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Winograd's algorithm for computing the discrete Fourier transform is extended considerably for certain large transform lengths. This is accomplished by performing the cyclic convolution, required by Winograd's method, by a fast transform over certain complex integer fields. This algorithm requires fewer multiplications than either the standard fast Fourier transform or Winograd's more conventional algorithms.
For certain long transform lengths, Winograd's algorithm for computing the discrete Fourier transform is extended considerably. This is accomplished by performing the cyclic convolution, required by Winograd's method, with the Mersenne-prime number theoretic transform. This new algorithm requires fewer multiplications than either the standard fast Fourier transform or Winograd's more conventional algorithm.
An algorithm based on the Winograd (1976) method is developed to compute a Fourier-like transform over Galois field GF(2 exp n) for n equal to 5 and 6. It is shown that this transform algorithm requires fewer multiplications than the more conventional fast transform algorithm described by Gentleman (1968). Such a transform can be used to encode and decode Reed-Solomon codes of length (2 exp n) -1.
In this paper for certain long transform lengths, Winograd's algorithm for computing the discrete Fourier transform (DFT) is extended considerably. This is accomplished by performing the cyclic convolution, required by Winograd's method, with the Mersenne prime number-theoretic transform developed originally by Rader. This new algorithm requires fewer multiplications than either the standard fast Fourier transform (FFT) or Winograd's more conventional algorithm. However, more additions are required.
The transformation permits a uniform mesh to be used in the computational coordinate which extends across the layer. This coordinate transformation uses the local value of the skin friction coefficient to scale the thickness of the wall layer region, and the local maximum value of turbulent viscosity to scale the boundary-layer thickness. Results are presented for two dimensional boundary layers in both positive and negative pressure gradients and comparisons are made with experimental data and conventional variable-grid results for low speed turbulent boundary-layers. The cases chosen illustrate the capability of this new transformation to capture the boundary layer growth over the full extent of laminar, transitional, and turbulent flow with no grid adjustment as well as its ability to consistently enlarge the wall layer region for accurate shear stress representation. Results of mesh refinement studies using the new coordinate transformation are presented.
The reported investigation represents a continuation of a study conducted by Reed and Truong (1979), who proposed a hybrid algorithm for computing the discrete Fourier transform (DFT). The proposed technique employs a Winograd-type algorithm in conjunction with the Mersenne prime-number theoretic transform to perform a DFT. The implementation of the technique involves a considerable number of additions. The new investigation shows an approach which can reduce the number of additions significantly. It is proposed to use Winograd's algorithm for computing the Mersenne prime-number theoretic transform in the transform portion of the hybrid algorithm.
Three methods for performing Hankel transforms with optical or digital processors are described. The first method is applicable when the input data is available in Cartesian (x-y) format and uses the close connection between generalized Hankel transform and the two dimensional Fourier transform in Cartesian coordinates. The second method is useful when the input data is in polar (r - theta) format and uses change of variables to perform the nth order Hankel transform as a correlation integral. The third method utilizes the von Neumann addition theorem for Bessel functions to extract the Hankel coefficients from a correlation between the radial part of the input and a Bessel function. Initial experimental results obtained for optical implementation of the first two methods are presented.
The stellar luminosity function that has been measured in the visual band into the R, I, J, and K bands, where it has not yet been obtained directly, is transformed. The transformation is effected by subdividing the total visual function, which includes all stars, into subluminosity functions for each luminosity class (supergiants through white dwarfs), applying the known (V - D) color, D = R, I, J, K for each spectral type, and then summing the resultant transformed subluminosity functions into a total luminosity function for the band D. Simple analytic forms that accurately fit the transformed luminosity functions are given. Consideration is also given to the possibility of a systematic error resulting from the existence of a very red stellar population not accounted for in the visual band luminosity function
Singular, nonlinear, and Liapunov unstable equations are made regular and linear through transformations that change the perturbed planar problem of two bodies into unperturbed and undamped harmonic oscillators with constant coefficients, so that the stable solution may be immediately written in terms of the new variables. The use of arbitrary and special functions for the transformations allows the systematic discussion of previously introduced and novel anomalies. For the case of the unperturbed two-body problem, it is proved that if transformations are power functions of the radial variable, only the eccentric and the true anomalies (with the corresponding transformations of the radial variable) will result in harmonic oscillators. The present method significantly reduces computation requirements in autonomous space operations.
In Riddle and Rajala (1981), an algorithm was presented which operates on an image sequence to identify all sets of pixels having the same velocity. The algorithm operates by performing a transformation in which all pixels with the same two-dimensional velocity map to a peak in a transform space. The transform can be decomposed into applications of the one-dimensional Fourier transform and therefore can gain from the computational advantages of the FFT. The aim of this paper is the concern with the fundamental limitations of that algorithm, particularly as relates to its sensitivity to image-disturbing parameters as noise, jitter, and clutter. A modification to the algorithm is then proposed which increases its robustness in the presence of these disturbances.
The 25-kVA space transformer was developed under contract by Thermal Technology Laboratory, Buffalo, N. Y. The NASA Lewis transformer technology program attempted to develop the baseline technology. For the 25-kVA transformer the input voltage was chosen as 200 V, the output voltage as 1500 V, the input voltage waveform as square wave, the duty cycle as continuous, the frequency range (within certain constraints) as 10 to 40 kHz, the operating temperatures as 85 deg. and 130 C, the baseplate temperature as 50 C, the equivalent leakage inductance as less than 10 micro-h, the operating environment as space, and the life expectancy as 10 years. Such a transformer can also be used for aircraft, ship and terrestrial applications.
Technology for design and fabrication of radically new type of conductioncooled high-power (25 kVA) lightweight transformer having outstanding thermal and electrical characteristics. Fulfills longstanding need for conduction-cooled transformers and magnetics with low internal thermal resistances. Development techniques limited to conductive heat transfer, since other techniques such as liquid cooling, forced liquid cooling, and evaporative cooling of transformers impractical in zero-gravity space environment. Transformer uniquely designed: mechanical structure also serves as thermal paths for conduction cooling of magnetic core and windings.
The effect of finite sample size on the kinetic law of phase transformations is considered. The case where the second phase develops by a nucleation and growth mechanism is treated under the assumption of isothermal conditions and constant and uniform nucleation rate. It is demonstrated that for spherical particle growth, a thin sample transformation formula given previously is an approximate version of a more general transformation law. The thin sample approximation is shown to be reliable when a certain dimensionless thickness is small. The latter quantity, rather than the actual sample thickness, determines when the usual law of transformation kinetics valid for bulk (large dimension) samples must be modified.
This note addresses the issue of 'conservatism' in the time domain stability robustness bounds obtained by the Liapunov approach. A state transformation is employed to improve the upper bounds on the linear time-varying perturbation of an asymptotically stable linear time-invariant system for robust stability. This improvement is due to the variance of the conservatism of the Liapunov approach with respect to the basis of the vector space in which the Liapunov function is constructed. Improved bounds are obtained, using a transformation, on elemental and vector norms of perturbations (i.e., structured perturbations) as well as on a matrix norm of perturbations (i.e., unstructured perturbations). For the case of a diagonal transformation, an algorithm is proposed to find the 'optimal' transformation. Several examples are presented to illustrate the proposed analysis.
Simple fixture quickly shows whether high-voltage transformer has excessive voids in dielectric materials and whether high-voltage lead wires too close to transformer case. Fixture is "go/no-go" indicator; corona appears if transformer contains such faults. Nests in wire mesh supported by cap of clear epoxy. If transformer has defects, blue glow of corona appears in mesh and is seen through cap.
A new method is described which directly transforms Malvern line-integral data into point measurements of the radial drop mean size distribution and liquid volume concentration distribution. The transformed results have been compared with experimental point measurements by photography and the phase/Doppler spray analyzer. The comparison reveals the relation between point measurements and line-of-sight measurements. Three kinds of nozzles were investigated. After tomographical transformation of the Malvern results the different structures of the spray are revealed. A newly derived formula simplifies the transformation procedure. This method provides a direct means to extend the applicability of the Malvern particle sizer and has the potential to be developed for use in unsymmetric sprays.
This letter introduces a discrete, separable, real-to-real transform, called the cas-cas transform. Theorems for the two-dimensional case are presented, and the cas-cas transform is compared to the Hartley transform as an alternative way to convolve two-dimensional arrays and compute two-dimensional power spectra.
Quantitative data were collected on dose-response curves of cultured mouse-embryo cells (C3H10T1/2) irradiated with heavy ions of various charges and energies. Results suggests that two breaks formed on DNA within 80 A may cause cell transformation and that two DNA breaks formed within 20 A may be lethal. From results of experiments with restriction enzymes which produce DNA damages at specific sites, it was found that DNA double strand breaks are important primary lesions for radiogenic cell transformation and that blunt-ended double-strand breaks can form lethal as well as transformational damages due to misrepair or incomplete repair in the cell. The RBE-LET relationship for high-LET radiation is similar to that for HGPRT locus mutation, chromosomal deletion, and cell transformation, indicating that common lesions may be involved in these radiation effects.