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NASA NTRS1974

Upper bounds on sequential decoding performance parameters

This paper presents the best obtainable random coding and expurgated upper bounds on the probabilities of undetectable error, of t-order failure (advance to depth t into an incorrect subset), and of likelihood rise in the incorrect subset, applicable to sequential decoding when the metric bias G is arbitrary. Upper bounds on the Pareto exponent are also presented. The G-values optimizing each of the parameters of interest are determined, and are shown to lie in intervals that in general have nonzero widths. The G-optimal expurgated bound on undetectable error is shown to agree with that for maximum likelihood decoding of convolutional codes, and that on failure agrees with the block code expurgated bound. Included are curves evaluating the bounds for interesting choices of G and SNR for a binary-input quantized-output Gaussian additive noise channel.

Jelinek, F.↗

NASA NTRS1974

Quantum graviton creation in a model universe

Consideration of the mechanism of production of gravitons in the empty, anisotropic, spatially inhomogeneous Gowdy three-torus cosmology. The Gowdy cosmology is an exact solution of the vacuum Einstein equations and is obtained as a generalization of the homogeneous empty Bianchi Type I (Kasner) cosmology by permitting the metric components to depend on one of the space variables in addition to time. The Hamiltonian methods of Arnowitt, Deser, and Misner are employed to identify the dynamical variables which are to be quantized. The WKB regime solution is identical to that found by Doroshkevich, Zel'dovich, and Novikov (DZN) for a universe containing collisionless anisotropic radiation. Using a procedure similar to that of Parker (1971) or Zel'dovich and Starobinskii (1971) for defining quantum number, it is found that the DZN large-time radiation consists of quanta (gravitons) created from an initial vacuum. The quantum behavior is much like the semiclassical enhancement of quantum number with the added feature of creation of quanta from vacuum fluctuations.

Berger, B. K.↗

NASA NTRS1974

Analysis of experimental NRL radar altimeter data

An X-band radar capable of continuously variable transmitted pulse durations down to 1 nsec is being flown to investigate the interaction of radar altimeter signals with the sea surface. There is good agreement between the observed radar altimeter leading edge rise time for a 1-nsec transmitted pulse and the rise time predicted from the radar parameters and the sea state determined by a laser profilometer. Using a threshold tracker on 29-pulse averages for a transmitted pulse of 24 nsec, it was found that the range noise varied linearly with the power level of the threshold over a considerable range. The altimeter range quantization was 9.35 cm, and a minimum range noise of 3.9 cm was obtained. A comparison of pulse-to-pulse correlation observed in the radar data with that predicted by a Monte Carlo simulation is used to obtain a measure of sea surface scatterer motion.

Walsh, E. J.↗

NASA NTRS1974

Modern sampled-data control theory: Design of the Large Space Telescope

This investigation was undertaken to determine the effect of varying the sampling period on the dynamic response of the sampled-data Large Space Telescope (LST) system. A range of sampling periods was recommended based on the criterion that self-sustained oscillations are to be avoided in the LST system. The step responses of the LST system were then investigated when various sampling periods are used. For small sampling periods, the dynamic behavior of the sampled-data system is very similar to that of the continuous-data system. When T is large (but less than 0.25 sec) the overshoot of the step response of the sampled-data becomes greater. However, the dynamic behavior of the sampled-data system may be improved by redesigning the controller. It appears that a sampling period as high as 0.1 second is feasible for the LST system. However, it should be noted that the conclusions are obtained with the existing system model. Other practical considerations such as noise, coupling effects and quantization errors, may restrict the sampling period to a lower value.

Kuo, B. C.↗

NASA NTRS1974

One way Doppler extractor. Volume 1: Vernier technique

A feasibility analysis, trade-offs, and implementation for a One Way Doppler Extraction system are discussed. A Doppler error analysis shows that quantization error is a primary source of Doppler measurement error. Several competing extraction techniques are compared and a Vernier technique is developed which obtains high Doppler resolution with low speed logic. Parameter trade-offs and sensitivities for the Vernier technique are analyzed, leading to a hardware design configuration. A detailed design, operation, and performance evaluation of the resulting breadboard model is presented which verifies the theoretical performance predictions. Performance tests have verified that the breadboard is capable of extracting Doppler, on an S-band signal, to an accuracy of less than 0.02 Hertz for a one second averaging period. This corresponds to a range rate error of no more than 3 millimeters per second.

Blasco, R. W.↗

NASA NTRS1975

Radar characteristics of cloud fields

Relations of several statistical parameters of the radio echo field to the types of cloud systems and weather phenomena in the cloud field are studied. Combinations of the statistical characteristics of radio echo are found which in certain cases permit the unique classification of cloud field according to the types of phenomena. The space-time variability of the radar characteristic was examined in connection with the transformation of the cloud field, and the question of the variation of the statistical characteristics of the echoes from cloud field was examined in connection with changes in the dimensions of the quantization cell.

Divinskaya, B. S.↗

NASA NTRS1975

ITOS VHRR on-board data compression study

Data compression methods for ITOS VHRR data were studied for a tape recorder record-and playback application. A playback period of 9 minutes was assumed with a nominal 18 minute record period for a 2-to-1 compression ratio. Both analog and digital methods were considered with the conclusion that digital methods should be used. Two system designs were prepared. One is a PCM system and the other is an entropy-coded predictive-quantization, sometimes called entropy-coded DPCM or just DPCM, system. Both systems use data management principles to transmit only the necessary data. Both systems use a medium capacity standard tape recorder from specifications provided by the technical officer. The 10 to the 9th power bit capacity of the recorder is the basic limitation on the compression ratio. Both systems achieve the minimum desired 2 to 1 compression ratio. A slower playback rate can be used with the DPCM system due to a higher compression factor for better link performance at a given CNR in terms of bandwidth utilization and error rate. The report is divided into two parts. The first part summarizes the theoretical conclusions of the second part and presents the system diagrams. The second part is a detailed analysis based upon an empirically derived random process model arrived at from specifications and measured data provided by the technical officer.

Gray, R. M.↗

NASA NTRS1975

Snow survey and vegetation growth in high mountains (Swiss Alps) and additional ERTS investigations in Switzerland

The author has identified the following significant results. Two different methods, an analog and a digital one, have been developed for rapid and accurate mapping of the areal extent and changes in snow cover in high mountains. The quick-look method is based on individual visual control of each image using a photo quantizer which provides exact references for density slicing with high resolution lith-film. The digital snow classification system is based on discriminant analysis with the data of the four multispectral bands as variables and contains all preprocessing, feature extraction, and mapping steps for an operational application. Two different sets of sampling groups were established which apply to different conditions of snow cover. The first one serves for the normal situation with a uniform dry and new cover. The second one serves for situations with partly thawing and/or frozen snow.

Haefner, H.↗

NASA NTRS1975

Radiometric performance of the Viking Mars lander cameras

The Viking lander cameras feature an array of 12 silicon photodiodes for electronic focus selection and multispectral imaging. Comparisons of absolute radiometric calibrations of the four cameras selected for the mission to Mars with performance predictions based on their design data revealed minor discrepancies. These discrepancies were caused primarily by the method used to calibrate the photosensor array and apparently also from light reflections internal to the array. The sensitivity and dynamic range of all camera channels are found to be sufficient for high quality pictures, providing that the commandable gains and offsets can be optimized for the scene radiance; otherwise, the quantization noise may be too high or the dynamic range too low for an adequate characterization of the scene.

Huck, F. O.↗

NASA NTRS1975

Digital simulation of a communication link for Pioneer Saturn Uranus atmospheric entry probe, part 1

A digital simulation study is presented for a candidate modulator/demodulator design in an atmospheric scintillation environment with Doppler, Doppler rate, and signal attenuation typical of the conditions of an outer planet atmospheric probe. The simulation results indicate that the mean channel error rate with and without scintillation are similar to theoretical characterizations of the link. The simulation gives information for calculating other channel statistics and generates a quantized symbol stream on magnetic tape from which error correction decoding is analyzed. Results from the magnetic tape data analyses are also included. The receiver and bit synchronizer are modeled in the simulation at the level of hardware component parameters rather than at the loop equation level and individual hardware parameters are identified. The atmospheric scintillation amplitude and phase are modeled independently. Normal and log normal amplitude processes are studied. In each case the scintillations are low pass filtered. The receiver performance is given for a range of signal to noise ratios with and without the effects of scintillation. The performance is reviewed for critical reciever parameter variations.

Hinrichs, C. A.↗

NASA NTRS1974

Quantum limit studies in single-crystal and pyrolytic graphite

The occupied regions of momentum space in graphite are confined to very elongated volumes near the hexagonal Brillouin zone edges. The elongation is along the hexagonal axis (c axis) so that cross-sectional areas perpendicular to that axis are very small. Hence, when magnetic fields are applied parallel to the c axis only the n = 0 Landau levels remain below the Fermi energy for fields above 7 T (Woollam, 1971). The energy bands in graphite can be described by a set of seven parameters (McClure, 1971) (including the Fermi energy as a parameter). In a quantizing magnetic field the Landau levels are described by a secular equation determined by diagonalizing the Hamiltonian (McClure, 1960). A major unusual feature for the levels along the Brillouin zone edge is that the n = 0 Landau level for electrons is independent of magnetic field, while that for holes is field dependent.

Woollam, J. A.↗

NASA NTRS1974

Summary of flight performance of the Skylab Earth Resources Experiment Package /EREP/

A group of six remote sensor systems (sensing visible, infrared, and microwave radiation) known as the Earth Resources Experiment Package (EREP) was flown on the NASA Skylab spacecraft to furnish data to numerous investigators in the earth sciences and in technology assessment. Inflight sensor performance in three categories (functional, geometric, and radiometric) was evaluated using: (1) ground measurements of surface, atmospheric, and illumination parameters; (2) ground deployment and operation of microwave receivers and transponders to monitor and excite the active EREP sensors; (3) measurement of surface and atmospheric parameters by instrumented aircraft on underflights of Skylab passes; and (4) analysis of the actual flight data. This resulted in identification and correction of anomalous sensor operation, quantization of geometric distortions or aberrations, improvement or confirmation of calibrations, and determination of sensitivity, accuracy, and stability of the sensors.

Potter, A. E.↗

NASA NTRS1974

Quantum descriptions of singularities leading to pair creation

A class of cosmological models is analyzed which provide a mathematically convenient (but idealized) description of a cosmological singularity that develops into a pair creation epoch and terminates in an adiabatic expansion with redshifting particle energies. This class of models was obtained by Gowdy (1971, 1974) as a set of exact solutions of the classical empty space Einstein equations describing inhomogeneous universes populated only by gravitational waves. It is shown that these models can be used to exhibit simplified models of quantized gravitational fields, and that a quantum description can be given arbitrarily near a cosmological singularity. Graviton pair creation occurs, and can be seen to convert anisotropic expansion rates into the energy of graviton pairs.

Misner, C. W.↗

NASA NTRS1974

Hardware realization of sampled-data controllers

This paper examines the hardware implementation process for digital controllers (filters), beginning with the desired z-domain transfer function of the digital compensator and ending in the selection of a hardware realization scheme. The final hardware realization is shown to be affected by quantization noise, dynamic range considerations, limit cycles, coefficient roundoff, and filter structure. A design example is included to illustrate the implementation process for a digital rate filter for vehicle control of the space shuttle. This paper develops open-loop techniques which may be extended to the closed-loop case.

Nagle, H. T., Jr.↗

NASA NTRS1974

Quantum mechanical streamlines. I - Square potential barrier

Exact numerical calculations are made for scattering of quantum mechanical particles hitting a square two-dimensional potential barrier (an exact analog of the Goos-Haenchen optical experiments). Quantum mechanical streamlines are plotted and found to be smooth and continuous, to have continuous first derivatives even through the classical forbidden region, and to form quantized vortices around each of the nodal points. A comparison is made between the present numerical calculations and the stationary wave approximation, and good agreement is found between both the Goos-Haenchen shifts and the reflection coefficients. The time-independent Schroedinger equation for real wavefunctions is reduced to solving a nonlinear first-order partial differential equation, leading to a generalization of the Prager-Hirschfelder perturbation scheme. Implications of the hydrodynamical formulation of quantum mechanics are discussed, and cases are cited where quantum and classical mechanical motions are identical.

Hirschfelder, J. O.↗

NASA NTRS1974

Quaternion wave equations in curved space-time

The quaternion formulation of relativistic quantum theory is extended to include curvilinear coordinates and curved space-time in order to provide a framework for a unified quantum/gravity theory. Six basic quaternion fields are identified in curved space-time, the four-vector basis quaternions are identified, and the necessary covariant derivatives are obtained. Invariant field equations are derived, and a general invertable coordinate transformation is developed. The results yield a way of writing quaternion wave equations in curvilinear coordinates and curved space-time as well as a natural framework for solving the problem of second quantization for gravity.

Edmonds, J. D., Jr.↗

NASA NTRS1976

Partition function corrections

The vibration-rotation interaction coupling in diatomic molecules is analyzed and first-order expressions for the energy levels are deduced. Corrections to the partition function to account for this coupling are derived. The effects of long-range intermolecular forces due to induced dipole-induced dipole interactions, dipole-induced dipole interactions, charge-dipole interactions, and charge-charge interactions are considered. London's quantized oscillator model of the induced dipole-induced dipole interaction is developed. The partition function including effects of such dispersion forces is derived and is shown to lead to the virial equation of state. For a model combining the hard sphere and long-range attractive type potentials, this is found to lead to the van der Waals equation of state. The equation of state near the critical point is presented in reduced form (thermodynamic variables expressed in units of critical point values). Finally, approximate corrections to the electronic partition functions are derived to account for perturbations of excited electronic states induced by neighboring neutral particles, heavy ions, and fast electron collisions.

Source record↗

NASA NTRS1976

Magnetic field generated resistivity maximum in graphite

In zero magnetic field, B, the electrical resistivity, rho(O,T) of highly oriented pyrolytic (polycrystalline) graphite drops smoothly with decreasing T, becoming constant below 4 K. However, in a fixed applied magnetic field B, the resistivity rho(B,T) goes through a maximum as a function of T, with larger maximum for larger B. The temperature of the maximum increases with B, but saturates to a constant value near 25 K (exact T depends on sample) at high B. In single crystal graphite a maximum in rho(B,T) as a function of T is also present, but has the effects of Landau level quantization superimposed. Several possible explanations for the rho(B,T) maximum are proposed, but a complete explanation awaits detailed calculations involving the energy band structure of graphite, and the particular scattering mechanisms involved.

Wollam, J. A.↗