ALBERT

Note: Contents Part I Unraveling Microbial Diversity and Their Processes Phagotrophic Protists: Central Roles in Microbial Food Webs / Evelyn B. Sherr and Barry F. Sherr Overview Protists as Elemental Recyclers Protists as Consumers of Bacteria Protists as Consumers of Phytoplankton Protists in High Latitude Food Webs Looking to the Future References Drivers That Structure Biodiversity in the Plankton / Tatiana A. Rynearson and Susanne Menden-Deuer Plankton Biodiversity Alternate Hypotheses That Explain the Paradox of the Plankton An Organismal Perspective on the Paradox of the Plankton: A Biodiversity Explosion from Within? Linking Individual Level Behaviors with Plankton Ecology Pervasive Intra-specific Variability in the Genetic Diversity, Physiological Capacity, and Behavioral Repertoire of Plankton Evolution: Generating and Structuring Diversity over the Long Term Opportunities for Progress References The Elongated, the Squat and the Spherical: Selective Pressures for Phytoplankton Shape / Lee Karp-Boss and Emmanuel Boss Introduction Effects of Shape on Diffusion Other Selective Pressures References Crossing the Freshwater/Saline Barrier: A Phylogenetic Analysis of Bacteria Inhabiting Both Freshwater and Marine Ecosystems / Mina Bižić-Ionescu and Danny Ionescu Introduction Recent Data on Shared Taxa Synthesis of Published Sequence Data Future Perspectives References Approaches and Challenges for Linking Marine Biogeochemical Models with the “Omics” Revolution / Victoria J. Coles and Raleigh R. Hood Introduction Bridging the Cultural and Structural Divide Relating Existing Omics to Current Biogeochemical Models Near-Term Innovation Conclusions References Part II Viewing Growth and Trophodynamics Through a Stoichiometric Lens Out of Africa and into Stoichiometry / Susan S. Kilham and Peter Kilham References Exploring the Implications of the Stoichiometric Modulation of Planktonic Predation / Aditee Mitra and Kevin J. Flynn Introduction Characterising the Predator–Prey Stoichiometric Link Elemental Stoichiometry and Commercial Microalgal Production Effects of Temperature, Ocean Acidification and Nutrient Excess Avoiding Predation Stoichiometry and Mixotrophy Conclusions References . Part III Understanding the Mysteries of Light and Nitrogen On Saturating Response Curves from the Dual Perspectives of Photosynthesis and Nitrogen Metabolism / Todd M. Kana and Patricia M. Glibert Introduction Static vs. Dynamic Behavior Gradient Signals and Dynamics of Response Curves Overall Perspective on Dynamic Kinetics References Nitrate Reductase: A Nexus of Disciplines, Organisms, and Metabolism / Erica B. Young and John A. Berges Introduction Why Nitrate Reductase? Understanding That Has Emerged from Recent NR Measurements Recent Advances and Emerging Challenges Conclusion References The Ammonium Paradox of an Urban High- Nutrient Low-Growth Estuary / Frances Wilkerson and Richard Dugdale High-Nutrient Low-Growth Estuaries and Oligotrophication Observation of an Ammonium Paradox Ammonium: The Gatekeeper Controlling Access to Nitrate References Why Is Planktonic Nitrogen Fixation So Rare in Coastal Marine Ecosystems? Insights from a Cross-Systems Approach / Roxanne Marino and Robert W. Howarth References Where Light and Nutrients Collide: The Global Distribution and Activity of Subsurface Chlorophyll Maximum Layers / Greg M. Silsbe and Sairah Y. Malkin At the Confluence of Light and Nutrients Distribution of Marine SCMLs Phytoplankton Production in SCMLs Subsurface Chlorophyll Maximum Layers in Lakes References Part IV Looking in the Rear View Mirror: The Long View on Changing Ecosystems An Ecosystem in Transition: The Emergence of Mixotrophy in the Arabian Sea / Joaquim I. Goes and Helga do R. Gomes Introduction Materials and Methods Results and Discussion References The Saint Lawrence Island Polynya: A 25-Year Evaluation of an Analogue for Climate Change in Polar Regions / Jacqueline M. Grebmeier and Lee W. Cooper Introduction Synthesis Results and Discussion The Northern Bering Sea: Interannual Variability and Change Benthivores Overall Summary References Ecological Processes and Nutrient Transfers from Land to Sea: A 25-Year Perspective on Research and Management of the Seine River System / Josette Garnier and Gilles Billen Introduction 1850–1990: Organic Pollution and Oxygen 1990–2000: Eutrophication and Algal Bloom 2000–2015: Agricultural Pollution and Nitrate Contamination Conclusion: From Microbial Ecology to Territorial Biogeochemistry References A Historical Perspective on Eutrophication in the Pensacola Bay Estuary, FL, USA / Jane M. Caffrey and Michael C. Murrell Introduction Pensacola Bay Physical Setting Human Colonization of Pensacola Bay River and Estuarine Water Quality Controls on Primary Production, Organic Matter, and Nutrient Cycling Summary References Unpublished Reports Websites Meeting in the Middle: On the Interactions Between Microalgae and Their Predators or Zooplankton and Their Food / Karen H. Wiltshire and Maarten Boersma Introduction Materials and Methods Results Discussion References Lake Transparency: A Window into Decadal Variations in Dissolved Organic Carbon Concentrations in Lakes of Acadia National Park, Maine / Collin Roesler and Charles Culbertson Introduction Methods Results Discussion References Part V Focusing on Unique Systems, Processes and Dynamics Phytoplankton Biodiversity in the Oligotrophic Northwestern Sargasso Sea / James L. Pinckney and Tammi L. Richardson Introduction Materials and Methods Results Discussion References Biological Oceanography of the Gulf of Carpentaria, Australia: A Review / Peter C. Rothlisberg and Michele A. Burford Introduction Study Area Currents and Hydrography Phytoplankton and the Role of Nutrients Zooplankton Penaeid Prawn Larval Ecology Larval Dispersal Mechanisms Summary Points References Discerning the Causes of Toxic Cyanobacteria (Lyngbya majuscula) Blooms in Moreton Bay, Australia / Judith M. O’Neil and William C. Dennison Introduction Nutrient Interactions Light Interactions Conceptual Model Broader Significance References Copepod, Ctenophore, and Schyphomedusae Control in Structuring the Chesapeake Bay Summer Mesohaline Planktonic Food Web / Kevin G. Sellner and Stella G. Sellner Introduction Methods Results and Discussion References Microbiogeochemical Ecophysiology of Freshwater Hydrothermal Vents in Mary Bay Canyon, Yellowstone Lake, Yellowstone National Park WY / Carmen Aguilar and Russell Cuhel Introduction Methods Big Picture Outcomes Closing Remarks References Index

Note: Contents Preface 1 Introduction to Ice Drilling Technology 1.1 Ice Drilling Targets and Aims 1.2 Structure of Ice Sheets and Glaciers 1.3 Classification of Ice Drilling Methods References 2 Yearly History of Ice Drilling from Nineteeth to the First Half of Twentieth Century References 3 Direct-Push Drilling 3.1 Drive Sampling 3.1.1 Basic Principles 3.1.2 Mt. Rose Sampler 3.1.3 Utah Snow Sampler 3.1.4 Federal Snow Sampler 3.1.5 Bowman Sampler 3.1.6 Rosen Sampler 3.1.7 Large Diameter Snow Samplers 3.1.8 Vibratory Drill 3.2 Penetrative Testing 3.2.1 Ski Pole Penetrometer 3.2.2 Ram Penetrometer 3.2.3 Snow Resistograph 3.2.4 Digital Thermo-Resistograph 3.2.5 Snow Micro-Penetrometer 3.2.6 SABRE Probe 3.2.7 Cone Penetrometer Testing 3.3 Summary References 4 Hand- and Power-Driven Portable Drills 4.1 Noncoring Augers 4.1.1 SFFEL Noncoring Auger 4.1.2 SIPRE/CRREL Ice Thickness Kit 4.1.3 Kovacs Ice Thickness Kit 4.1.4 AARI Portable Sled-Mounted Drilling Rig 4.1.5 Handheld Coal-Boring Augers 4.1.6 Ice Augers for Winter Fishing 4.2 Noncoring “Piston” Drill 4.3 Core Augers. 4.3.1 General Principles 4.3.2 SFFEL Auger 4.3.3 SIPRE Auger 4.3.4 CRREL Auger 4.3.5 Rand Auger 4.3.6 Big John 12″ Auger 4.3.7 PICO Lightweight Auger 4.3.8 Kovacs Auger 4.3.9 IGAS Hand Auger 4.3.10 Swiss Hand Auger 4.3.11 UCPH Hand Auger 4.3.12 “Prairie Dog” Auger 4.3.13 “Sidewinder” 4.3.14 IDDO Hand Auger 4.4 Core Drills with Teeth and Annular Bits 4.4.1 Taku Glacier Hand Drill 4.4.2 Canadian Portable Ice Drill 4.4.3 Tsykin’s Hand Drill 4.4.4 5th CAE Drill 4.4.5 Ice Core Drill with Annular Bit PI-8 4.5 Mini Drills 4.5.1 Livingston Island Mini Drill 4.5.2 Chipmunk Drill 4.6 Summary References 5 Percussion Drills 5.1 Cable-Tool Drill Rigs 5.1.1 IGAS Cable-Tool Rig 5.1.2 Cable-Tool of California Institute of Technology 5.1.3 Star Iron Works Cable-Tool 5.2 Pneumatic Drills 5.3 Rotary-Percussion Drills 5.4 Summary References 6 Conventional Machine-Driven Rotary Drill Rigs 6.1 Dry Drilling 6.1.1 Expéditions Polaires Françaises in Greenland 6.1.2 Baffin Island Expedition 6.1.3 Norwegian-British-Swedish Antarctic Expedition 6.1.4 Mirny Station, Antarctica 6.2 Auger Drilling 6.2.1 Mirny Station, Antarctica 6.2.2 McMurdo Station, Antarctica 6.2.3 Amundsen–Scott Station, South Pole 6.2.4 Subglacial Lake Ellsworth Camp 6.3 Commercial Drill Rigs for Ice Fishing 6.4 Air Rotary Drilling 6.4.1 Mirny, Antarctica 6.4.2 Site 2, Greenland 6.4.3 Byrd Station, Antarctica 6.4.4 Little America V, Antarctica 6.4.5 Franz Josef Land, Russian Arctic 6.4.6 Base Roi Baudouin, Antarctica 6.5 Rotary Drilling with Fluid Circulation 6.5.1 Taku Glacier, Alaska 6.5.2 Mer de Glace, French Alps 6.5.3 South Leduc Glacier, British Columbia 6.5.4 McMurdo Station, Antarctica 6.6 Wire-Line Drills 6.6.1 International Antarctic Glaciological Project, East Antarctica 6.6.2 Ross Ice Shelf Project 6.6.3 Base Druzhnaya, Antarctica 6.6.4 Black Rapids Glacier, Alaska 6.6.5 Isua Greenstone Belt, Southwestern Greenland 6.6.6 Foremore Glacier, British Columbia, Western Canada 6.6.7 Rapid Access Ice Drill (RAID) 6.6.8 Agile Sub-ice Geological (ASIG) Drill 6.7 Drilling in Rock Glaciers 6.7.1 Overview of Projects Using Conventional Drilling Equipment 6.7.2 Koci Drill 6.8 Summary References 7 Flexible Drill-Stem Drill Rigs 7.1 Rapid Shallow Drill Rigs 7.2 Rapid-Access Drill Rigs 7.2.1 Thermomechanical Drill 7.2.2 Coiled-Tubing Drill Rigs 7.2.3 RADIX 7.2.4 SUBGLACIOR Drilling Probe 7.3 Summary References 8 Cable-Suspended Electromechanical Auger Drills 8.1 Basic Principles 8.2 University of Iceland (UI) Drill 8.3 University of Bern (UB) Drills 8.3.1 Rufli Drill 8.3.2 Further Improved UB Drills 8.4 CRREL Drill 8.5 Institute of Low Temperature Science (ILTS) Drills 8.5.1 First Prototypes 8.5.2 ID-140 Drill 8.5.3 ILTS-140 Drill 8.5.4 MID-140 Drill 8.5.5 Portable ILTS-130 and -100 Drills 8.5.6 ILTS-130E(F) and ILTS-150 Drills 8.5.7 New Portable ILTS Drill 8.6 University of Copenhagen (UCPH) Drill 8.7 Laboratoire de Glaciologie et Géophysique de l’Environnement (LGGE) Drills 8.8 National Hydrology Research Institute (NHRI) Drill 8.9 Polar Ice Coring Office (PICO) 4″ Drill 8.10 Alfred-Wegener Institute (AWI) Drills 8.11 Australian National Antarctic Research Expedition (ANARE) Drill 8.12 BZXJ Drills 8.13 Geo Tecs Drills 8.13.1 Geo Tecs Prototype Shallow Drill 8.13.2 Further Improvements 8.13.3 Field Testing and Operations 8.14 Hilda/Simon/Eclipse Drills 8.14.1 Hilda/Simon Drills 8.14.2 Eclipse Drill 8.14.3 Field Testing and Coring 8.14.4 Badger-Eclipse Drill 8.15 Byrd Polar Research Center (BPRC) Drills 8.16 British Antarctic Survey (BAS) Drills 8.16.1 BAS/IMAU Drill 8.16.2 Rapid-Access Isotope Drill 8.17 FELICS Drills 8.17.1 3″ Drill 8.17.2 “Backpack Drill” 8.18 Blue Ice Drill (BID) 8.18.1 BID General Fescription 8.18.2 Operation and Performance 8.18.3 BID-Deep System 8.19 Summary References 9 Cable-Suspended Electromechanical Drills with Bottom-Hole Circulation 9.1 CRREL Electromechanical Drill 9.1.1 Drilling Equipment 9.1.2 Camp Century, Greenland 9.1.3 Byrd Station, Antarctica 9.2 ISTUK Drill 9.2.1 Drill System 9.2.2 Dye 3, Greenland (GISP) 9.2.3 Summit, Greenland (GRIP) 9.2.4 Law Dome, Antarctica 9.3 LGGE Electromechanical Drills 9.4 PICO-5.2″ Electromechanical Drill 9.4.1 Drill System 9.4.2 Summit, Greenland (GISP2) 9.4.3 Taylor Dome, Antarctica 9.4.4 Siple Dome, Antarctica 9.5 KEMS Electromechanical Drill 9.5.1 Drill System 9.5.2 Severnaya Zemlya, Russian Arctic 9.5.3 Vostok Station, Antarctica 9.6 JARE Electromechanical Drill 9.6.1 Drill System 9.6.2 Preliminary Tests 9.6.3 First Deep Ice Coring Project at Dome F, Antarctica 9.6.4 Second Deep Ice Coring Project at Dome F, Antarctica 9.6.5 Kunlun Station (Dome A), Antarctica 9.7 Hans Tausen (HT) Electromechanical Drill and Its Modifications 9.7.1 Basic Drill System 9.7.2 Hans Tausen Ice Cap, Greenland 9.7.3 NorthGRIP, Greenland 9.7.4 EPICA Dome C, Antarctica 9.7.5 EPICA-DML, Kohnen Station, Antarctica 9.7.6 Berkner Island, Antarctica 9.7.7 Talos Dome, Antarctica (TALDICE) 9.7.8 Flade Isblink Ice Cap, Greenland 9.7.9 NEEM Deep Ice Core Drilling, Greenland 9.7.10 James Ross Island, Antarctica 9.7.11 Fletcher Promontory, Antarctica 9.7.12 Roosevelt Island, Antarctica 9.7.13 NEEM, Greenland (UCPH Intermediate-Depth Ice Core Drilling System) 9.7.14 Aurora Basin North, Antarctica 9.7.15 Renland Ice Cap, Greenland 9.7.16 Summit, Greenland (IDDO Intermediate-Depth Drill) 9.7.17 South Pole, Antarctica (SPICE) 9.8 IDRA Drill 9.9 DISC Electromechanical Drill 9.9.1 Drill System 9.9.2 Field Testing at Summit, Greenland 9.9.3 WAIS Divide, Antarctica 9.9.4 Replicate Coring, WAIS Divide, Antarctica 9.10 IBED Drill 9.11 Summary References 10 Drilling Challenges and Perspectives for Future Development 10.1 Low-Temperature Drilling Fluids 10.1.1 Drilling Fluid Compositions 10.1.2 ESTISOL™ 240/COASOL™ Drilling Fluid 10.1.3 ESTISOL™ 140 Drilling Fluid 10.1.4 Low-Molecular Weight Dimethyl Siloxane Oils 10.1.5 Low-Molecular Weight Esters 10.1.6 Kerosene-Based Drilling Fluids Mixed with Fourth-Generation Foam-Expansion Agents 10.2 Ice Drilling Under Complicated Conditions 10.2.1 Permeable Snow-Firn 10.2.2 Brittle Ice Zone 10.2.3 Warm Ice 10.2.4 Debris-Containing Ice 10.2.5 Bedrock 10.2.6 Elimination of Sticking Drills 10.3 Advanced Drilling Systems 10.3.1 Rapid-Access Ice Drilling Systems for Subglacial Bedrock Drilling 10.3.2 Sidewall Drilling 10.3.3 Automated Drilling Systems References Appendix A: Records of Mechanical Drilling in Ice Appendix B: Abbreviations of Institutes, Organizations, and Projects

Note: Contents: 1 Introduction. - 1.1 Chapter Summary. - 1.2 The Meaning of the Book’s Title. - 1.3 Historical Background. - 1.4 How to Read This Book. - 1.5 Further Reading. - References. - PART 1 BASIC THEORETICAL CONCEPTS. - 2 Discrete-Time Signals and Systems. - 2.1 Chapter Summary. - 2.2 Basic Definitions and Concepts. - 2.3 Discrete-Time Signals: Sequences. - 2.3.1 Basic Sequence Operations. - 2.3.2 Basic Sequences. - 2.3.3 Deterministic and Random Signals. - 2.4 Linear Time-Invariant (LTI) Systems. - 2.4.1 Impulse Response of an LTI System and Linear Convolution. - 2.4.2 An Example of Linear Convolution. - 2.4.3 Interconnections of LTI Systems. - 2.4.4 Effects of Stability and Causality Constraints on the Impulse Response of an LTI System. - 2.4.5 Finite (FIR) and Infinite (IIR) Impulse Response Systems. - 2.4.6 Linear Constant-Coefficient Difference Equation (LCCDE). - 2.4.7 Examples of LCCDE. - 2.4.8 The Solutions of an LCCDE. - 2.4.9 From the LCCDE to the Impulse Response: Examples. - 2.4.10 Eigenvalues and Eigenfunctions of LTI Systems. - References. - 3 Transforms of Discrete-Time Signals. - 3.1 Chapter Summary. - 3.2 z-Transform. - 3.2.1 Examples of z-Transforms and Special Cases. - 3.2.2 Rational z-Transforms. - 3.2.3 Inverse z-Transform. - 3.2.4 The z-Transform on the Unit Circle. - 3.2.5 Selected z-Transform Properties. - 3.2.6 Transfer Function of an LTI System. - 3.2.7 Output Sequence of an LTI System. - 3.2.8 Zeros and Poles: Forms for Rational Transfer Functions. - 3.2.9 Inverse System. - 3.3 Discrete-Time Fourier Transform (DTFT). - 3.3.1 An Example of DTFT Converging in the Mean-Square Sense. - 3.3.2 Line Spectra. - 3.3.3 Inverse DTFT. - 3.3.4 Selected DTFT Properties. - 3.3.5 The DTFT of a Finite-Length Causal Sequence. - 3.4 Discrete Fourier Series (DFS). - 3.4.1 Selected DFS Properties. - 3.4.2 Sampling in the Frequency Domain and Aliasing in the Time Domain. - 3.5 Discrete Fourier Transform (DFT). - 3.5.1 The Inverse DFT in Terms of the Direct DFT. - 3.5.2 Zero Padding. - 3.5.3 Selected DFT Properties. - 3.5.4 Circular Convolution Versus Linear Convolution. - 3.6 Fast Fourier Transform (FFT). - 3.7 Discrete Trigonometric Expansion. - 3.8 Appendix: Mathematical Foundations of Signal Representation. - 3.8.1 Vector Spaces. - 3.8.2 Inner Product Spaces. - 3.8.3 Bases in Vector Spaces. - 3.8.4 Signal Representation by Orthogonal Bases. - 3.8.5 Signal Representation by Standard Bases. - 3.8.6 Frames and Biorthogonal Bases. - 3.8.7 Summary and Complements. - References. - 4 Sampling of Continuous-Time Signals. - 4.1 Chapter Summary. - 4.2 Sampling Theorem. - 4.3 Reconstruction of a Continuous-Time Signal from Its Samples. - 4.4 Aliasing in the Frequency Domain and Anti-Aliasing Filter. - 4.5 The Uncertainty Principle for the Analog Fourier Transform. - 4.6 Support of a Continuous-Time Signal in the Time and Frequency Domains. - 4.7 Appendix: Analog and Digital Frequency Variables. - References. - 5 Spectral Analysis of Deterministic Discrete-Time Signals. - 5.1 Chapter Summary. - 5.2 Issues in Practical Spectral Analysis. - 5.2.1 The Effect of Windowing. - 5.2.2 The Effect of Spectral Sampling. - 5.3 Classical Windows. - 5.4 The Kaiser Window. - 5.5 Energy and Power Signals and Their Spectral Representations. - 5.6 Correlation of Deterministic Discrete-Time Signals. - 5.6.1 Correlation of Energy Signals. - 5.6.2 Correlation of Power Signals. - 5.6.3 Effect of an LTI System on Correlation Properties of Input and Output Signals. - 5.7 Wiener-Khinchin Theorem. - 5.7.1 Energy Signals and Energy Spectrum. - 5.7.2 Power Signals and Power Spectrum. - References. - PART 2 DIGITAL FILTERS. - 6 Digital Filter Properties and Filtering Implementation. - 6.1 Chapter Summary. - 6.2 Frequency-Selective Filters. - 6.3 Real-Causal-Stable-Rational (RCSR) Filters. - 6.4 Amplitude Response. - 6.5 Phase Response. - 6.5.1 Phase Discontinuities and Zero-Phase Response. - 6.5.2 Linear Phase (LP). - 6.5.3 Generalized Linear Phase (GLP). - 6.5.4 Constraints on GLP Filters. - 6.6 Digital Filtering Implementation. - 6.6.1 Direct Forms. - 6.6.2 Transposed-Direct Forms. - 6.6.3 FIR Direct and Transposed-Direct Forms. - 6.6.4 Direct and Transposed-Direct Forms for LP FIR Filters. - 6.6.5 Cascade and Parallel Forms. - 6.7 Zero-Phase Filtering. - 6.8 An Incorrect Approach to Filtering. - 6.9 Filtering After Downsampling. - 6.9.1 Theory of Downsampling. - 6.9.2 An Example of Filtering After Downsampling. - References. - 7 FIR Filter Design. - 7.1 Chapter Summary. - 7.2 Design Process. - 7.3 Specifications of Digital Filters. - 7.3.1 Constraints on the Magnitude Response. - 7.3.2 Constraints on the Phase Response. - 7.4 Selection of Filter Type: IIR or FIR?. - 7.5 FIR-Filter Design Methods and Approximation Criteria. - 7.6 Properties of GLP FIR Filters. - 7.6.1 Factorization of the Zero-Phase Response. - 7.6.2 Zeros of the Transfer Function. - 7.6.3 Another Form of the Adjustable Term. - 7.7 Equiripple FIR Filter Approximations: Minimax Design. - 7.8 Predicting the Minimum Filter Order. - 7.9 MPR Algorithm. - 7.10 Properties of Equiripple FIR Filters. - 7.11 The Minimax Method for Bandpass Filters. - References. - 8 IIR Filter Design. - 8.1 Chapter Summary. - 8.2 Design Process. - 8.3 Lowpass Analog Filters. - 8.3.1 Laplace Transform. - 8.3.2 Transfer Function and Design Parameters. - 8.4 Butterworth Filters. - 8.5 Chebyshev Filters. - 8.5.1 Chebyshev-I Filters. - 8.5.2 Chebyshev-II Filters. - 8.6 Elliptic Filters. - 8.7 Normalized and Non-normalized Filters. - 8.8 Comparison Among the Four Analog Filter Types. - 8.9 From the Analog Lowpass Filter to the Digital One. - 8.9.1 Bilinear Transformation. - 8.9.2 Design Procedure. - 8.9.3 Examples. - 8.10 Frequency Transformations. - 8.10.1 From a Lowpass to a Highpass Filter. - 8.10.2 From a Lowpass to a Bandpass Filter. - 8.10.3 From a Lowpass to a Bandstop Filter . - 8.11 Direct Design of IIR Filters. - 8.12 Appendix. - 8.12.1 Trigonometric Functions with Complex Argument. - 8.12.2 Elliptic Integrals. - 8.12.3 Jacobi Elliptic Functions. - 8.12.4 Landen-Gauss Transformation. - 8.12.5 Elliptic Rational Function. - References. - PART 3 SPECTRAL ANALYSIS. - 9 Statistical Approach to Signal Analysis. - 9.1 Chapter Summary. - 9.2 Preliminary Considerations. - 9.3 Random Variables. - 9.4 Ensemble Averages. - 9.5 Stationary Random Processes and Signals. - 9.6 Ergodicity. - 9.7 Wiener-Khinchin Theorem for Random Signals and Power Spectrum. - 9.8 Cross-Power Spectrum of Two Random Signals. - 9.9 Effect of an LTI System on a Random Signal. - 9.10 Estimation of the Averages of Ergodic Stationary Signals. - 9.10.1 General Concepts in Estimation Theory. - 9.10.2 Mean and Variance Estimation. - 9.10.3 Autocovariance Estimation. - 9.10.4 Cross-Covariance Estimation. - 9.11 Appendix: A Road Map to the Analysis of a Data Record. - References. - 10 Non-Parametric Spectral Methods. - 10.1 Chapter Summary. - 10.2 Power Spectrum Estimation. - 10.3 Periodogram. - 10.3.1 Bias. - 10.3.2 Variance. - 10.3.3 Examples. - 10.3.4 Variance Reduction by Band- and Ensemble-Averaging. - 10.4 Bartlett’s Method. - 10.5 Modified Periodogram. - 10.6 Welch’s Method. - 10.7 Blackman-Tukey Method. - 10.8 Statistical Significance of Spectral Peaks. - 10.9 MultiTaper Method. - 10.10 Estimation of the Cross-Power Spectrum of Two Random Signals. - 10.11 Use of the FFT in Power Spectrum Estimation. - 10.12 Power Spectrum Normalization. - References. - 11 Parametric Spectral Methods. - 11.1 Chapter Summary. - 11.2 Signals with Rational Spectra . - 11.3 Stochastic Models and Processes. - 11.3.1 Autoregressive-Moving Average (ARMA) Model. - 11.3.2 Autoregressive (AR) Model. - 11.3.3 Moving Average (MA) Model. - 11.3.4 How the AR and MA Modeling Approaches Are Theoretically Related. - 11.3.5 First-Order AR and MA Models: White, Red and Blue Noise. - 11.3.6 Higher-Order AR Models. - 11.4 The AR Approach to Spectral Estimation. - 11.5 AR Modeling and Linear Prediction. - 11.6