G. Longo - Böcker

The morphological scheme devised by Hubble and followers to classify galaxies has, over many decades, proved to be quite effective in directing the quest for the fundamental parameters describing the extragalactic manifold. This statement, however, is far more true for spirals than for ellipticals. In the last few years efforts have been made to search for a more meaningful classification of ellipticals, at the same time the classical question of whether E galaxies form a physically homogenous family has been brushed up once more. This book pictures the transition process from the morphological to the physical "era' in the classification of galaxies.

The concept of time and frequency representation of signal dates back to the first notation for music: a sequence of notes to be played in time, s(t), each note being associated with a fundamental frequency and its higher harmonics. From a mathematical viewpoint we can associate the time function s(t) to its Fourier transform S(f). However, S(f) is independent of time and gives no indication as to the note to be played at each particular time instant. It would therefore be useful to introduce a representation of signals simultaneously in time and frequency. This is the aim of this book.

The general problem studied by information theory is the reliable transmission of information through unreliable channels. Channels can be unreliable either because they are disturbed by noise or because unauthorized receivers intercept the information transmitted. In the first case, the theory of error-control codes provides techniques for correcting at least part of the errors caused by noise. In the second case cryptography offers the most suitable methods for coping with the many problems linked with secrecy and authentication. Now, both error-control and cryptography schemes can be studied, to a large extent, by suitable geometric models, belonging to the important field of finite geometries. This book provides an updated survey of the state of the art of finite geometries and their applications to channel coding against noise and deliberate tampering. The book is divided into two sections, "Geometries and Codes" and "Geometries and Cryptography". The first part covers such topics as Galois geometries, Steiner systems, circle geometry and applications to algebraic coding theory.This volume recommends itself to engineers dealing with communication problems, to mathematicians and to research workers in the fields of algebraic coding theory, cryptography and information theory.

The four chapters of this volume, written by prominent workers in the field of adaptive processing and linear prediction, address a variety of problems, ranging from adaptive source coding to autoregressive spectral estimation. The first chapter, by T.C. Butash and L.D. Davisson, formulates the performance of an adaptive linear predictor in a series of theorems, with and without the Gaussian assumption, under the hypothesis that its coefficients are derived from either the (single) observation sequence to be predicted (dependent case) or a second, statistically independent realisation (independent case). The contribution by H.V. Poor reviews three recently developed general methodologies for designing signal predictors under nonclassical operating conditions, namely the robust predictor, the high-speed Levinson modeling, and the approximate conditional mean nonlinear predictor. W. Wax presents the key concepts and techniques for detecting, localizing and beamforming multiple narrowband sources by passive sensor arrays. Special coding algorithms and techniques based on the use of linear prediction now permit high-quality voice reproduction at remorably low bit rates. The paper by A. Gersho reviews some of the main ideas underlying the algorithms of major interest today.

The morphological scheme devised by Hubble and followers to classify galaxies has proven over many decades to be quite effective in directing our quest for the fundamental pa­ rameters describing the extragalactic manifold. This statement is however far more true for spirals than for ellipticals. Echoing the concluding remarks in Scott Tremaine's sum­ mary talk at the Princeton meeting on Structure and Dynamics of Elliptical Galaxies, "the Hubble classification of spirals is useful because many properties of spirals (gas con­ tent, spiral arm morphology, bulge prominence, etc. ) all correlate with Hubble time. By contrast, almost nothing correlates with the elliptical Hubble sequence El to E7. " During the last few years much effort has been put into the search for a more meaningful classification of ellipticals than Hubble's. Concomitantly, forwarded by some provocative conjectures by R. Michard, the classical question of whether E galaxies form a physically homogeneous family has been brushed up once more. Results of these and other parallel studies look rather promising and point to suture part of the dichotomy between ellipticals and disk galaxies which had become popular in the early eighties, owing to dynamical arguments. At the same time it appears more and more clear that, besides the usual genetic varieties of galaxies, products of environmental evolution must also be contemplated in building our modern picture of the "reign of galaxies" . The above considerations prompted us to solicit Prof.