Showing papers in "IEEE Assp Magazine in 1987"

An introduction to computing with neural nets

Abstract: Artificial neural net models have been studied for many years in the hope of achieving human-like performance in the fields of speech and image recognition. These models are composed of many nonlinear computational elements operating in parallel and arranged in patterns reminiscent of biological neural nets. Computational elements or nodes are connected via weights that are typically adapted during use to improve performance. There has been a recent resurgence in the field of artificial neural nets caused by new net topologies and algorithms, analog VLSI implementation techniques, and the belief that massive parallelism is essential for high performance speech and image recognition. This paper provides an introduction to the field of artificial neural nets by reviewing six important neural net models that can be used for pattern classification. These nets are highly parallel building blocks that illustrate neural net components and design principles and can be used to construct more complex systems. In addition to describing these nets, a major emphasis is placed on exploring how some existing classification and clustering algorithms can be performed using simple neuron-like components. Single-layer nets can implement algorithms required by Gaussian maximum-likelihood classifiers and optimum minimum-error classifiers for binary patterns corrupted by noise. More generally, the decision regions required by any classification algorithm can be generated in a straightforward manner by three-layer feed-forward nets.

Quadrature mirror filter banks, M-band extensions and perfect-reconstruction techniques

Abstract: In this paper, quadrature mirror filters (QMF) are reviewed. After a brief introduction to multirate building blocks, the two-band QMF bank is discussed. Various distortions caused by the structure, and methods to eliminate these distortions are outlined. Perfect-reconstruction structures for the two-band case are reviewed, and the results are extended to the case of arbitrary number of channels. The relation between perfect-reconstruction QMF banks and the concept of losslessness in transfers-matrices is indicated. New lattice structures are presented, which perform the perfect reconstruction, sometimes even under coefficient quantization.

An inverse scattering framework for several problems in signal processing

Abstract: The aim of this paper is to show that a general inverse scattering formulation illuminates alternative, computationally efficient solution methods for several classes of signal processing problems. Inverse scattering problems arise in physics, transmission-line synthesis, geophysics and acoustics and in one class of formulations they require a procedure to determine the parameters of a layered wave propagation medium from measurements taken at the boundary. There exists a close relationship between the physical inverse scattering problems and some important issues in signal processing such as the design of digital filters, the development of linear prediction algorithms and their lattice filter implementations and cascade synthesis of systems with a given impulse response (realization problems). For many of these problems several efficient algorithms already exist in the literature, but the connection between the different solutions was not always clear. Recently, the push to VLSI implementations led to the realization that, in spite of their apparent similarity, the alternative algorithms possess radically different properties when, say, a parallel implementation is sought. In this paper we shall show that alternative procedures that are usually arrived at by various clever tricks, in fact correpond to two conceptually extremely simple, basic ways of solving inverse scattering problems: the so called "layer-peeling" and "layer-adjoining" methods. Examples include the Schur vs Levinson methods for determining the optimal filters for prediction of stationary stochastic processes, and the generalized Lanczos vs Berlekamp-Massey methods for the partial realization (Pade approximation) problem, and also several recent design procedures for some classes of digital filters.

Einstein's 1914 paper on the theory of irregularly fluctuating series of observations

Abstract: The author makes various observations on Albert Einstein's short note of 1914 ["Method for the determination of the statistical values of observations concerning quantities subject to irregular fluctuations," Arch. Sci. Phys. et Natur., 37, ser. 4, 254-56 (1914)] on methods of reducing fluctuating series of observations. He argues that it foreshadows the theory behind the Fast Fourier Transform (FFT). The paper seems not to have attracted much attention when it was given, and was soon nearly forgotten. In any case, the present author has found no reference to it, either in a bulky index of literature on the theory of time series or in the tens of monographs, symposia and detailed reviews on this topic that he has examined. Only in 1979, in connection with the worldwide observance of the Einstein centenary, did the East German H. Melcher draw attention to the existence of the little-known paper (without discussing its content).

Method for the determinination of the statistical values of observations concerning quantities subject to irregular fluctuations

Abstract: Albert Einstein introduces the concepts of the autocorrelation and cross-correlation functions and proves that automatic instruments can be devised for their experimental determination. However, the main point of the paper is that he introduces the concept of a power spectrum (without the use of this term, which - like "correlation function" and "stationary"- do not appear until much later) and elucidates its physical meaning. He also indicates two possible ways of calculating such spectra from experimental data. The stress Einstein laid on the importance of the spectrum of power (of "intensity," as he called it) of fluctuating time series F(t) shows a striking physical intuition since no applications existed for this concept in 1914.

Introduction to Einstein's contribution to time-series analysis

Abstract: HE HISTORY of ideas evolves endlessly, sometimes becoming more accurate with the passage of time, sometimes more distorted. This is so even for ideas originating as recently as 100 years ago. In spite of the documentation provided by published books and papers, personal letters, and recollections, historians are inevitably limited by the substantial loss of information with the passing of participants and by the unavoidable subjectivityof the historians’ own interpretations of the available information. The recent discovery of a long forgotten early paper by Albert Einstein on the topic of time-series analysis [I] provides an interesting example of the evolutionary process of tracing the history of ideas. This very brief paper, entitled ”Method for the determination of the statistical values of observations concerning quantities subject to irregular fluctuations,’’ was originally published in the Archives des Sciences Physiques et Naturelles in 1914 following an oral presentation at a meeting of the Swiss Physical Society earlier that year. An English translation of this paper is reproduced in this issue of the ASSP Magazine. The paper discusses the autocorrelation function and its relationship to the spectral content of a time-series, the crosscorrelation function as a measure of interdependence of two time-series, and two methods for measurementor computation of spectral content: the frequency-smoothed periodogram method and the Fourier-transformed autocorrelation method. Two experts in the field of time-series analysis, Professor A. M. Yaglom from the Instituteof Atmospheric Physics, Academy of Sciences of the USSR, and Professor P. R. Masani from the Department of Mathematics, University of Pittsburgh, have written extensive commentaries on this paper and its place in the history of time-series analysis [2], [3]. The differences in the backgrounds and points of view of this physicist and this mathematician have led to some interesting differences in their interpretations of Einstein‘s accomplishments in his paper.