Spectrum Data Analysis and Probability


Book Description

With the help of Spectrum(R) Data Analysis and Probability for grades 6 to 8, children develop problem-solving math skills they can build on. This standards-based workbook focuses on middle school concepts like operations, ratios, probability, graph interpretation, and more. --Middle school is known for its challengesÑlet Spectrum(R) ease some stress. Developed by education experts, the Spectrum(R) Middle School Math series strengthens the important home-to-school connection and prepares children for math success. Filled with easy instructions and rigorous practice, Spectrum(R) Data Analysis and Probability helps children soar in a standards-based classroom!




Spectrum Data Analysis and Probability


Book Description

With the help of Spectrum Data Analysis and Probability for grades 6 to 8, children develop problem-solving math skills they can build on. This standards-based workbook focuses on middle school concepts like operations, ratios, probability, graph interpretation, and more. Middle school is known for its challenges—let Spectrum ease some stress. Developed by education experts, the Spectrum Middle School Math series strengthens the important home-to-school connection and prepares children for math success. Filled with easy instructions and rigorous practice, Spectrum Data Analysis and Probability helps children soar in a standards-based classroom!




Data Analysis and Probability, Grades 6 - 8


Book Description

Spectrum Data Analysis and Probability Grades 6-8 helps young learners improve and strengthen their math skills, such as ratios, graph interpretation, and measures of central tendency. The best-selling SpectrumT series provides standards-based exercises developed to supplement and solidify the skills students learn in school. Each full-color title includes an answer key.




The Spectral Analysis of Time Series


Book Description

The Spectral Analysis of Time Series describes the techniques and theory of the frequency domain analysis of time series. The book discusses the physical processes and the basic features of models of time series. The central feature of all models is the existence of a spectrum by which the time series is decomposed into a linear combination of sines and cosines. The investigator can used Fourier decompositions or other kinds of spectrals in time series analysis. The text explains the Wiener theory of spectral analysis, the spectral representation for weakly stationary stochastic processes, and the real spectral representation. The book also discusses sampling, aliasing, discrete-time models, linear filters that have general properties with applications to continuous-time processes, and the applications of multivariate spectral models. The text describes finite parameter models, the distribution theory of spectral estimates with applications to statistical inference, as well as sampling properties of spectral estimates, experimental design, and spectral computations. The book is intended either as a textbook or for individual reading for one-semester or two-quarter course for students of time series analysis users. It is also suitable for mathematicians or professors of calculus, statistics, and advanced mathematics.




Bayesian Spectrum Analysis and Parameter Estimation


Book Description

This work is essentially an extensive revision of my Ph.D. dissertation, [1J. It 1S primarily a research document on the application of probability theory to the parameter estimation problem. The people who will be interested in this material are physicists, economists, and engineers who have to deal with data on a daily basis; consequently, we have included a great deal of introductory and tutorial material. Any person with the equivalent of the mathematics background required for the graduate level study of physics should be able to follow the material contained in this book, though not without eIfort. From the time the dissertation was written until now (approximately one year) our understanding of the parameter estimation problem has changed extensively. We have tried to incorporate what we have learned into this book. I am indebted to a number of people who have aided me in preparing this docu ment: Dr. C. Ray Smith, Steve Finney, Juana Sunchez, Matthew Self, and Dr. Pat Gibbons who acted as readers and editors. In addition, I must extend my deepest thanks to Dr. Joseph Ackerman for his support during the time this manuscript was being prepared.




Information-Spectrum Methods in Information Theory


Book Description

From the reviews: "This book nicely complements the existing literature on information and coding theory by concentrating on arbitrary nonstationary and/or nonergodic sources and channels with arbitrarily large alphabets. Even with such generality the authors have managed to successfully reach a highly unconventional but very fertile exposition rendering new insights into many problems." -- MATHEMATICAL REVIEWS




Probability, Statistical Optics, and Data Testing


Book Description

A basic skill in probability is practically demanded nowadays in many bran ches of optics, especially in image science. On the other hand, there is no text presently available that develops probability, and its companion fields stochastic processes and statistics, from the optical perspective. [Short of a book, a chapter was recently written for this purpose; see B. R. Frieden (ed. ): The Computer in Optical Research, Topics in Applied Physics, Vol. 41 (Springer, Berlin, Heidelberg, New York 1980) Chap. 3] Most standard texts either use illustrative examples and problems from electrical engineering or from the life sciences. The present book is meant to remedy this situation, by teaching probability with the specific needs of the optical researcher in mind. Virtually all the illustrative examples and applications of the theory are from image science and other fields of optics. One might say that photons have replaced electrons in nearly all considera tions here. We hope, in this manner, to make the learning of probability a pleasant and absorbing experience for optical workers. Some of the remaining applications are from information theory, a con cept which complements image science in particular. As will be seen, there are numerous tie-ins between the two concepts. Students will be adequately prepared for the material in this book if they have had a course in calculus, and know the basics of matrix manipulation.




The Spectral Analysis of Time Series


Book Description

To tailor time series models to a particular physical problem and to follow the working of various techniques for processing and analyzing data, one must understand the basic theory of spectral (frequency domain) analysis of time series. This classic book provides an introduction to the techniques and theories of spectral analysis of time series. In a discursive style, and with minimal dependence on mathematics, the book presents the geometric structure of spectral analysis. This approach makes possible useful, intuitive interpretations of important time series parameters and provides a unified framework for an otherwise scattered collection of seemingly isolated results.The books strength lies in its applicability to the needs of readers from many disciplines with varying backgrounds in mathematics. It provides a solid foundation in spectral analysis for fields that include statistics, signal process engineering, economics, geophysics, physics, and geology. Appendices provide details and proofs for those who are advanced in math. Theories are followed by examples and applications over a wide range of topics such as meteorology, seismology, and telecommunications.Topics covered include Hilbert spaces; univariate models for spectral analysis; multivariate spectral models; sampling, aliasing, and discrete-time models; real-time filtering; digital filters; linear filters; distribution theory; sampling properties ofspectral estimates; and linear prediction. - Hilbert spaces - univariate models for spectral analysis - multivariate spectral models - sampling, aliasing, and discrete-time models - real-time filtering - digital filters - linear filters - distribution theory - sampling properties of spectral estimates - linear prediction




Spectrum Grade 6


Book Description

Spectrum(R) Grade Specific for Grade 6 includes focused practice for reading, language arts, and math mastery. Skills include grammar and usage, parts of speech and sentence types, vocabulary acquisition and usage, multiplying and dividing fractions and decimals, equations and inequalities, problem solving in the coordinate plane, probability and statistics, and ratios, rates, and percents. --Each Spectrum(R) Grade Specific workbook includes a writer's guide and step-by-step instructions, helping children with planning, drafting, revising, proofreading, and sharing writing. Children in grades 1 to 6 will find lessons and exercises that help them progress through increasingly difficult subject matter. Aligned to current state standards, Spectrum is your childÕs path to language arts and math mastery.




Random Data


Book Description

RANDOM DATA A TIMELY UPDATE OF THE CLASSIC BOOK ON THE THEORY AND APPLICATION OF RANDOM DATA ANALYSIS First published in 1971, Random Data served as an authoritative book on the analysis of experimental physical data for engineering and scientific applications. This Fourth Edition features coverage of new developments in random data management and analysis procedures that are applicable to a broad range of applied fields, from the aerospace and automotive industries to oceanographic and biomedical research. This new edition continues to maintain a balance of classic theory and novel techniques. The authors expand on the treatment of random data analysis theory, including derivations of key relationships in probability and random process theory. The book remains unique in its practical treatment of nonstationary data analysis and nonlinear system analysis, presenting the latest techniques on modern data acquisition, storage, conversion, and qualification of random data prior to its digital analysis. The Fourth Edition also includes: A new chapter on frequency domain techniques to model and identify nonlinear systems from measured input/output random data New material on the analysis of multiple-input/single-output linear models The latest recommended methods for data acquisition and processing of random data Important mathematical formulas to design experiments and evaluate results of random data analysis and measurement procedures Answers to the problem in each chapter Comprehensive and self-contained, Random Data, Fourth Edition is an indispensible book for courses on random data analysis theory and applications at the upper-under-graduate and graduate level. It is also an insightful reference for engineers and scientists who use statistical methods to investigate and solve problems with dynamic data.