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Efficient Two-Dimensional-FFT Program

Program computes 64 X 64-point fast Fourier transform in less than 17 microseconds. Optimized 64 X 64 Point Two-Dimensional Fast Fourier Transform combines performance of real- and complex-valued one-dimensional fast Fourier transforms (FFT's) to execute two-dimensional FFT and coefficients of power spectrum. Coefficients used in many applications, including analyzing spectra, convolution, digital filtering, processing images, and compressing data. Source code written in C, 8086 Assembly, and Texas Instruments TMS320C30 Assembly languages.

Miko, J.↗

Efficient demultiplexing algorithm for noncontiguous carriers

A channel separation algorithm for the frequency division multiple access/time division multiplexing (FDMA/TDM) scheme is presented. It is shown that implementation using this algorithm can be more effective than the fast Fourier transform (FFT) algorithm when only a small number of carriers need to be selected from many, such as satellite Earth terminals. The algorithm is based on polyphase filtering followed by application of a generalized Walsh-Hadamard transform (GWHT). Comparison of the transform technique used in this algorithm with discrete Fourier transform (DFT) and FFT is given. Estimates of the computational rates and power requirements to implement this system are also given.

Thanawala, A. A.↗

Predicting Ecologically Important Vegetation Variables from Remotely Sensed Optical/Radar Data Using Neural Networks

A number of satellite sensor systems will collect large data sets of the Earth's surface during NASA's Earth Observing System (EOS) era. Efforts are being made to develop efficient algorithms that can incorporate a wide variety of spectral data and ancillary data in order to extract vegetation variables required for global and regional studies of ecosystem processes, biosphere-atmosphere interactions, and carbon dynamics. These variables are, for the most part, continuous (e.g. biomass, leaf area index, fraction of vegetation cover, vegetation height, vegetation age, spectral albedo, absorbed photosynthetic active radiation, photosynthetic efficiency, etc.) and estimates may be made using remotely sensed data (e.g. nadir and directional optical wavelengths, multifrequency radar backscatter) and any other readily available ancillary data (e.g., topography, sun angle, ground data, etc.). Using these types of data, neural networks can: 1) provide accurate initial models for extracting vegetation variables when an adequate amount of data is available; 2) provide a performance standard for evaluating existing physically-based models; 3) invert multivariate, physically based models; 4) in a variable selection process, identify those independent variables which best infer the vegetation variable(s) of interest; and 5) incorporate new data sources that would be difficult or impossible to use with conventional techniques. In addition, neural networks employ a more powerful and adaptive nonlinear equation form as compared to traditional linear, index transformations, and simple nonlinear analyses. These neural networks attributes are discussed in the context of the authors' investigations of extracting vegetation variables of ecological interest.

Kimes, Daniel S.↗

Under the Weather: Space Weather. The Magnetic Field of the Heliosphere

Normally, only people in the far north can enjoy the dancing beauty of the aurora borealis; however, an intense collision of charged solar particles with the Earth's magnetic field can magnify the Northern Lights so much that they are visible in the southern United States. Behind the light show lies enough flux of energetic particles carried by solar wind to render our planet uninhabitable. The Earth's magnetic field, also known as the magnetosphere, is the only thing that shields us from the Sun. Even the magnetosphere cannot fully guard us from the wrath of the Sun. In March 1989, a powerful solar flare hit Earth with such energy that it burned out transformers in Quebec's electrical grid, plunging Quebec and the eastern United States into darkness for more than 9 hours. Northern lights and energy grid overloads are not the only ways that a solar wind can affect us. A solar storm in July 1999 interrupted radio broadcasts. Solar activity can disorient radars and satellite sensors, break up cell phone connections, and threaten the safety of astronauts. A large bombardment of solar particles can even reduce the amount of ozone in the upper atmosphere. Magnetohydrodynamics (MHD), the study of magnetic fields in magnetized plasmas, can help scientists predict, and therefore prepare for, the harmful side effects of solar weather in the magnetosphere.

Roberts, Aaron↗

Analysis of Dynamic Data from Supersonic Retropropulsion Experiments in NASA Langley's Unitary Plan Wind Tunnel

Recent experimental supersonic retropropulsion tests were conducted at the NASA Langley Research Center Unitary Plan Wind Tunnel Test Section 2 for a range of Mach numbers from 2.4 to 4.6. A 5-inch 70-degree sphere-cone forebody model with a 10-inch cylindrical aftbody experimental model was used which is capable of multiple retrorocket configurations. These configurations include a single central nozzle on the center point of the forebody, three nozzles at the forebody half-radius, and a combination of the first two configurations with no jets being plugged. A series of measurements were achieved through various instrumentation including forebody and aftbody pressure, internal pressures and temperatures, and high speed Schlieren visualization. Specifically, several high speed pressure transducers on the forebody and in the plenum were implemented to look at unsteady flow effects. The following work focuses on analyzing frequency traits due to the unsteady flow for a range of thrust coefficients for single, tri, and quad-nozzle test cases at freestream Mach 4.6 and angle of attack ranging from -8 degrees to +20 degrees. This analysis uses Matlab s fast Fourier transform, Welch's method (modified average of a periodogram), to create a power spectral density and analyze any high speed pressure transducer frequency traits due to the unsteady flow.

Codoni, Joshua R.↗

TransFormers for Ensuring Long-Term Operations in Lunar Extreme Environments

"Surviving Extreme Space Environments" (EE) is one of NASA's Space Technology Grand Challenges. Power generation and thermal control are the key survival ingredients that allow a robotic explorer to cope with the EE using resources available to it, for example, by harvesting the local solar energy or by utilizing an onboard radioisotope thermoelectric generator (RTG). TransFormers (TFs) are a new technology concept designed to transform a localized area within a harsh extreme environment into a survivable micro-environment by projecting energy to the precise location where robots or humans operate. For example, TFs placed at a location on the rim of Shackleton Crater, which is illuminated by solar radiation for most of the year, would be able to reflect solar energy onto robots operating in the dark cold crater. TFs utilize a shape transformation mechanism to un-fold from a compact volume to a large reflective surface, and to control how much-and where-the energy is projected, and by adjusting for the changing position of the sun. TFs would enable in-situ resource utilization (ISRU) activities within locations of high interest that would normally be unreachable because of their extreme environment

ISRU↗

Multidimensional Generalized Functions in Aeroacoustics and Fluid Mechanics: Basic Concepts and Operations - Part 1

This paper is the first part of a three part tutorial on multidimensional generalized functions (GFs) and their applications in aeroacoustics and fluid mechanics. The subject is highly fascinating and essential in many areas of science and, in particular, wave propagation problems. In this tutorial, we strive to present rigorously and clearly the basic concepts and the tools that are needed to use GFs in applications effectively and with ease. We give many examples to help the readers in understanding the mathematical ideas presented here. The first part of the tutorial is on the basic concepts of GFs. Here we define GFs, their properties and some common operations on them. We define the important concept of generalized differentiation and then give some interesting elementary and advanced examples on Green's functions and wave propagation problems. Here, the analytic power of GFs in applications is demonstrated with ease and elegance. Part 2 of this tutorial is on the diverse applications of generalized derivatives (GDs). Part 3 is on generalized Fourier transformations and some more advanced topics. One goal of writing this tutorial is to convince readers that, because of their powerful operational properties, GFs are absolutely essential and useful in engineering and physics, particularly in aeroacoustics and fluid mechanics.

Farassat, Fereidoun↗

A series expansion of the acoustic power radiated from planar sources

A series expansion in ascending powers of the wavenumber k is derived for the acoustic power delivered by baffled or unbaffled planar sources. This series provides a relatively simple means of derving expressions for the power radiated by a baffled source with a known velocity distribution and can be used for unbaffled plates when the velocity field outside the plate is also known. The terms in the series are calculated from the moments of this velocity distribution in the plane containing the source. If these moments are written as derivaties in wavenumber space, it is shown that a MacLaurin expansion of the Fourier transformed velocity provides an easy technique for computing the first few terms of the acoustic power. Examples are provided for baffled, rectangular plates with various boundary conditions. The arbirarily shaped plate with free boundaries is particularly interesting. It is proven that the volume flow across it surface must be zero and as a result corner and edge mode radiation cannot exist for this kind of source.

Willams, E. G.↗

Numerical comparisons of nonlinear convergence accelerators

As part of a continuing program of numerical tests of convergence accelerators, the iterated Aitken's Delta-squared method, Wynn's epsilon algorithm, Brezinski's theta algorithm, and Levin's u transform are compared on a broad range of test problems: linearly convergence alternating, monotone, and irregular-sign series, logarithmically convergent series, power method and Bernoulli method sequences, alternating and monotone asymptotic series, and some perturbation series arising in applications. In each category either the epsilon algorithm or the u transform gives the best results of the four methods tested. In some cases differences among methods are slight, and in others they are quite striking.

Smith, D. A.↗

Laser power transmission.

Description of studies which have led to the design of a conceptual device in which the limitation of transforming heat into coherent radiation can be examined. By exploring the basic thermodynamic relationships controlling the operation of this device, it is concluded that a closed-cycle gasdynamic laser is possible in which all of the shaft energy supplied can be turned into laser radiation. Hence, it is possible in principle to convert heat into coherent radiation with approximately the same efficiency with which heat may be converted into electricity. By modifying the closed-cycle-gasdynamic-laser system, this system can be operated in reverse and the incoming radiation may be used to pump the gas in the loop so that shaft power can be extracted. By carefully controlling the temperature distribution in this machine, laser energy can be converted into useful shaft energy with an efficiency approaching 1 .

Ahlstrom, H. G.↗

Description of a 20 Kilohertz power distribution system

A single phase, 440 VRMS, 20 kHz power distribution system with a regulated sinusoidal wave form is discussed. A single phase power system minimizes the wiring, sensing, and control complexities required in a multi-sourced redundantly distributed power system. The single phase addresses only the distribution link; mulitphase lower frequency inputs and outputs accommodation techniques are described. While the 440 V operating potential was initially selected for aircraft operating below 50,000 ft, this potential also appears suitable for space power systems. This voltage choice recognizes a reasonable upper limit for semiconductor ratings, yet will direct synthesis of 220 V, 3 power. A 20 kHz operating frequency was selected to be above the range of audibility, minimize the weight of reactive components, yet allow the construction of single power stages of 25 to 30 kW. The regulated sinusoidal distribution system has several advantages. With a regulated voltage, most ac/dc conversions involve rather simple transformer rectifier applications. A sinusoidal distribution system, when used in conjunction with zero crossing switching, represents a minimal source of EMI. The present state of 20 kHz power technology includes computer controls of voltage and/or frequency, low inductance cable, current limiting circuit protection, bi-directional power flow, and motor/generator operating using standard induction machines. A status update and description of each of these items and their significance is presented.

Hansen, I. G.↗

Description of a 20 kilohertz power distribution system

A single phase, 440 VRMS, 20 kHz power distribution system with a regulated sinusoidal wave form is discussed. A single phase power system minimizes the wiring, sensing, and control complexities required in a multi-sourced redundantly distributed power system. The single phase addresses only the distribution links multiphase lower frequency inputs and outputs accommodation techniques are described. While the 440 V operating potential was initially selected for aircraft operating below 50,000 ft, this potential also appears suitable for space power systems. This voltage choice recognizes a reasonable upper limit for semiconductor ratings, yet will direct synthesis of 220 V, 3 power. A 20 kHz operating frequency was selected to be above the range of audibility, minimize the weight of reactive components, yet allow the construction of single power stages of 25 to 30 kW. The regulated sinusoidal distribution system has several advantages. With a regulated voltage, most ac/dc conversions involve rather simple transformer rectifier applications. A sinusoidal distribution system, when used in conjunction with zero crossing switching, represents a minimal source of EMI. The present state of 20 kHz power technology includes computer controls of voltage and/or frequency, low inductance cable, current limiting circuit protection, bi-directional power flow, and motor/generator operating using standard induction machines. A status update and description of each of these items and their significance is presented.

Hansen, I. G.↗

Onsite testing of pressure sampling

Portable test instrument containing controller, pressure port identification, 5-V power source for transducer excitation, and digital voltmeter to test pressure sampling valves completely, including leak and plug check before, during, or after installation in any location or environment. Controller comprises 117/24-Vac 100-watt transformer, bridge rectifier, capacitive-discharge stepper, and constant voltage source for homing sampling valve. It also includes 5-V regulated power supply and bipolar digital voltmeter having 10-uV resolution.

Mallory, R.↗

Lossy radial diffusion of relativistic Jovian electrons

The radial diffusion equation with synchrotron losses was solved by the Laplace transform method for near-equatorially mirroring relativistic electrons. The evolution of a power law distribution function was found and the characteristics of synchrotron burn-off are stated in terms of explicit parameters for an arbitrary diffusion coefficient. Emissivity from the radiation belts of Jupiter was studied. Asymptotic forms for the distribution in the strong synchrotron loss regime are provided.

Barbosa, D. D.↗

Lossy radial diffusion of relativistic Jovian electrons

The radial diffusion equation with synchrotron losses is solved by the Laplace-transform method for near equatorially mirroring relativistic electrons. The evolution of a power-law distribution function is found, and the characteristics of synchrotron burnoff are stated in terms of explicit parameters for an arbitrary diffusion coefficient of a specific form. The peaking of the 10.4-cm volume emissivity from Jupiter at an L shell of about 1.8 provides an estimate of the diffusion coefficient in the radiation belts; one value is suggested as the appropriate modification, for an equatorial field strength of 4.2 G, of the Birmingham et al. (1974) result. Nonsynchrotron losses are included phenomenologically; from the phase-space densities reported by McIlwain and Fillius (1975), the particle lifetime is estimated. Asymptotic forms for the distribution in the strong synchrotron loss regime are provided.

Barbosa, D. D.↗

The effective penetration distance of ultrahigh-energy electrons and photons traversing a cosmic blackbody photon gas

The effective average energy loss for an energetic (at least about 10 to the 15th power eV) particle traversing the microwave background radiation is evaluated. Electron-photon transformations by Compton scattering and pair production (in photon-photon collisions) are computed, with the energy loss considered to be carried away by the least energetic of the outgoing particles. Considering the most energetic of the outgoing particles as the high-energy particle, the relative probability and mean time for the particle to be a photon or electron (or positron) is evaluated. The effects of synchrotron losses for electrons and positrons are emphasized and compared with Compton losses to determine a critical energy (for given magnetic field) above which synchrotron losses dominate. Magnetic deflections are also treated for the case where the magnetic field is disordered, having a characteristic 'cell' size.

Gould, R. J.↗