Synopsis
A bridge between non-Gaussian models and Gaussian behavior
This work presents an infinite family of random processes that share the same correlation function, yet are non-Gaussian for most values of a key parameter. The construction starts from a shot-noise (Poisson) process and builds a stationary, random step function whose features can be calculated in principle. As the parameter grows, the processes gradually resemble a Gaussian process with the same power spectrum, highlighting the limits of using only second-order statistics to characterize randomness.
The approach lets you see how higher-order statistics matter in practice and how a single spectrum can correspond to many different stochastic behaviors. By specifying shot timings and rectangular shot shapes, the author shows how to derive univariate and multivariate distributions, and how sample functions look under different shot-density regimes. The results are grounded in a familiar method, yet give a complete, theory-backed view of a clearly non-Gaussian family that transitions toward Gaussianity.- Learn how a stationary shot-noise construction yields an isospectral family of processes
- See the relationship between correlation functions, power spectra, and higher-order statistics
- Discover how non-Gaussian models converge to Gaussian behavior as a parameter changes
- Explore visual examples illustrating low, medium, and high shot-density cases
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An Isospectral Family of Random Processes: January, 1960 (Classic Reprint)
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Paperback. Condition: New. Print on Demand. This book explores the concept of creating a family of non-Gaussian random step functions, all sharing the same power spectrum, that converge to the Gaussian process with the same spectrum as the number of members in the family becomes very large. The author illustrates how to calculate the multivariate distribution of processes and shows how a constructed univariate entropy can serve as an indicator of the extent to which the family has approached the Gaussian limit. The author's findings give insight into the inadequacy of correlation functions and power spectra as a means of characterizing random processes and emphasize the need for higher-order statistics. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Seller Inventory # 9781332145607_0
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An Isospectral Family of Random Processes January, 1960 Classic Reprint
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An Isospectral Family of Random Processes: January, 1960 (Classic Reprint)
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Condition: Used - Very Good. VG paperback. Scanned digital reprint of Research Report EM-151 (1960, NYU). Minor crease at corner of front cover Used - Very Good. VG paperback. Seller Inventory # BOOKS337459I
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An Isospectral Family of Random Processes January, 1960 Classic Reprint
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