(1970). A Computer Movie Simulating Urban Growth in the Detroit Region. Economic Geography: Vol. 46, PROCEEDINGS International Geographical Union Commission on Quantitative Methods, pp. 234-240.

https://www.jstor.org/stable/pdfplus/143141.pdf

A Computer Movie Simulating Urban Growth in the Detroit Region

This paper gives an exposition of linear prediction in the analysis of discrete signals The signal is modeled as a linear combination of its past values and present and past values of a hypothetical input to a system whose output is the given signal In the frequency domain, this is equivalent to modeling the signal spectrum by a pole-zero spectrum The major part of the paper is devoted to all-pole models The model parameters are obtained by a least squares analysis in the time domain Two methods result, depending on whether the signal is assumed to be stationary or nonstationary The same results are then derived in the frequency domain The resulting spectral matching formulation allows for the modeling of selected portions of a spectrum, for arbitrary spectral shaping in the frequency domain, and for the modeling of continuous as well as discrete spectra This also leads to a discussion of the advantages and disadvantages of the least squares error criterion A spectral interpretation is given to the normalized minimum prediction error Applications of the normalized error are given, including the determination of an "optimal" number of poles The use of linear prediction in data compression is reviewed For purposes of transmission, particular attention is given to the quantization and encoding of the reflection (or partial correlation) coefficients Finally, a brief introduction to pole-zero modeling is given

Linear prediction: A tutorial review

In the choice of an estimator for the spectrum of a stationary time series from a finite sample of the process, the problems of bias control and consistency, or "smoothing," are dominant. In this paper we present a new method based on a "local" eigenexpansion to estimate the spectrum in terms of the solution of an integral equation. Computationally this method is equivalent to using the weishted average of a series of direct-spectrum estimates based on orthogonal data windows (discrete prolate spheroidal sequences) to treat both the bias and smoothing problems. Some of the attractive features of this estimate are: there are no arbitrary windows; it is a small sample theory; it is consistent; it provides an analysis-of-variance test for line components; and it has high resolution. We also show relations of this estimate to maximum-likelihood estimates, show that the estimation capacity of the estimate is high, and show applications to coherence and polyspectrum estimates.

Spectrum estimation and harmonic analysis

A summary of many of the new techniques developed in the last two decades for spectrum analysis of discrete time series is presented in this tutorial. An examination of the underlying time series model assumed by each technique serves as the common basis for understanding the differences among the various spectrum analysis approaches. Techniques discussed include the classical periodogram, classical Blackman-Tukey, autoregressive (maximum entropy), moving average, autotegressive-moving average, maximum likelihood, Prony, and Pisarenko methods. A summary table in the text provides a concise overview for all methods, including key references and appropriate equations for computation of each spectral estimate.

Spectrum analysis&#8212;A modern perspective

1. Introduction to wavelets 2. Review of Fourier theory and filters 3. Orthonormal transforms of time series 4. The discrete wavelet transform 5. The maximal overlap discrete wavelet transform 6. The discrete wavelet packet transform 7. Random variables and stochastic processes 8. The wavelet variance 9. Analysis and synthesis of long memory processes 10. Wavelet-based signal estimation 11. Wavelet analysis of finite energy signals Appendix. Answers to embedded exercises References Author index Subject index.

/pdf/wavelet-methods-for-time-series-analysis-1m2hg2nm53.pdf

Wavelet Methods for Time Series Analysis

/pdf/statistical-spectral-analysis-a-nonprobabilistic-theory-4p5r6cdblq.pdf

Statistical Spectral Analysis—A Nonprobabilistic Theory

“This text, an introduction to geophysical signal analysis, is concerned with the construction, analysis, and interpretation of mathematical and statistical models. In general, it is intended to provide material of interest to upper undergraduate students in mathematics, science, and engineering. Much of this book requires only a knowledge of elementary algebra. However, at some points, a familiarity with elementary calculus and matrix algebra is needed. The practical use of the concepts and techniques developed is illustrated by numerous applications. Care has been taken to choose examples that are of interest to a variety of readers. Therefore, the book contains material of interest to both geophysicists and those engaged in digital signal analysis in disciplines other than geophysics. This book is a reprint of the 1980 Prentice-Hall volume of the same title.”

Geophysical Signal Analysis

In exploration seismology, a charge of dynamite is exploded under controlled conditions, and the resulting vibrations at various points on the surface of the ground are detected by geophones and are recorded as seismic traces on the seismogram. The analysis of such seismic records yields valuable information about the structure of the sedimentary rock layers in potential oil producing areas, and such information is of considerable economic value in increasing the probability of locating new oil fields.

Predictive decomposition of time series with application to seismic exploration

(1969). Multichannel Time Series Analysis with Digital Computer Programs. Technometrics: Vol. 11, No. 2, pp. 408-409.

Multichannel Time Series Analysis With Digital Computer Programs

The generalized harmonic analysis, or spectral decomposition, of a time series results in its representation in terms of its harmonic, or sinusoidal, components. This paper, on the other hand, develops in an expository manner the generalized regression analysis, or predictive decomposition, of a time series. This decomposition results in the representation of the time series at any moment in terms of its own observable past history plus an unpredictable, random‐like innovation. For the purposes of this paper, it is assumed that a seismic trace (recorded with automatic volume control) is additively composed of many overlapping seismic wavelets which arrive as time progresses. It is assumed that each wavelet has the same stable, one‐sided, minimum‐phase shape and that the arrival times and strengths of these wavelets may be represented by a time sequence of uncorrelated random variables. By applying the predictive decomposition theorem, it is shown how the wavelet shape may be extracted from the trace, leav...

Enders A. Robinson

Papers

Statistical Spectral Analysis—A Nonprobabilistic Theory

Geophysical Signal Analysis

Predictive decomposition of time series with application to seismic exploration

Multichannel Time Series Analysis With Digital Computer Programs

Predictive decomposition of seismic traces