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NASA NTRS2001

Performance of the Wavelet Decomposition on Massively Parallel Architectures

Traditionally, Fourier Transforms have been utilized for performing signal analysis and representation. But although it is straightforward to reconstruct a signal from its Fourier transform, no local description of the signal is included in its Fourier representation. To alleviate this problem, Windowed Fourier transforms and then wavelet transforms have been introduced, and it has been proven that wavelets give a better localization than traditional Fourier transforms, as well as a better division of the time- or space-frequency plane than Windowed Fourier transforms. Because of these properties and after the development of several fast algorithms for computing the wavelet representation of any signal, in particular the Multi-Resolution Analysis (MRA) developed by Mallat, wavelet transforms have increasingly been applied to signal analysis problems, especially real-life problems, in which speed is critical. In this paper we present and compare efficient wavelet decomposition algorithms on different parallel architectures. We report and analyze experimental measurements, using NASA remotely sensed images. Results show that our algorithms achieve significant performance gains on current high performance parallel systems, and meet scientific applications and multimedia requirements. The extensive performance measurements collected over a number of high-performance computer systems have revealed important architectural characteristics of these systems, in relation to the processing demands of the wavelet decomposition of digital images.

El-Ghazawi, Tarek A.↗

NASA NTRS1995

Nonperiodic variations in astrophysical systems: Investigating frequency evolution

We present a method related to the wavelet transform, the Gabor transform, for investigating astronomical time series containing nonconsistent frequencies. Instances in which such data sets may arise include variable star light curves, numerical studies of the gravitational three-body problem, X-ray binaries, and signals from more exotic objects such as planets around pulsars and mass infall from accretion structures onto compact objects. As an illustration of its power, we apply the technique to a numerical data set of a gravitational three-body interaction and to photometry of the rapidly oscillating peculiar A star HD 60435. In the three-body example, the method provides an insightful shorthand that allows for the determination of episodes where the system behaves as two nearly Keplerian orbits. For HD 60435, the power in the main frequency exhibits unusual evolution over the duration of the observation.

Boyd, Patricia T.↗

NASA NTRS1994

Apparatus and method for determining the mass density of a filament

A method and apparatus for determining the mass density of a moving filament is provided. The method includes the steps of providing a filament across two supports, tensioning the filament, inducing a vibration into the filament segment between the supports, reinforcing the vibration using an amplified feedback signal, detecting the vibrational frequency data, processing the data using a fast-fourier transform analysis, and then displaying the frequency. The use of the feedback signal results in a self-tuning resonant loop. Open loop versions may also be used. The apparatus includes a base supporting a fixed support and a transducer which in turn supports a moveable support. The transducer vibrates the moveable support transversely to the direction of travel of the filament, thereby inducing a transverse vibrational mode. The output of the transducer is amplified and used to drive a second amplifier to produce a self-tuning resonant loop. In the open loop version a signal generator is used to drive the transducer through a frequency range, during which the amplitude peak is identified.

Hinkley, Jeffrey A.↗

NASA NTRS1997

Tailored Excitation for Multivariable Stability-Margin Measurement Applied to the X-31A Nonlinear Simulation

Safety and productivity of the initial flight test phase of a new vehicle have been enhanced by developing the ability to measure the stability margins of the combined control system and vehicle in flight. One shortcoming of performing this analysis is the long duration of the excitation signal required to provide results over a wide frequency range. For flight regimes such as high angle of attack or hypersonic flight, the ability to maintain flight condition for this time duration is difficult. Significantly reducing the required duration of the excitation input is possible by tailoring the input to excite only the frequency range where the lowest stability margin is expected. For a multiple-input/multiple-output system, the inputs can be simultaneously applied to the control effectors by creating each excitation input with a unique set of frequency components. Chirp-Z transformation algorithms can be used to match the analysis of the results to the specific frequencies used in the excitation input. This report discusses the application of a tailored excitation input to a high-fidelity X-31A linear model and nonlinear simulation. Depending on the frequency range, the results indicate the potential to significantly reduce the time required for stability measurement.

Bosworth, John T.↗

NASA NTRS1997

Apparatus and Method for Determining the Mass Density of a Filament

A method and apparatus for determining the mass density of a moving filament is provided. The method includes the steps of providing a filament across two supports, tensioning the filament. inducing a vibration into the filament segment between the supports, reinforcing the vibration using an amplified feedback signal, detecting the vibrational frequency data. processing the data using a fast-fourier transform analysis. and then displaying the frequency. The use of the feedback signal results in a self-tuning resonant loop. Open loop versions may also be used. The apparatus includes a base supporting a fixed support and a transducer which in turn supports a moveable support. The transducer vibrates the moveable support transversely to the direction of travel of the filament, thereby inducing a transverse vibrational mode. The output of the transducer is amplified and used to drive a second amplifier to produce a self-tuning resonant loop. In the open loop version a signal generator is used to drive the transducer through a frequency range, during which the amplitude peak is identified.

Hinkley, Jeffrey A.↗

NASA NTRS1989

Cascaded resonant bridge converters

A converter for converting a low voltage direct current power source to a higher voltage, high frequency alternating current output for use in an electrical system where it is desired to use low weight cables and other circuit elements. The converter has a first stage series resonant (Schwarz) converter which converts the direct current power source to an alternating current by means of switching elements that are operated by a variable frequency voltage regulator, a transformer to step up the voltage of the alternating current, and a rectifier bridge to convert the alternating current to a direct current first stage output. The converter further has a second stage series resonant (Schwarz) converter which is connected in series to the first stage converter to receive its direct current output and convert it to a second stage high frequency alternating current output by means of switching elements that are operated by a fixed frequency oscillator. The voltage of the second stage output is controlled at a relatively constant value by controlling the first stage output voltage, which is accomplished by controlling the frequency of the first stage variable frequency voltage controller in response to second stage voltage. Fault tolerance in the event of a load short circuit is provided by making the operation of the first stage variable frequency voltage controller responsive to first and second stage current limiting devices. The second stage output is connected to a rectifier bridge whose output is connected to the input of the second stage to provide good regulation of output voltage wave form at low system loads.

Stuart, Thomas A.↗

NASA NTRS1980

Study of power management technology for orbital multi-100KWe applications. Volume 2: Study results

The preliminary requirements and technology advances required for cost effective space power management systems for multi-100 kilowatt requirements were identified. System requirements were defined by establishing a baseline space platform in the 250 KE KWe range and examining typical user loads and interfaces. The most critical design parameters identified for detailed analysis include: increased distribution voltages and space plasma losses, the choice between ac and dc distribution systems, shuttle servicing effects on reliability, life cycle costs, and frequency impacts to power management system and payload systems for AC transmission. The first choice for a power management system for this kind of application and size range is a hybrid ac/dc combination with the following major features: modular design and construction-sized minimum weight/life cycle cost; high voltage transmission (100 Vac RMS); medium voltage array or = 440 Vdc); resonant inversion; transformer rotary joint; high frequency power transmission line or = 20 KHz); energy storage on array side or rotary joint; fully redundant; and 10 year life with minimal replacement and repair.

Mildice, J. W.↗

NASA NTRS1993

Rough surface scattering from moving ocean surfaces as an indicator of scattering mechanisms

Ever since Crombie used the Doppler spectrum of RF signals scattered from the ocean surface to provide conclusive evidence for Bragg resonant scattering, scattering from the ocean surface has served as a testing ground for the identification of governing scattering mechanisms in rough surface scattering. The moving ocean surface has the advantage for rough surface scattering that, being a dispersive medium, features with different spatial scales the tendency to travel at different speeds. Thus, by looking at the temporal signature of the scattered field, one can try to isolate the scattering mechanism. This feature has been exploited by various authors. To give a recent example, we cite the work of Plant, who examined the Doppler spectrum of the return signal to infer the presence of two-scale scattering in scattering at medium incidence angles. The problem with restricting oneself to the examination of the Doppler spectrum, as has been done traditionally, is that one restricts the phenomena under investigation to temporally homogeneous phenomena: transient phenomena, which are localized in time, are not localized in frequency space. There is increasing evidence that this type of phenomena, due to specular scattering or breaking waves, may also play an important role in determining the scattering mechanism in ocean-like surfaces. To overcome this problem, we introduce the use of the Wavelet Transform to study the frequency-temporal signatures of the scattered field from moving ocean waves. We calculate this signature using various analytic scattering theories and show that the Wavelet Transform provides a useful tool for separating the different scattering mechanisms operating in scattering in ocean-like surfaces. Next we simulate realistic nonlinear moving ocean waves and calculate the temporal scattered field signature by using the method of moments and the stop-start approximation: the surface is assumed stationary during a scattering event, but moves between incident EM pulses. We compute and compare the Doppler frequency spectrum and the Wavelet Transform of the resulting signal for various types of surfaces and show how different scattering mechanisms may be isolated by this technique. Finally, we compare these numerical results against the analytical predictions in order to obtain the domain of applicability of various scattering theories for moving ocean surfaces which may include wave breaking and specular glints.

Rodriguez, Ernesto↗

NASA NTRS1970

Exponential absolute stability of discrete systems

Nonlinear discrete systems absolute stability exponential property proved by modified frequency condition, applying analog transformation to Szego-Kalman equations

Siljak, D. D.↗

NASA NTRS1970

A frequency domain solution for the linear attitude-control problem of spacecraft with flexible appendages

Linear interaction problem between spacecraft attitude control and flexible appendages solved in frequency domain using Fourier transform

Trubert, M. R.↗

NASA NTRS1972

Toroidal transformer design program with application to inverter circuitry

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.

Dayton, J. A., Jr.↗

NASA NTRS1976

A synthetic aperture processor using CCD signal processing techniques

Synthetic aperture radar (SAR) imaging was the most suitable technique for achieving high resolution imagery through atmospheric cloud cover. This feature was important for planetary as well as earth orbiting satellite systems, and for military aircraft applications. Such applications require onboard data processing or wide-band data transmission systems in order to handle the large amounts of raw data produced by such systems. A number of techniques were utilized in implementing SAR processors. Frequency filtering and Fourier transform operations using both optical and digital techniques were utilized in SAR processing.

Bailey, W. H.↗

NASA NTRS1979

Time history solution program, L225 (TEV126). Volume 2: Supplemental system design and maintenance document

The time history solution program L225 (TEV126) is described. The program calculates the time responses of a linear system by convoluting the impulsive response functions with the time dependent excitation. 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. The design and structure of the program is presented.

Tornallyay, A.↗

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 NTRS1986

On the existence of oscillations in solar filaments observed in H alpha and C IV lines

Time sequence observations of filaments in both the H alpha line and the 1548 A C IV line were analyzed with the Fourier transform technique in the frequency range (1 - 10 mHz). No oscillation is detected in filaments except at the footpoints where a steady velocity gradient is large. The energy is probably due to convective motions rather than pressure oscillations.

Schmieder, B.↗

NASA NTRS1987

Profile modification to minimize spur gear dynamic loading

An analytical computer simulation program for dynamic modeling of low-contact-ratio spur gear systems is presented. The procedure computes the static transmission error of the gears operating under load and uses a fast Fourier transform to generate the frequency spectrum of the static transmission error at various tooth profile modifications. The dynamic loading response of an unmodified (perfect involute) gear pair was compared with that of gears with various profile modifications. Correlations were found between various profile modifications and the resulting dynamic loads. An effective error, obtained from frequency domain analysis of the static transmission error of the gears, gave a very good indication of the optimum profile modification to reduce gear dynamic loading. Design curves generated by dynamic simulation at various profile modifications are given for gear systems operated at various loads. Optimum profile modifications can be determined from these design curves for improved gear design.

Lin, Hsiang Hsi↗

NASA NTRS1989

Profile modification to minimize spur gear dynamic loading

Lin, H. H.↗

NASA NTRS1991

Adiabatic properties of pulsating DA white dwarfs. I - The treatment of the Brunt-Vaisala frequency and the region of period formation

The fundamental issue of the region of period formaton in a degenerate star is examined, with special attention given to the treatment of the Brunt-Vaisala frequency. It is shown that, in order to obtain reliable numerical results in degenerate stellar models, the Brunt-Vaisala frequency must be appropriately transformed, because it is defined in terms of a difference between two numbers which become nearly equal in highly degenerate matter, causing serious numerical problems and systematic errors. An alternative expression is derived, which is valid for multicomponent nonideal partially degenerate and partially ionized plasmas such as those encountered in white dwarf envelopes. This expression is used to compute the period structure of the same white dwarf considered by Pesnell (1987). It is shown that the implicit numerical differencing used in the Lagrangian pulsation code of Pesnell leads to very serious difficulties when used with models of degenerate stars.

Brassard, P.↗