TAPAN K. SARKAR, PhD, is a professor at the Department of Electrical Engineering and Computer Science at Syracuse University, NY, USA. Professor Sarkar has previously published seven books with Wiley. MAGDALENA SALAZAR-PALMA, PhD, is a professor at the Department of Signal Theory and Communications, Carlos III University of Madrid, Leganes, Madrid, Spain. MING DA ZHU, PhD, is an associate professor at the School of Electronic Engineering at Xidian University, Xian, Shaanxi, China. HENG CHEN, PhD, is a research assistant at the Department of Electrical Engineering and Computer Science at Syracuse University, NY, USA.
Preface xiii Acknowledgments xxi Tribute to Tapan K. Sarkar Magdalena Salazar Palma, Ming Da Zhu, and Heng Chen xxiii 1 Mathematical Principles Related to Modern System Analysis 1 Summary 1 1.1 Introduction 1 1.2 Reduced-Rank Modelling: Bias Versus Variance Tradeoff 3 1.3 An Introduction to Singular Value Decomposition (SVD) and the Theory of Total Least Squares (TLS) 6 1.3.1 Singular Value Decomposition 6 1.3.2 The Theory of Total Least Squares 15 1.4 Conclusion 19 References 20 2 Matrix Pencil Method (MPM) 21 Summary 21 2.1 Introduction 21 2.2 Development of the Matrix Pencil Method for Noise Contaminated Data 24 2.2.1 Procedure for Interpolating or Extrapolating the System Response Using the Matrix Pencil Method 26 2.2.2 Illustrations Using Numerical Data 26 220.127.116.11 Example 1 26 18.104.22.168 Example 2 29 2.3 Applications of the MPM for Evaluation of the Characteristic Impedance of a Transmission Line 32 2.4 Application of MPM for the Computation of the S-Parameters Without any A Priori Knowledge of the Characteristic Impedance 37 2.5 Improving the Resolution of Network Analyzer Measurements Using MPM 44 2.6 Minimization of Multipath Effects Using MPM in Antenna Measurements Performed in Non-Anechoic Environments 57 2.6.1 Application of a FFT-Based Method to Process the Data 61 2.6.2 Application of MPM to Process the Data 64 2.6.3 Performance of FFT and MPM Applied to Measured Data 67 2.7 Application of the MPM for a Single Estimate of the SEM-Poles When Utilizing Waveforms from Multiple Look Directions 74 2.8 Direction of Arrival (DOA) Estimation Along with Their Frequency of Operation Using MPM 81 2.9 Efficient Computation of the Oscillatory Functional Variation in the Tails of the Sommerfeld Integrals Using MPM 85 2.10 Identification of Multiple Objects Operating in Free Space Through Their SEM Pole Locations Using MPM 91 2.11 Other Miscellaneous Applications of MPM 95 2.12 Conclusion 95 Appendix 2A Computer Codes for Implementing MPM 96 References 99 3 The Cauchy Method 107 Summary 107 3.1 Introduction 107 3.2 Procedure for Interpolating or Extrapolating the System Response Using the Cauchy Method 112 3.3 Examples to Estimate the System Response Using the Cauchy Method 112 3.3.1 Example 1 112 3.3.2 Example 2 116 3.3.3 Example 3 118 3.4 Illustration of Extrapolation by the Cauchy Method 120 3.4.1 Extending the Efficiency of the Moment Method Through Extrapolation by the Cauchy Method 120 3.4.2 Interpolating Results for Optical Computations 123 3.4.3 Application to Filter Analysis 125 3.4.4 Broadband Device Characterization Using Few Parameters 127 3.5 Effect of Noise Contaminating the Data and Its Impact on the Performance of the Cauchy Method 130 3.5.1 Perturbation of Invariant Subspaces 130 3.5.2 Perturbation of the Solution of the Cauchy Method Due to Additive Noise 131 3.5.3 Numerical Example 136 3.6 Generating High Resolution Wideband Response from Sparse and Incomplete Amplitude-Only Data 138 3.6.1 Development of the Interpolatory Cauchy Method for Amplitude-Only Data 139 3.6.2 Interpolating High Resolution Amplitude Response 142 3.7 Generation of the Non-minimum Phase Response from Amplitude-Only Data Using the Cauchy Method 148 3.7.1 Generation of the Non-minimum Phase 149 3.7.2 Illustration Through Numerical Examples 151 3.8 Development of an Adaptive Cauchy Method 158 3.8.1 Introduction 158 3.8.2 Adaptive Interpolation Algorithm 159 3.8.3 Illustration Using Numerical Examples 160 3.8.4 Summary 171 3.9 Efficient Characterization of a Filter 172 3.10 Extraction of Resonant Frequencies of an Object from Frequency Domain Data 176 3.11 Conclusion 180 Appendix 3A MATLAB Codes for the Cauchy Method 181 References 187 4 Applications of the Hilbert Transform A Nonparametric Method for Interpolation/Extrapolation of Data 191 Summary 191 4.1 Introduction 192 4.2 Consequence of Cau