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NASA NTRS1979

A new approach to the solution of large, full matrix equations: A two-dimensional potential flow feasibility study

An approach to the solution of matrix problems resulting from integral equations of mathematical physics is presented. Based on the inherent smoothness in such equations, the problem is reformulated using a set of orthogonal basis vectors, leading to an equivalent coefficient problem which can be of lower order without significantly impairing the accuracy of the solution. This approach was evaluated using a two-dimensional Neumann problem describing the inviscid, incompressible flow over an airfoil. Two different kinds of mode functions were investigated, namely eigenfunction series and Fourier series. The method using Fourier series was found preferable. It uses all of the coefficients from a Fast Fourier Transform algorithm in an approximate method which exploits the known structure of the transformed coefficient matrix and very promising results for the flow over a realistic airfoil are obtained. On the basis of the results presented here, an order of magnitude reduction in this computer time can be expected for such problems as compared with the time for a direct matrix solution.

James, R. M.↗

NASA NTRS1979

Time history solution program, L225 (TEV126). Volume 1: Engineering and usage

Volume 1 of a two volume document is presented. The usage of the convolution program L225 (TEV 126) is described. The program calculates the time response of a linear system by convoluting the impulsive response function with the time-dependent excitation function. The convolution is performed as a multiplication in the frequency domain. Fast Fourier transform techniques are used to transform the product back into the time domain to obtain response time histories. A brief description of the analysis used is presented.

Kroll, R. I.↗

NASA NTRS1979

Application of abstract harmonic analysis to the high-speed recognition of images

Methods are constructed for rapidly computing correlation functions using the theory of abstract harmonic analysis. The theory developed includes as a particular case the familiar Fourier transform method for a correlation function which makes it possible to find images which are independent of their translation in the plane. Two examples of the application of the general theory described are the search for images, independent of their rotation and scale, and the search for images which are independent of their translations and rotations in the plane.

Usikov, D. A.↗

NASA NTRS1977

Advances in laser technology for the atmospheric sciences; Proceedings of the Seminar, San Diego, Calif., August 25, 26, 1977

These papers deal with recent research, developments, and applications in laser and electrooptics technology, particularly with regard to atmospheric effects in imaging and propagation, laser instrumentation and measurements, and particle measurement. Specific topics include advanced imaging techniques, image resolution through atmospheric turbulence over the ocean, an efficient method for calculating transmittance profiles, a comparison of a corner-cube reflector and a plane mirror in folded-path and direct transmission through atmospheric turbulence, line-spread instrumentation for propagation measurements, scaling laws for thermal fluctuations in the layer adjacent to ocean waves, particle sizing by laser photography, and an optical Fourier transform analysis of satellite cloud imagery. Other papers discuss a subnanosecond photomultiplier tube for laser application, holography of solid propellant combustion, diagnostics of turbulence by holography, a camera for in situ photography of cloud particles from a hail research aircraft, and field testing of a long-path laser transmissometer designed for atmospheric visibility measurements.

Trolinger, J. D.↗

NASA NTRS1978

Doppler lidar processing for atmospheric turbulence measurements

A Doppler lidar is described, its processing methods are characterized, and two alternate techniques are considered. The described system uses a CO2 laser transmitting at 10.6 microns and a bank of narrow band filters for the spectrum analysis. Typical results obtained with this system are presented. The two alternate techniques involve computation of the discrete spectrum by use of the discrete Fourier transform. The first technique involves single-pulse processing and incoherent integration, while the second technique performs coherent processing on the train of received pulses.

Polge, R. J.↗

NASA NTRS1979

Maximum likelihood identification of aircraft parameters with unsteady aerodynamic modelling

A simplified aerodynamic force model based on the physical principle of Prandtl's lifting line theory and trailing vortex concept has been developed to account for unsteady aerodynamic effects in aircraft dynamics. Longitudinal equations of motion have been modified to include these effects. The presence of convolution integrals in the modified equations of motion led to a frequency domain analysis utilizing Fourier transforms. This reduces the integro-differential equations to relatively simple algebraic equations, thereby reducing computation time significantly. A parameter extraction program based on the maximum likelihood estimation technique is developed in the frequency domain. The extraction algorithm contains a new scheme for obtaining sensitivity functions by using numerical differentiation. The paper concludes with examples using computer generated and real flight data

Keskar, D. A.↗

NASA NTRS1978

Comparison of modal test methods on the Voyager payload

A comparison of the performance of modern modal data analysis methods on test data from the Voyager Jupiter/Saturn payload is presented. Four different test/data-analysis combinations are compared - multiple-point sine excitation tests, single-point random-excitation tests using two different techniques of manipulating Fourier transform data, and a time-domain method for analyzing random data. Results indicate that all four methods can give comparable results. Of the four, the time-domain approach detects more modes in the test data and, at the same time, shows the greatest promise for reducing the time and cost of modal testing.

Hanks, B. R.↗

NASA NTRS1978

The comparison between the synthetic aperture radar imageries and the surface truth of ocean waves

Ocean waves measured offshore of Marineland, Florida, by the synthetic aperture radar (SAR) are compared with the surface truth data. The Fourier transform of SAR imageries are taken and the corrections of the wave directions and wave lengths due to the relative velocities between SAR and waves are considered. Favorable comparisons are obtained for the peak frequencies, wave directions, and directional distributions. However, the one-dimensional SAR spectra are quite different from the surface truth wave height spectra.

Hsiao, S. V.↗

NASA NTRS1979

The spatial variability of coastal surface water temperature during upwelling

Thermal scanner imagery acquired during a field experiment designed to study an upwelling event in Lake Superior is investigated. Temperature data were measured by the thermal scanner, with a spatial resolution of 7 m. These data were correlated with temperatures measured from boats. One- and two-dimensional Fourier transforms of the data were calculated and temperature variances as a function of wavenumber were plotted. A k-to-the-minus-three dependence of the temperature variance on wavenumber was found in the wavenumber range of 1-25/km. At wavenumbers greater than 25/km, a k-to-the-minus-five-thirds dependence was found.

Scarpace, F. L.↗

NASA NTRS1979

A comparison of WFTA and FFT programs

Bounds on the minimum number of data transfers (i.e., loads and stores) required by WFTA (Winograd Fourier Transform Algorithm) and FFT programs are presented. The analysis is applicable to those general-purpose computers with a small number of general processor registers (e.g., the IBM370, PDP-11, etc.). It is shown that the 1008-point WFTA requires about 21% more data transfers than the 1024-point radix-4 FFT; on the other hand, the 120-point WFTA has about 22% fewer data transfers than the 128-point radix-2 FFT. Finally, comparisons of the 'total' program execution times (multiplications, additions, and data transfers, but not indexing or permutations) are presented.

Nawab, H.↗

NASA NTRS1978

Solid state photochemistry of polycarbonates

The quantum yield of photoFries rearrangement in a polycarbonate film has been analyzed as a function of temperature and humidity on the basis of previously reported (Koyler and Mann, 1977) experimental data. Results indicate that in the homogeneous amorphous phase, photoFries rearrangement is a concerted process proceeding either from the pi star reversed arrow n singlet, in which case it must be subject to considerable self quenching, or from a triplet, presumably the first triplet since the lifetime of higher triplets is expected to be very short in the solid phase. If the parent excited state is the first triplet, chain scission is possibly an independent process, probably occurring from the pi star reversed arrow n singlet. Evidence of chain scission on photodegradation in the solid state includes loss of C-O and C-C bond intensities revealed in the Fourier transform infrared spectra, gel permeation chromotography elution profiles of degraded film samples dissolved in CHCl3, and a decrease in tensile strength and T sub g as photodegradation proceeds. Chain scission is apparently inhibited as photoFries products accumulate.

Gupta, A.↗

NASA NTRS1979

Techniques for interpretation of geoid anomalies

For purposes of geological interpretation, techniques are developed to compute directly the geoid anomaly over models of density within the earth. Ideal bodies such as line segments, vertical sheets, and rectangles are first used to calculate the geoid anomaly. Realistic bodies are modeled with formulas for two-dimensional polygons and three-dimensional polyhedra. By using Fourier transform methods the two-dimensional geoid is seen to be a filtered version of the gravity field, in which the long-wavelength components are magnified and the short-wavelength components diminished.

Chapman, M. E.↗

NASA NTRS1979

A method of mapping compact structure in radio sources using VLBI observations

A two-part technique is described for determining the angular structure of the compact components of radio sources from VLBI observations. With this technique, the source structure is first approximated, using both amplitudes and closure phases, by a model consisting of circularly symmetric Gaussian components located on a grid of positions on the sky. The second part begins by employing this model to predict the visibility phase corresponding to each observed visibility amplitude; these estimated visibility phases are then adjusted to agree with the observed closure phases. The resulting estimates of the visibility phases and the observed visibility amplitudes are then combined in a direct Fourier transform to produce a 'dirty' source map that is deconvolved via the CLEAN procedure on the basis of the point-source response. Some examples based on data generated from test models are provided.

Cotton, W. D.↗

NASA NTRS1979

Alternative signal processing techniques for a pulsed laser Doppler velocimeter system

The laser Doppler velocimeter system (LDV) being tested at NASA MSFC, Alabama, relies on a bank of classical filters for processing the returned lidar signal. Due to the complexity of this conventional filter system, alternative signal processing methods have been proposed for obtaining the Doppler spectrum. The fast Fourier transform (FFT) and the pulse-pair estimator are two techniques which appear to offer some advantages over the existing system. The work reported employs digital computer simulation to compare and evaluate these two processing methods for determining the first and second moments of the LDV velocity spectrum.

Calhoun, M. D.↗

NASA NTRS1979

Influence of phase cancellation and pulse shape artifacts on ultrasonic spectrum analysis

Both continuous wave and Fourier transformed pulse ultrasonic spectroscopy are being applied to material and flow characterization. Ideal samples and flaws (flat, parallel, and homogeneous) and ideal ultrasonic apparatus (producing delta function stress waves) provide acoustic spectra which can be partially inverted. However, in the presence of material inhomogeneity, lack of sample flatness or parallelism, or finite risetime pulses, the spectra become quite complex and produce phase cancellations at the transducer as well as pulse shape spectral artifacts. In this paper, we examine the nature of these artifacts for both simple and practical samples. Sample spectra are contrasted for several different transducer/electronic systems. Spectra obtained with a phase insensitive acousto-electric transducer (AET) combined with a frequency tracked tone-burst spectroscopy (TBS) method are presented. Analysis of the test configuration is shown to produce spectra consistent with that obtained with the AET-TBS combination.

Heyman, J. S.↗

NASA NTRS1979

SETI - High sensitivity searches at NASA with high speed tape recorders

The paper reports the two observing programs conducted to compare two techniques which have been proposed as methods for performing the requisite Fourier transformations in very large multichannel spectrum analysers (MCSA): the direct digital FFT and optical transform processor. The details of the observations at NRAO utilizing a direct digital FFT are given. A description of the NAIC, Arecibo observations utilizing an optical processor at the Environmental Research Institute of Michigan (ERIM) and a microdensitometer at Electromagnetics System Laboratories (ESL) is presented. For both observing programs, statistical analysis of the power spectra produced by the nonreal-time MCSAs (or post-processing) was accomplished.

Tarter, J.↗

NASA NTRS1979

Dynamic response of damaged angleplied fiber composites

The effects of low level damage induced by monotonic load, cyclic load and/or residual stresses on the vibration frequencies and damping factors of fiber composite angleplied laminates were investigated. Two different composite systems were studied - low modulus fiber and ultra high modulus fiber composites. The results obtained show that the frequencies and damping factors of angleplied laminates made from low modulus fiber composites are sensitive to low level damage while those made from ultra high modulus composites are not. Vibration tests may not be sufficiently sensitive to assess concentrated local damage in angleplied laminates. Dynamic response determined from low-velocity impact coupled with the Fast Fourier Transform and packaged in a minicomputer can be a convenient procedure for assessing low-level damage.

Chamis, C. C.↗

NASA NTRS1980

Symbolic-numeric interface: A review

A survey of the use of a combination of symbolic and numerical calculations is presented. Symbolic calculations primarily refer to the computer processing of procedures from classical algebra, analysis, and calculus. Numerical calculations refer to both numerical mathematics research and scientific computation. This survey is intended to point out a large number of problem areas where a cooperation of symbolic and numerical methods is likely to bear many fruits. These areas include such classical operations as differentiation and integration, such diverse activities as function approximations and qualitative analysis, and such contemporary topics as finite element calculations and computation complexity. It is contended that other less obvious topics such as the fast Fourier transform, linear algebra, nonlinear analysis and error analysis would also benefit from a synergistic approach.

Ng, E. W.↗