A practical step-by-step guide to wavelet analysis is given, with examples taken from time series of the El Nino–Southern Oscillation (ENSO). The guide includes a comparison to the windowed Fourier transform, the choice of an appropriate wavelet basis function, edge effects due to finite-length time series, and the relationship between wavelet scale and Fourier frequency. New statistical significance tests for wavelet power spectra are developed by deriving theoretical wavelet spectra for white and red noise processes and using these to establish significance levels and confidence intervals. It is shown that smoothing in time or scale can be used to increase the confidence of the wavelet spectrum. Empirical formulas are given for the effect of smoothing on significance levels and confidence intervals. Extensions to wavelet analysis such as filtering, the power Hovmoller, cross-wavelet spectra, and coherence are described. The statistical significance tests are used to give a quantitative measure of change...

https://atoc.colorado.edu/research/wavelets/bams_79_01_0061.pdf

A Practical Guide to Wavelet Analysis.

[1] Using observed data sets mainly for the period 1979–2005, we find that anomalous warming events different from conventional El Nino events occur in the central equatorial Pacific. This unique warming in the central equatorial Pacific associated with a horseshoe pattern is flanked by a colder sea surface temperature anomaly (SSTA) on both sides along the equator. empirical orthogonal function (EOF) analysis of monthly tropical Pacific SSTA shows that these events are represented by the second mode that explains 12% of the variance. Since a majority of such events are not part of El Nino evolution, the phenomenon is named as El Nino Modoki (pseudo-El Nino) (“Modoki” is a classical Japanese word, which means “a similar but different thing”). The El Nino Modoki involves ocean-atmosphere coupled processes which include a unique tripolar sea level pressure pattern during the evolution, analogous to the Southern Oscillation in the case of El Nino. Hence the total entity is named as El Nino–Southern Oscillation (ENSO) Modoki. The ENSO Modoki events significantly influence the temperature and precipitation over many parts of the globe. Depending on the season, the impacts over regions such as the Far East including Japan, New Zealand, western coast of United States, etc., are opposite to those of the conventional ENSO. The difference maps between the two periods of 1979–2004 and 1958–1978 for various oceanic/atmospheric variables suggest that the recent weakening of equatorial easterlies related to weakened zonal sea surface temperature gradient led to more flattening of the thermocline. This appears to be a cause of more frequent and persistent occurrence of the ENSO Modoki event during recent decades.

El Niño Modoki and its possible teleconnection

SUMMARY Plate motions relative to the hotspots over the past 4 to 7 Myr are investigated with a goal of determining the shortest time interval over which reliable volcanic propagation rates and segment trends can be estimated. The rate and trend uncertainties are objectively determined from the dispersion of volcano age and of volcano location and are used to test the mutual consistency of the trends and rates. Ten hotspot data sets are constructed from overlapping time intervals with various durations and starting times. Our preferred hotspot data set, HS3, consists of two volcanic propagation rates and eleven segment trends from four plates. It averages plate motion over the past ≈5.8 Myr, which is almost twice the length of time (3.2 Myr) over which the NUVEL-1A global set of relative plate angular velocities is estimated. HS3-NUVEL1A, our preferred set of angular velocities of 15 plates relative to the hotspots, was constructed from the HS3 data set while constraining the relative plate angular velocities to consistency with NUVEL-1A. No hotspots are in significant relative motion, but the 95 per cent confidence limit on motion is typically ±20 to ±40 km Myr −1 and ranges up to ±145 km Myr −1 . The uncertainties of the new angular velocities of plates relative to the hotspots are smaller than those of previously published HS2-NUVEL1 (Gripp & Gordon 1990), while being averaged over a shorter and much more uniform time interval. Nine of the fourteen HS2-NUVEL1 angular velocities lie outside the 95 per cent confidence region of the corresponding HS3NUVEL1A angular velocity, while all fourteen of the HS3-NUVEL1A angular velocities lie inside the 95 per cent confidence region of the corresponding HS2-NUVEL1 angular velocity. The HS2-NUVEL1 Pacific Plate angular velocity lies inside the 95 per cent confidence region of the HS3-NUVEL1A Pacific Plate angular velocity, but the 0 to 3 Ma Pacific Plate angular velocity of Wessel & Kroenke (1997) lies far outside the confidence region. We show that the change in trend of the Hawaiian hotspot over the past 2 to 3 Myr has no counterpart on other chains and therefore provides no basis for inferring a change in Pacific Plate motion relative to global hotspots. The current angular velocity of the Pacific Plate can be shown to differ from the average over the past 47 Myr in rate but not in orientation, with the current rotation being about 50 per cent faster (1.06 ± 0.10 deg Myr −1 ) than the average (0.70 deg Myr −1 ) since the 47-Myr-old bend in the Hawaiian‐Emperor chain.

/pdf/young-tracks-of-hotspots-and-current-plate-velocities-4qm8vsz8fm.pdf

Young tracks of hotspots and current plate velocities

From the Publisher:
Orthogonal frequency-division multiplexing (OFDM) is a method of digital modulation in which a signal is split into several narrowband channels at different frequencies.
CDMA is a form of multiplexing, which allows numerous signals to occupy a single transmission channel, optimising the use of available bandwidth. Multiplexing is sending multiple signals or streams of information on a carrier at the same time in the form of a single, complex signal and then recovering the separate signals at the receiving end.
Multi-Carrier (MC) CDMA is a combined technique of Direct Sequence (DS) CDMA (Code Division Multiple Access) and OFDM techniques. It applies spreading sequences in the frequency domain.
Wireless communications has witnessed a tremendous growth during the past decade and further spectacular enabling technology advances are expected in an effort to render ubiquitous wireless connectivity a reality.
This technical in-depth book is unique in its detailed exposure of OFDM, MIMO-OFDM and MC-CDMA. A further attraction of the joint treatment of these topics is that it allows the reader to view their design trade-offs in a comparative context.
Divided into three main parts:
Part I provides a detailed exposure of OFDM designed for employment in various applications
Part II is another design alternative applicable in the context of OFDM systems where the channel quality fluctuations observed are averaged out with the aid of frequency-domain spreading codes, which leads to the concept of MC-CDMA
Part III discusses how to employ multiple antennas at the base station for the sake of supporting multiple users in the uplink
Portrays theentire body of knowledge currently available on OFDMProvides the first complete treatment of OFDM, MIMO(Multiple Input Multiple Output)-OFDM and MC-CDMAConsiders the benefits of channel coding and space time coding in the context of various application examples and features numerous complete system design examplesConverts the lessons of Shannon's information theory into design principles applicable to practical wireless systemsCombines the benefits of a textbook with a research monograph where the depth of discussions progressively increase throughout the book

This all-encompassing self-contained treatment will appeal to researchers, postgraduate students and academics, practising research and development engineers working for wireless communications and computer networking companies and senior undergraduate students and technical managers.

OFDM and MC-CDMA for Broadband Multi-User Communications, WLANs and Broadcasting

This paper studies the joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin. The time of ruin is analyzed in terms of its Laplace transforms, which can naturally be interpreted as discounting. Hence the classical risk theory model is generalized by discounting with respect to the time of ruin. We show how to calculate an expected discounted penalty, which is due at ruin and may depend on the deficit at ruin and on the surplus immediately before ruin. The expected discounted penalty, considered as a function of the initial surplus, satisfies a certain renewal equation, which has a probabilistic interpretation. Explicit answers are obtained for zero initial surplus, very large initial surplus, and arbitrary initial surplus if the claim amount distribution is exponential or a mixture of exponentials. We generalize Dickson’s formula, which expresses the joint distribution of the surplus immediately prior to and at ruin in terms of the probability of ult...

On the Time Value of Ruin

Supplying a collection of mathematical formulas and numerical tables, this text covers elementary concepts in algebra, geometry and more advanced concepts in differential equations and vector analysis.

Mathematical Handbook of Formulas and Tables

This "Schaum's Study Guide" is the perfect tool for getting a handle on statistics. Fully stocked with solved problems 508 of them it shows you how to work problems that may not have been fully explained in class. Plus you get 694 additional problems to use for practice, with answers at the back of the book. Ideal for independent study, brushup before exams, or preparation for professional tests, this "Schaum's" guide is clear, complete, and well-organized. It even prepares you for computer solutions of statistical problems, fully explaining the use of Minitab, the most popular statistical software. It's the perfect supplement for any course in statistics, and a super helper for the math-challenged.

Schaum's Outline of Theory and Problems of Statistics

Theory and problems of statistics ....

Part I: Probability Chapter 1: Basic Probability Chapter 2: Random Variables and Probability Distributions Chapter 3: Mathematical Expectation Chapter 4: Special Probability Distributions Part II: Statistics Chapter 5: Sampling Theory Chapter 6: Estimation Theory Chapter 7: Tests of Hypotheses and Significance Chapter 8: Curve Fitting, Regression, and Correlation Chapter 9: Analysis of Variance Chapter 10: Nonparametric Tests Appendices Index Index for Solved Problems

Schaum's Outline of Theory and Problems of Probability and Statistics

The Laplace Transform. The Inverse Laplace Transform. Applications to Differential Equations. Applications to Integral and Difference Equations. Complex Variable Theory. Fourier Series and Integrals. The Complex Inversion Formula. Applications to Boundary-Value Problems. Appendix A: Table of General Properties of Laplace Transforms. Appendix B: Table of Special Laplace Transforms. Appendix C: Table of Special Functions.

Murray R. Spiegel

Papers

Mathematical Handbook of Formulas and Tables

Schaum's Outline of Theory and Problems of Statistics

Theory and problems of statistics ....

Schaum's Outline of Theory and Problems of Probability and Statistics

Schaum's outline of theory and problems of laplace transforms