A unified theory of information

"February 1, 1956." "This report is indentical with a thesis submitted to the Department of Electrical Engineering, M.I.T., 1956, in partial fulfillment of the requirements for the degree of Doctor of Science."Bibliography: p. 104-105.Army Signal Corps Contract DA36-039-sc-42607 Project 102B Dept. of the Army Project 3-99-10-022Kerns H. Powers

Two Dimensional Signal Representation Using Prolate Spheroidal Functions

The most widely used methods of signal representation are the time function and the frequency function or spectrum representations. This work is concerned with the development of a representation which is a combination of these two. Two previous attempts at defining this type of signal representation, which is referred to as two dimensional representation, have been made and a summary and evaluation of these attempts is presented. The primary objective of the work reported here was to develop a practical two dimensional representation which has the desired two dimensional conceptual properties as well as mathematical convenience. The representations defined are based on the angular prolate spheroidal functions. These functions have a number of desirable properties among which are the followings they are orthogonal over both a finite and the infinite interval, they are bandlimited, and they have certain properties concerning their maximal proximity to being timelimited. The procedure used in defining the first two dimensional representation is to make an orthogonal expansion, using the prolate spheroidal functions, of each timelimited portion of each bandlimited portion of the signal to be represented. The second two dimensional representation is defined from an orthogonal expansion of each bandlimited portion of each timelimited portion of the signal to be represented. For both of these, the summation over all time intervals and all frequency intervals results in the complete representation of the signal. It is seen from this that since it is not possible to timelimit and bandlimit simultaneously, these limiting processes have been carried out serially. Due to the peculiar properties of the prolate spheroidal functions, as the number of orthogonal function terms is increased, the representation of a timelimited function converges first in a certain bandwidth, and the representation of a band- limited function converges first in a certain time interval. It is demonstrated that both series representations will converge to either a timelimited, or a bandlimited portion of the represented signal upon inclusion of the proper terms. Following this, several applications of the representations are presented. First, it is shown that the result of the convolution of 2 two dimensionally represented functions may be determined at discrete values of time from the expansion coefficients alone. The spectrum of the product of two functions may be determined in a similar manner at discrete values of frequency. As a result, it is possible to determine the contribution made to the output of a linear system at any time due to the portion of the input in any time and frequency interval. A technique is also developed for the solution of this same problem for the more general time variable linear system with the output being determined in continuous form rather than only at discrete values. It is somewhat more difficult to calculate the coefficients in this case, however. Another application demonstrated is a method by which the value of Woodward\u27s ambiguity function may be calculated for discrete values of the time and frequency variables. The two dimensional nature of the representation is demonstrated by two numerical examples using very elementary time functions. A further numerical example is provided for the case of the determination of the output of a linear system at discrete values of time. This work is concluded by a brief listing of further problems which seem amenable to solution as a result of this type of analysis. This list includes such problems as biological system signal analysis, signal design, and random process representation

Application of the Wigner distribution to monitoring cutting tool condition

This thesis is about the application of the Wigner distribution to cutting tool monitoring and control. After reviewing traditional methods, a new method is proposed. This is to regard the surface texture and geometric error of form of a machined workpiece as the fingerprint of a cutting process, to analyse it, and to extract cutting tool vibration information from it, which can then be used for cutting tool monitoring. In order to analyse the surface texture effectively, three analysing tools, i.e. the Fourier transform, the ambiguity function, the Wigner distribution (WD), are examined and compared with each other, and it is concluded that the WD is best able to analyse both stationary and nonstationary signals. Furthermore, computer simulation of both chirp signals and frequency modulated signals is then carried out, and it is shown that the WD can be used to extract useful parameters successively. In order to demonstrate the suitability of the WD for machine tool condi- tion monitoring, first cutting tool vibration are measured directly by two linear variable differential transformers mounted on the cutting tool, and then these measured data about vibration are used to verify those parameters extracted from the surface of the machined workpiece by the WD. It is found that • the extracted frequencies in both horizontal and vertical direction are within 10% of those measured, • the extracted amplitudes in both horizontal and vertical direction are highly correlated with those measured. This result confirms the feasibility of this technique. In spite of being an off-line process, this technique is simple, reliable, and can reveal the direct effect of cutting processes

Effects of turbulence on aerofoils at high incidence

Imperial Users onl

Advances in numerical and applied mathematics

This collection of papers covers some recent developments in numerical analysis and computational fluid dynamics. Some of these studies are of a fundamental nature. They address basic issues such as intermediate boundary conditions for approximate factorization schemes, existence and uniqueness of steady states for time dependent problems, and pitfalls of implicit time stepping. The other studies deal with modern numerical methods such as total variation diminishing schemes, higher order variants of vortex and particle methods, spectral multidomain techniques, and front tracking techniques. There is also a paper on adaptive grids. The fluid dynamics papers treat the classical problems of imcompressible flows in helically coiled pipes, vortex breakdown, and transonic flows

Abstracts on Radio Direction Finding (1899 - 1995)

The files on this record represent the various databases that originally composed the CD-ROM issue of "Abstracts on Radio Direction Finding" database, which is now part of the Dudley Knox Library's Abstracts and Selected Full Text Documents on Radio Direction Finding (1899 - 1995) Collection. (See Calhoun record https://calhoun.nps.edu/handle/10945/57364 for further information on this collection and the bibliography). Due to issues of technological obsolescence preventing current and future audiences from accessing the bibliography, DKL exported and converted into the three files on this record the various databases contained in the CD-ROM. The contents of these files are: 1) RDFA_CompleteBibliography_xls.zip [RDFA_CompleteBibliography.xls: Metadata for the complete bibliography, in Excel 97-2003 Workbook format; RDFA_Glossary.xls: Glossary of terms, in Excel 97-2003 Workbookformat; RDFA_Biographies.xls: Biographies of leading figures, in Excel 97-2003 Workbook format]; 2) RDFA_CompleteBibliography_csv.zip [RDFA_CompleteBibliography.TXT: Metadata for the complete bibliography, in CSV format; RDFA_Glossary.TXT: Glossary of terms, in CSV format; RDFA_Biographies.TXT: Biographies of leading figures, in CSV format]; 3) RDFA_CompleteBibliography.pdf: A human readable display of the bibliographic data, as a means of double-checking any possible deviations due to conversion

Annual Report of the Board of Regents of the Smithsonian Institution, showing the operations, expenditures, and condition of the Institution to July, 1885

Annual Report of the Smithsonian Institution. 17 July. HMD 15 (pts. 1 and 2) , 49-1. v25-26, 2235p. [2431-2432] Research related to the American India