1-4200-9048-2

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Einband

Gebundene Ausgabe

Erscheinungsdatum

22.06.2009

Abbildungen

schwarz-weiss Illustrationen, Tabellen, schwarz-weiss

Verlag

Taylor & Francis

Seitenzahl

1344

Maße (L/B/H)

25.4/17.8/6.9 cm

Gewicht

2517 g

Sprache

Englisch

ISBN

978-1-4200-9048-2

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Continuous-Time and Discrete-Time Signals and Systems Introduction Continuous-Time Signals Periodic Functions Unit Step Function Graphical Representation of Functions Even and Odd Parts of a Function Dirac-Delta Impulse Basic Properties of the Dirac-Delta Impulse Other Important Properties of the Impulse Continuous-Time Systems Causality, Stability Examples of Electrical Continuous-Time Systems Mechanical Systems Transfer Function and Frequency Response Convolution and Correlation A Right-Sided and a Left-Sided Function Convolution with an Impulse and Its Derivatives Additional Convolution Properties Correlation Function Properties of the Correlation Function Graphical Interpretation Correlation of Periodic Functions Average, Energy and Power of Continuous-Time Signals Discrete-Time Signals Periodicity Difference Equations Even/Odd Decomposition Average Value, Energy and Power Sequences Causality, Stability Problems Answers to Selected Problems Fourier Series Expansion Trigonometric Fourier Series Exponential Fourier Series Exponential versus Trigonometric Series Periodicity of Fourier Series Dirichlet Conditions and Function Discontinuity Proof of the Exponential Series Expansion Analysis Interval versus Function Period Fourier Series as a Discrete-Frequency Spectrum Meaning of Negative Frequencies Properties of Fourier Series Differentiation of Discontinuous Functions Fourier Series of an Impulse Train Expansion into Cosine or Sine Fourier Series Deducing a Function Form from Its Expansion Truncated Sinusoid Spectral Leakage The Period of a Composite Sinusoidal Signal Passage through a Linear System Parseval's Relations Use of Power Series Expansion Inverse Fourier Series Problems Answers to Selected Problems Laplace Transform Introduction Bilateral Laplace Transform Conditions of Existence of Laplace Transform Basic Laplace Transforms Notes on the ROC of Laplace Transform Properties of Laplace Transform Applications of the Differentiation Property Transform of Right-Sided Periodic Functions Convolution in Laplace Domain Cauchy's Residue Theorem Inverse Laplace Transform Case of Conjugate Poles The Expansion Theorem of Heaviside Application to Transfer Function and Impulse Response Inverse Transform by Differentiation and Integration Unilateral Laplace Transform Gamma Function Table of Additional Laplace Transforms Problems Answers to Selected Problems Fourier Transform Definition of the Fourier Transform Fourier Transform as a Function of f From Fourier Series to Fourier Transform Conditions of Existence of the Fourier Transform Table of Properties of the Fourier Transform System Frequency Response Even-Odd Decomposition of a Real Function Causal Real Functions Transform of the Dirac-Delta Impulse Transform of a Complex Exponential and Sinusoid Sign Function Unit Step Function Causal Sinusoid Table of Fourier Transforms of Basic Functions Relation between Fourier and Laplace Transforms Relation to Laplace Transform with Poles on Imaginary Axis Convolution in Time Linear System Input-Output Relation Convolution in Frequency Parseval's Theorem Energy Spectral Density Average Value versus Fourier Transform Fourier Transform of a Periodic Function Impulse Train Fourier Transform of Powers of Time System Response to a Sinusoidal Input Stability of a Linear System Fourier Series versus Transform of Periodic Functions Transform of a Train of Rectangles Fourier Transform of a Truncated Sinusoid Gaussian Function Laplace and Fourier Transform Inverse Transform by Series Expansion Fourier Transform in omega and f Fourier Transform of the Correlation Function Ideal Filters Impulse Response Time and Frequency Domain Sampling Ideal Sampling Reconstruction of a Signal from its Samples Other Sampling Systems Ideal Sampling of a Bandpass Signal Sampling an Arbitrary Signal Sampling the Fourier Transform Problems Answers to Selected Problems System Modeling, Time and Frequency Response Transfer Function Block Diagram Reduction Galvanometer DC Motor A Speed-Control System Homology Transient and Steady-State Response Step Response of Linear Systems First Order System Second Order System Model Settling Time Second Order System Frequency Response Case of a Double Pole The Over-Damped Case Evaluation of the Overshoot Causal System Response to an Arbitrary Input System Response to a Causal Periodic Input Response to a Causal Sinusoidal Input Frequency Response Plots Decibels, Octaves, Decades Asymptotic Frequency Response Bode Plot of a Composite Linear System Graphical Representation of a System Function Vectorial Evaluation of Residues Vectorial Evaluation of the Frequency Response A First Order All-Pass System Filtering Properties of Basic Circuits Lowpass First Order Filter Minimum Phase Systems General Order All-Pass Systems Signal Generation Application of Laplace Transform to Differential Equations Transformation of Partial Differential Equations Problems Answers to Selected Problems Discrete-Time Signals and Systems Introduction Linear Time-Invariant Systems Linear Constant-Coefficient Difference Equations The z-Transform Convergence of the z-Transform Inverse z-Transform Inverse z-Transform by Partial Fraction Expansion Inversion by Long Division Inversion by a Power Series Expansion Inversion by Geometric Series Summation Table of Basic z-Transforms Properties of the z-Transform Geometric Evaluation of Frequency Response Comb Filters Causality and Stability Delayed Response and Group Delay Discrete-Time Convolution and Correlation Discrete-Time Correlation in One Dimension Convolution and Correlation as Multiplications Response of a Linear System to a Sinusoid Notes on the Cross-Correlation of Sequences LTI System Input/Output Correlation Sequences Energy and Power Spectral Density Two-Dimensional Signals Linear Systems, Convolution and Correlation Correlation of Two-Dimensional Signals IIR and FIR Digital Filters Discrete-Time All-Pass Systems Minimum-Phase and Inverse System Unilateral z-Transform Problems Answers to Selected Problems Discrete-Time Fourier Transform Laplace, Fourier and z-Transform Relations Discrete-Time Processing of Continuous-Time Signals A/D Conversion Quantization Error D/A Conversion Continuous versus Discrete Signal Processing Interlacing with Zeros Sampling Rate Conversion Fourier Transform of a Periodic Sequence Table of Discrete-Time Fourier Transforms Reconstruction of the Continuous-Time Signal Stability of a Linear System Table of Discrete-Time Fourier Transform Properties Parseval's Theorem Fourier Series and Transform Duality Discrete Fourier Transform Discrete Fourier Series DFT of a Sinusoidal Signal Deducing the z-Transform from the DFT DFT versus DFS Properties of DFS and DFT Circular Convolution Circular Convolution Using the DFT Sampling the Spectrum Table of Properties of DFS Shift in Time and Circular Shift Table of DFT Properties Zero Padding Discrete z-Transform Fast Fourier Transform An Algorithm for a Wired-In Radix-2 Processor Factorization of the FFT to a Higher Radix Feedback Elimination for High-Speed Signal Processing Problems Answers to Selected Problems State Space Modeling Introduction Note on Notation State Space Model System Transfer Function System Response with Initial Conditions Jordan Canonical Form of State Space Model Eigenvalues and Eigenvectors Matrix Diagonalization Similarity Transformation of a State Space Model Solution of the State Equations General Jordan Canonical Form Circuit Analysis by Laplace Transform and State Variables Trajectories of a Second Order System Second Order System Modeling Transformation of Trajectories between Planes Discrete-Time Systems Solution of the State Equations Transfer Function Change of Variables Second Canonical Form State Space Model Problems Answers to Selected Problems Filters of Continuous-Time Domain Lowpass Approximation Butterworth Approximation Denormalization of Butterworth Filter Prototype Denormalized Transfer Function The Case epsilon 6= 1 Butterworth Filter Order Formula Nomographs Chebyshev Approximation Pass-Band Ripple Transfer Function of the Chebyshev Filter Maxima and Minima of Chebyshev Filter Response The Value of epsilon as a Function of Pass-Band Ripple Evaluation of Chebyshev Filter Gain Chebyshev Filter Tables Chebyshev Filter Order Denormalization of Chebyshev Filter Prototype Chebyshev's Approximation: Second Form Response Decay of Butterworth and Chebyshev Filters Chebyshev Filter Nomograph Elliptic Filters Properties, Poles and Zeros of the sn Function Pole Zero Alignment and Mapping of Elliptic Filter Poles of H(s) Zeros and Poles of G(omega) Zeros, Maxima and Minima of the Magnitude Spectrum Points of Maxima/Minima Elliptic Filter Nomograph N = 9 Example Tables of Elliptic Filters Bessel's Constant Delay Filters A Note on Continued Fraction Expansion Evaluating the Filter Delay Bessel Filter Quality Factor and Natural Frequency Maximal Flatness of Bessel and Butterworth Response Bessel Filter's Delay and Magnitude Response Denormalization and Deviation from Ideal Response Bessel Filter's Magnitude and Delay Bessel Filter's Butterworth Asymptotic Form Delay of Bessel-Butterworth Asymptotic Form Filter Delay Plots of Butterworth Asymptotic Form Bessel Filter Bessel Filters Frequency Normalized Form Poles and Zeros of Asymptotic and Frequency Normalized Bessel Filter Forms Response and Delay of Normalized Form Bessel Filter Bessel Frequency Normalized Form Attenuation Setting Bessel Filter Nomograph Frequency Transformations Lowpass to Bandpass Transformation Lowpass to Band-Stop Transformation Lowpass to Highpass Transformation Note on Lowpass to Normalized Band-Stop Transformation Windows Rectangular Window Triangle (Bartlett) Window Hanning Window Hamming Window Problems Answers to Selected Problems Passive and Active Filters Design of Passive Filters Design of Passive Ladder Lowpass Filters Analysis of a General Order Passive Ladder Network Input Impedance of a Single-Resistance Terminated Network Evaluation of the Ladder Network Components Matrix Evaluation of Input Impedance Bessel Filter Passive Ladder Networks Tables of Single-Resistance Ladder Network Components Design of Doubly Terminated Passive LC Ladder Networks Tables of Double-Resistance Terminated Ladder Network Components Closed Forms for Circuit Element Values Elliptic Filter Realization as a Passive Ladder Network Table of Elliptic Filter Passive Network Components Element Replacement for Frequency Transformation Realization of a General Order Active Filter Inverting Integrator Biquadratic Transfer Functions General Biquad Realization First Order Filter Realization A Biquadratic Transfer Function Realization Sallen-Key Circuit Problems Answers to Selected Problems Digital Filters Introduction Signal Flow Graphs IIR Filter Models First Canonical Form Transposition Second Canonical Form Transposition of the Second Canonical Form Structures Based on Poles and Zeros Cascaded Form Parallel Form Matrix Representation Finite Impulse Response (FIR) Filters Linear Phase FIR Filters Conversion of Continuous-Time to Discrete-Time Filter Impulse Invariance Approach Impulse Invariance Approach Corrected Backward-Rectangular Approximation Forward Rectangular and Trapezoidal Approximations Bilinear Transform Lattice Filters Finite Impulse Response All-Zero Lattice Structures One-Zero FIR Filter Two-Zeros FIR Filter General Order All-Zero FIR Filter All-Pole Filter First Order One-Pole Filter Second Order All-Pole Filter General Order All-Pole Filter Pole-Zero IIR Lattice Filter All-Pass Filter Realization Schur-Cohn Stability Criterion Frequency Transformations Least Squares Digital Filter Design Pad'e Approximation Error Minimization in Prony's Method FIR Inverse Filter Design Impulse Response of Ideal Filters Spectral Leakage Windows Ideal Digital Filters Rectangular Window Hanning Window Hamming Window Triangular Window Comparison of Windows Spectral Parameters Linear-Phase FIR Filter Design Using Windows Even- and Odd-Symmetric FIR Filter Design Linear Phase FIR Filter Realization Sampling the Unit Circle Impulse Response Evaluation from Unit Circle Samples Problems Answers to Selected Problems Energy and Power Spectral Densities Energy Spectral Density Average, Energy and Power of Continuous-Time Signals Discrete-Time Signals Energy Signals Autocorrelation of Energy Signals Energy Signal through a Linear System Impulsive and Discrete-Time Energy Signals Power Signals Cross-Correlation Power Spectrum Conversion of a Linear System Impulsive and Discrete-Time Power Signals Periodic Signals Power Spectral Density of an Impulse Train Average, Energy and Power of a Sequence Energy Spectral Density of a Sequence Autocorrelation of an Energy Sequence Power Density of a Sequence Passage through a Linear System Problems Answers to Selected Problems Introduction to Communication Systems Introduction Amplitude Modulation (AM) of Continuous-Time Signals Frequency Modulation Discrete Signals Digital Communication Systems PCM-TDM Systems Frequency Division Multiplexing (FDM) Problems Answers to Selected Problems Fourier-, Laplace- and z-Related Transforms Walsh Transform Rademacher and Haar Functions Walsh Functions The Walsh (Sequency) Order Dyadic (Paley) Order Natural (Hadamard) Order Discrete Walsh Transform Discrete-Time Walsh Transform Discrete-Time Walsh-Hadamard Transform Natural (Hadamard) Order Fast Walsh-Hadamard Transform Dyadic (Paley) Order Fast Walsh-Hadamard Transform Sequency Ordered Fast Walsh-Hadamard Transform Generalized Walsh Transform Natural Order Generalized Sequency Order Generalized Walsh-Paley (p-adic) Transform Walsh-Kaczmarz Transform Generalized Walsh Factorizations for Parallel Processing Generalized Walsh Natural Order GWN Matrix Generalized Walsh-Paley GWP Transformation Matrix GWK Transformation Matrix High Speed Optimal Generalized Walsh Factorizations GWN Optimal Factorization GWP Optimal Factorization GWK Optimal Factorization Karhunen Lo'eve Transform Hilbert Transform Hilbert Transformer Discrete Hilbert Transform Hartley Transform Discrete Hartley Transform Mellin Transform Mellin Transform of ejx Hankel Transform Fourier Cosine Transform Discrete Cosine Transform (DCT) Fractional Fourier Transform Discrete Fractional Fourier Transform Two-Dimensional Transforms Two-Dimensional Fourier Transform Continuous-Time Domain Hilbert Transform Relations HI (jomega) versus HR(jomega) with No Poles on Axis Case of Poles on the Imaginary Axis Hilbert Transform Closed Forms Wiener-Lee Transforms Discrete-Time Domain Hilbert Transform Relations Problems Answers to Selected Problems Digital Signal Processors: Architecture, Logic Design Introduction Systems for the Representation of Numbers Conversion from Decimal to Binary Integers, Fractions and the Binary Point Representation of Negative Numbers Integer and Fractional Representation of Signed Numbers Addition Subtraction Full Adder Cell Addition/Subtraction Implementation in 2's Complement Controlled Add/Subtract (CAS) Cell Multiplication of Unsigned Numbers Multiplier Implementation 3-D Multiplier A Direct Approach to 2's Complement Multiplication Division Cellular Array for Nonrestoring Division Carry Look Ahead (CLA) Cell 2's Complement Nonrestoring Division Convergence Division Evaluation of the nth Root Function Generation by Chebyshev Series Expansion An Alternative Approach to Chebyshev Series Expansion Floating Point Number Representation Square Root Evaluation Cellular Array for Nonrestoring Square Root Extraction Binary Coded Decimal (BCD) Representation Memory Elements Design of Synchronous Sequential Circuits Realization of a Counter Using T Flip-Flops State Minimization Asynchronous Sequential Machines State Reduction Control Counter Design for Generator of Prime Numbers Fast Transform Processors Programmable Logic Arrays (PLAs) Field Programmable Gate Arrays (FPGAs) DSP with Xilinx FPGAs Texas Instruments TMS320C6713B Floating-Point DSP Central Processing Unit (CPU) CPU Data Paths and Control Instruction Syntax TMS320C6000 Control Register File Addressing Mode Register (AMR) Syntax for Load/Store Address Generation Programming the T.I. DSP A Simple C Program The Generated Assembly Code Fibonacci Series in C Calling Assembly-Language Function Finite Impulse Response (FIR) Filter Infinite Impulse Response (IIR) Filter on the DSP Real-Time DSP Applications Using MATLAB-Simulink Detailed Steps for DSP Programming in C++ and Simulink MOS FET Logic Circuit Realization Problems Answers to Selected Problems Random Signal Processing Nonparametric Methods of Power Spectrum Estimation Correlation of Continuous-Time Random Signals Passage through an LTI System Wiener Filtering in Continuous-Time Domain Causal Wiener Filter Random Sequences From Statistical to Time Averages Correlation and Covariance in z-Domain Random Signal Passage through an LTI System PSD Estimation of Discrete-Time Random Sequences Fast Fourier Transform (FFT) Evaluation of the Periodogram Parametric Methods for PSD Estimation The Yule-Walker Equations System Modeling for Linear Prediction, Adaptive Filtering and Spectrum Estimation Wiener and Least-Squares Models Wiener Filtering Least-Squares Filtering Forward Linear Prediction Backward Linear Prediction Lattice MA FIR Filter Realization AR Lattice of Order p ARMA(p, q) Process Power Spectrum Estimation FIR Wiener Filtering of Noisy Signals Two-Sided IIR Wiener Filtering Causal IIR Wiener Filter Wavelet Transform Discrete Wavelet Transform Important Signal Processing MATLAB Functions lpc Yulewalk dfilt logspace FIR Filter Design fir2 Power Spectrum Estimation Using MATLAB Parametric Modeling Functions prony A z-Domain Counterpart to Prony's Method Problems Answers to Selected Problems Distributions Introduction Distributions as Generalizations of Functions What is a Distribution? The Impulse as the Limit of a Sequence Properties of Distributions Approximating the Impulse Other Approximating Sequences and Functions of the Impulse Test Functions Convolution Multiplication by an Impulse Derivative The Dirac-Delta Impulse as a Limit of a Gaussian Function Fourier Transform of Unity The Impulse of a Function Multiplication by t Time Scaling Some Properties of the Dirac-Delta Impulse Additional Fourier Transforms Riemann-Lebesgue Lemma Generalized Limits Fourier Transform of Higher Impulse Derivatives The Distribution t-k Initial Derivatives of the Transform The Unit Step Function as a Limit Inverse Fourier Transform and Gibbs Phenomenon Ripple Elimination Transforms of |t| and tu(t) The Impulse Train as a Limit Sequence of Distributions Poisson's Summation Formula Moving Average Problems Answers to Selected Problems Generalization of Distributions Theory, Extending Laplace-, z- and Fourier-Related Transforms Introduction An Anomaly Generalized Distributions for Continuous-Time Functions Properties of the Generalized Impulse in s Domain Generalized Impulse as a Limit of a Three-Dimensional Sequence Discrete-Time Domain 3-D Test Function as a Possible Generalization Properties of the Generalized Impulse in z-Domain Additional Generalized Impulse Properties Generalized Impulse as Limit of a 3-D Sequence Extended Laplace and z-Transforms Generalization of Fourier-, Laplace- and z-Related Transforms Hilbert Transform Generalization Generalizing the Discrete Hilbert Transform Generalized Hartley Transform Generalized Discrete Hartley Transform Generalization of the Mellin Transform Multidimensional Signals and the Solution of Differential Equations Problems Answers to Selected Problems Appendix Symbols Frequently Needed Expansions Important Trigonometric Relations Orthogonality Relations Frequently Encountered Functions Mathematical Formulae Frequently Encountered Series Sums Biographies of Pioneering Scientists Plato (428 BC-347 BC) Euclid (circa 300 BC) Ptolemy (circa 90-168 AD) Abu Jafar Muhammad ibn Musa Al-Khwarizmi (780-850 AD) Nicolaus Copernicus (1473-1543) Galileo Galilei (1564-1642) Sir Isaac Newton (1643-1727) Guillaume-Fran,cois-Antoine de L'Hopital (1661-1704) Pierre-Simon Laplace (1749-1827) Gaspard Clair Fran,cois Marie, Baron Riche de Prony (1755-1839) Jean Baptiste Joseph Fourier (1768-1830) Johann Carl Friedrich Gauss (1777-1855) Friedrich Wilhelm Bessel (1784-1846) Augustin-Louis Cauchy (1789-1857) Niels Henrik Abel (1802-1829) Johann Peter Gustav Lejeune Dirichlet (1805-1859) Pafnuty Lvovich Chebyshev (1821-1894) Paul A.M. Dirac