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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.
A digital resampling technique for LANDSAT data is reported that incorporates a deconvolution concept to minimize spatial and radiometric degradation of data during resampling for geometric correction. A quantitative comparison of cubic convolution and digital restoration methods establishes the latter as the superior technique.
Joints for use in interconnecting adjacent segments of an hermetically sealed spacesuit which have low torques, low leakage and a high degree of reliability are described. Each of the joints is a special purpose joint characterized by substantially constant volume and low torque characteristics. Linkages which restrain the joint from longitudinal distension and a flexible, substantially impermeable diaphragm of tubular configuration spanning the distance between pivotally supported annuli are featured. The diaphragms of selected joints include rolling convolutions for balancing the joints, while various joints include wedge-shaped sections which enhance the range of motion for the joints.
In the rat, infusion of a volume of isotonic saline equal to 2% of body weight resulted in an 82% increase in the delivery of filtrate out of the proximal tubule but little or, in some animals, no change in the urinary excretion of sodium. By contrast, further degrees of volume expansion resulted in lesser increases in the distal delivery of filtrate, but were associated with a marked increase in the urinary excretion of sodium. Sixty minutes following completion of volume expansion, while the animals were still in positive sodium balance, the urinary excretion of sodium decreased 52% compared to a decrease of only 24% in the distal delivery of filtrate. During the course of progressive volume expansion and during the recovery phase, there was a dissociation between alterations in sodium reabsorption in the proximal convoluted tubule and in the whole kidney. These studies indicate that although the proximal tubule is more sensitive to changes in the extracellular fluid volume, distal nephron sites are ultimately responsible both for the natriuresis of volume expansion and the relative antinatriuresis of the recovery periods.
Winograd (1976) has developed a new class of algorithms which depend heavily on the computation of a cyclic convolution for computing the conventional DFT (discrete Fourier transform); this new algorithm, for a few hundred transform points, requires substantially fewer multiplications than the conventional FFT algorithm. Reed and Truong have defined a special class of finite Fourier-like transforms over GF(q squared), where q = 2 to the p power minus 1 is a Mersenne prime for p = 2, 3, 5, 7, 13, 17, 19, 31, 61. In the present paper it is shown that Winograd's algorithm can be combined with the aforementioned Fourier-like transform to yield a new algorithm for computing the DFT. A fast method for accurately computing the DFT of a sequence of complex numbers of very long transform-lengths is thus obtained.
As part of the continuing effort to introduce standardization of spacecraft and ground equipment in satellite systems, NASA's Goddard Space Flight Center and other NASA facilities have supported the development of a set of standards for the use of error control coding in telemetry subsystems. These standards are intended to ensure compatibility between spacecraft and ground encoding equipment, while allowing sufficient flexibility to meet all anticipated mission requirements. The standards which have been developed to date cover the application of block codes in error detection and error correction modes, as well as short and long constraint length convolutional codes decoded via the Viterbi and sequential decoding algorithms, respectively. Included are detailed specifications of the codes, and their implementation. Current effort is directed toward the development of standards covering channels with burst noise characteristics, channels with feedback, and code concatenation.
A method has been developed for far-field evaluation from measurements taken on a cylinder. The antenna and probe fields are represented by superpositions of plane waves, and two integral equations are derived whose functions are the elevation and azimuthal components of the antenna pattern. The known components are the measurements taken by either two probes or a single probe with two geometrical orientations. The convolutional nature of the integral equations makes Fourier analysis techniques applicable to a straightforward solution and an efficient computational procedure. Good agreement has been found between experimental and reconstructed patterns for both nominal and cross polarized field components.
The paper describes turbulence simulation experiments based on the principles of control system theory, that is, the construction of a system characterized by a system function such that upon exciting the system with prescribed noise processes the output of the system is a realization of a random processing the desired statistical attributes of turbulence. An experimental autocorrelation of Jimsphere measurements of wind velocity was approximated to simulate turbulent wind. From the approximate autocorrelation function, the required system function is obtained, and a discrete time system is designed. Another method of simulation is to solve the convolution integral by filter techniques. Other methods include discrete Fourier simulation and self-similar simulation.
Digital convolutional decoder circuit for data communication receiver employs Viterbi decoding algorithm to quickly and efficiently decode data on basis of "maximum likelihood" computations.
Two schemes of closing turbulent moment equations are proposed both of which make double correlation equations separated into single-point equations. The first is based on neglected triple correlation, leading to an equation differing from small perturbed gasdynamic equations where the separation constant appears as the frequency. Grid-produced turbulence is described in this light as time-independent, cylindrically-isotropic turbulence. Application to wall turbulence guided by a new asymptotic method for the Orr-Sommerfeld equation reveals a neutrally stable mode of essentially three dimensional nature. The second closure scheme is based on an assumption of identity of the separated variables through which triple and quadruple correlations are formed. The resulting equation adds, to its equivalent of the first scheme, an integral of nonlinear convolution in the frequency describing a role due to triple correlation of direct energy-cascading.
The performance of certain block codes on a Gaussian channel is evaluated. The BCH codes are markedly superior to convolutional codes currently used for deep space missions. The algorithm is used to derive results, which provides a basis for a simple, almost optimum procedure for decoding these codes.
A novel and numerically efficient method of far field evaluation from measurements taken on a cylinder is based on the representation of both the antenna and the probe fields as superpositions of plane waves. A system of two integral equations are established whose unknown functions are the azimuthal and elevation components of the antenna pattern and whose known terms are the set of measurement data taken with two different probes - the second probe in most practical instances being simply the same probe with a different geometrical orientation. The equations express the known data - for each angular position of the antenna under measurement - as the integrals of the products of the corresponding components of the unknown antenna and known probe patterns multiplied by a phase term. The convolutional nature of the integral equations makes their solutions straight-forward. If, as is virtually always the case, the probe is small or of moderate size so that the axis of rotation of the antenna mount is in the far field of the probe, the intervention of asymptotic techniques makes the solution numerically very efficient. The agreement of calculated and experimental patterns is excellent.
When the amplitude and timing biases are removed from the GEOS-3 Sample and Hold (S&H) gates, the mean return waveforms can be excellently fitted with a theoretical template which represents the convolution of: (1) the radar point target response; (2) the range noise (jitter) in the altimeter tracking loop; (3) the sea surface height distribution; and (4) the antenna pattern as a function of the range to mean sea level. Several techniques of varying complexity to remove the effect of the tracking loop jitter in computing the wave height are considered. They include: (1) realigning the S&H gates to their actual positions with respect to mean sea level before averaging; (2) using the observed standard deviation on the altitude measurement to remove the integrated effect of the tracking loop jitter, and (3) using a look-up table to correct for the expected value of range noise. Analysis of skewness in the GEOS return waveform demonstrates the potential of a satellite radar altimeter to determine the dominant wavelength of ocean waves.
Pressure suit mobility joints are for use in interconnecting adjacent segments of an hermetically sealed spacesuit in which low torques, low leakage and a high degree of reliability are required. Each of the joints is a special purpose joint characterized by substantially constant volume and low torque characteristics and includes linkages which restrain the joint from longitudinal distension and includes a flexible, substantially impermeable diaphragm of tubular configuration spanning the distance between pivotally supported annuli. The diaphragms of selected joints include rolling convolutions for balancing the joints, while various joints include wedge-shaped sections which enhance the range of motion for the joints.
The development of a high-speed reconstruction processor and a channelized architecture to use with a high-resolution tomographic unit is discussed with attention to the convolution reconstruction algorithm. By means of this algorithm, input data and intermediate result precision required throughout the algorithm execution have been studied with computer simulation using profile data derived from mathematically simulated test objects and experimental animal data. A prototype section for a highly parallel all-digital system executes 60 million arithmetic operations per second, and the full-scale version is expected to reconstruct 500 to 1000 cross sections per second.
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
A general technique for calculating the sensitivities, uncertainties and overall imprecision of a model to a set of input parameters is described and applied to the calculation of CFM (chlorofluoromethane) induced stratospheric ozone depletion. The input data set used is reaction rates and the technique highlights those that most need further study in the laboratory. The convolution of individual uncertainties to obtain an overall imprecision gives good agreement with the results of Monte-Carlo calculations using the same model.
A class of time-invariant binary convolutional codes is defined, called partial-unit-memory codes. These codes are optimal in the sense of having maximum free distance for given values of R, k (the number of encoder inputs), and mu (the number of encoder memory cells). Optimal codes are given for rates R = 1/4, 1/3, 1/2, and 2/3, with mu not greater than 4 and k not greater than mu + 3, whenever such a code is better than previously known codes. An infinite class of optimal partial-unit-memory codes is also constructed based on equidistant block codes.