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The application of various orthogonal transformations to communication was investigated, with particular emphasis placed on speech and visual signal processing. The fundamentals of the one- and two-dimensional orthogonal transforms and their application to speech and visual signals are treated in detail.
The design of the most efficient toroidal transformer that can be built given the frequency, volt-ampere rating, magnetic flux density, window fill factor, and materials is described. With the above all held constant and only the dimensions of the magnetic core varied, the most efficient design occurs when the copper losses equal 60 percent of the iron losses. When this criterion is followed, efficiency is only slightly dependent on design frequency and fill factor. The ratios of inside diameter to outside diameter and height to build of the magnetic core that result in transformers of maximum efficiency are computed.
Estimates of temperature, weight, efficiency, regulation, and final dimensions are included in the output of the computer program for the design of transformers for use in the basic parallel inverter. The program, written in FORTRAN 4, selects a tape wound toroidal magnetic core and, taking temperature, materials, core geometry, skin depth, and ohmic losses into account, chooses the appropriate wire sizes and number of turns for the center tapped primary and single secondary coils. Using the program, 2- and 4-kilovolt-ampere transformers are designed for frequencies from 200 to 3200 Hz and the efficiency of a basic transistor inverter is estimated.
Basic formulations for developing coordinate transformations and motion equations used with free-flight and wind-tunnel data reduction are presented. The general forms presented include axes transformations that enable transfer back and forth between any of the five axes systems that are encountered in aerodynamic analysis. Equations of motion are presented that enable calculation of motions anywhere in the vicinity of the earth. A bibliography of publications on methods of analyzing flight data is included.
Discrete forms of the Fourier, Hadamard, and Karhunen-Loeve transforms are examined for their capacity to reduce the bit rate necessary to transmit speech signals. To rate their effectiveness in accomplishing this goal the quantizing error (or noise) resulting for each transformation method at various bit rates is computed and compared with that for conventional companded PCM processing. Based on this comparison, it is found that Karhunen-Loeve provides a reduction in bit rate of 13.5 kbits/s, Fourier 10 kbits/s, and Hadamard 7.5 kbits/s as compared with the bit rate required for companded PCM. These bit-rate reductions are shown to be somewhat independent of the transmission bit rate.
This paper develops performance criteria for evaluating transform data coding schemes under computational constraints. Computational constraints that conform with the proposed basis-restricted model give rise to suboptimal coding efficiency characterized by a rate-distortion relation R(D) similar in form to the theoretical rate-distortion function. Numerical examples of this performance measure are presented for Fourier, Walsh, Haar, and Karhunen-Loeve transforms.
Report is announced which studied magnetic properties of candidate materials for use in spacecraft transformers, static inverters, converters, and transformer-rectifier power supplies. Included are material characteristics for available alloy compositions in tabular form, including: trade names, saturated flux density, dc coercive force, loop squareness, material density, and watts per pound at 3 KHz.
The employment of a high-resolution Fourier Transform Spectrometer (FTS) is described for planetary and other astronomical spectroscopy in conjunction with the 88-inch telescope at Mauna Kea Observatory. The FTS system is designed for a broad range of uses, including double-beam laboratory spectroscopy, infrared gas chromatography, and nuclear magnetic resonance spectroscopy. The data system is well-suited to astronomical applications because of its great speed in acquiring and transforming data, and because of the enormous storage capability of the magnetic tape unit supplied with the system. The basic instrument is outlined 2nd some of the initial results from the first attempted use on the Mauna Kea 88-inch telescope are reported.
This investigation was to determine the transformation parameters (three rotations, three translations and a scale factor) between two Cartesian coordinate systems from sets of coordinates given in both systems. The objective was the determination of well separated transformation parameters with reduced correlations between each other, a problem especially relevant when the sets of coordinates are not well distributed. The above objective is achieved by preliminarily determining the three rotational parameters and the scale factor from the respective direction cosines and chord distances (these being independent of the translation parameters) between the common points, and then computing all the seven parameters from a solution in which the rotations and the scale factor are entered as weighted constraints according to their variances and covariances obtained in the preliminary solutions. Numerical tests involving two geodetic reference systems were performed to evaluate the effectiveness of this approach.
The protection of composite turbine fan blades against impact forces has prompted the study of dynamic stresses in composites due to transient loads. The mathematical model treats the laminated plate as an equivalent anisotropic material. The use of Mindlin's approximate theory of crystal plates results in five two-dimensional stress waves. Three of the waves are flexural and two involve in-plane extensional strains. The initial value problem due to a transient distributed transverse force on the plate is solved using Laplace and Fourier transforms. A fast computer program for inverting the two-dimensional Fourier transform is used. Stress contours for various stresses and times after application of load are obtained for a graphite fiber-epoxy matrix composite plate. Results indicate that the points of maximum stress travel along the fiber directions.
Complex digital computer is not required, only summing amplifiers and attenuators are used for transformation of signal. Continuous transform system may be used for spectrum analysis, filtering, transfer function synthesis, and communications.
A Hadamard-transform spectrometer was used to obtain a spectrum of Jupiter from 880-770/cm. Three ammonia absorption features stood out at 870, 851, and 833/cm. The general shape of the spectrum implied an atmosphere with a monotonically decreasing temperature profile up to the 125 K level. Transmission profiles of the earth's atmosphere were taken between 16 microns and 25 for five consecutive nights under varying amounts of atmospheric water and air mass. There are many saturated lines, but nightly variations were fairly constant and agreed well with a theoretical profile. These results show that the Hadamard-transform technique is a useful method for obtaining astronomical spectra.
We present a Backlund transformation operating on solutions of the Korteweg-de Vries equation. It provides a unifying approach to the theory of solitary waves (solutions). Recursive application of the transformation to any solution of the Korteweg-de Vries equation generates a hierarchy of solutions for which an algebraic recursion relation is obtained. Every such hierarchy (one of which is the known family of pure multisoliton solutions) thus admits a nonlinear superposition principle.
The purpose of the first application of the "Successive Transformations Method" described in the second report was to determine, for a manned spacecraft, the optimum landing site on the moon. The results obtained, made by extrapolating the temperature TO furnished by Surveyor, can be summarized as follows: (1) The method is efficient in allowing selection of the optimum landing area. ( 2 ) The zrea selected is extensive and relatively flat; consequently, it is sufficient to allow trine for the difficult landing operation which results from the high speed of the spacecraft when reaching the moon. ( 3 ) The relative temperature obtained is lower than that where Surveyor landed. In this third report, a second application of the "Successive Transformations" is described to determine the safest conditions of a given landing site for the astronaut, especially in relation to determining the composition of the lunar surface material. As a means of accomplishing this task, it is the intent of this paper to analyze lunar craters since they are present over so much of the lunar surface.
The author has identified the following significant results. Representative faults and lineaments, natural features on the Mojave Desert, and cultural features of the southern California area were studied on ERTS-1 images. The relative appearances of the features were compared on a band 4 and 5 subtraction image, its pseudocolor transformation, and pseudocolor images of bands 4, 5, and 7. Selected features were also evaluated in a test given students at the University of California, Los Angeles. Observations and the test revealed no significant improvement in the ability to detect and locate faults and lineaments on the pseudocolor transformations. With the exception of dry lake surfaces, no enhancement of the features studied was observed on the bands 4 and 5 subtraction images. Geologic and geographic features characterized by minor tonal differences on relatively flat surfaces were enhanced on some of the pseudocolor images.
Several theorems related to the Householder transformation and separability criteria are proven. Orthogonal transformations, topology, divergence, mathematical matrices, and group theory are discussed.
An automatic Fourier transform diffraction pattern sampling system, used to investigate techniques for forestry classification of six band multispectral aerial photography is presented. Photographs and diagrams of the design, development and fabrication of a hybrid optical-digital Fourier transform detector are shown. The detector was designed around a concentric ring fiber optic array. This array was formed from many optical fibers which were sorted into concentric rings about a single fiber. All the fibers in each ring were collected into a bundle and terminated into a single photodetector. An optical/digital interface unit consisting of a high level multiplexer, and an analog-to-digital amplifier was also constructed and is described.
The verification accomplished to assure correct computation of the many geometrical relationships between the several coordinate systems and transformation matrices defined for the Saturn 1B mission was discussed. This is accomplished by demonstrating the following: (1) the program has the ability to correctly establish the initial vector coordinate system from external input data for use as a reference, (2) the program logic is capable of properly executing the calculations necessary to transform vectorial parameters from one coordinate system to another, and (3) the presettings used for vector component calculations are valid.