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Fermat number transformation convolutes two digital data sequences. Very-large-scale integration (VLSI) applications, such as image and radar signal processing, X-ray reconstruction, and spectrum shaping, linear convolution of two digital data sequences of arbitrary lenghts accomplished using Fermat number transform (ENT).
New procedures and software have been developed for geometric transformation of images to support digital cartography of the planets. The procedures involve the correction of spacecraft camera orientation of each image with the use of ground control and the transformation of each image to a Sinusoidal Equal-Area map projection with an algorithm which allows the number of transformation calculations to vary as the distortion varies within the image. When the distortion is low in an area of an image, few transformation computations are required, and most pixels can be interpolated. When distortion is extreme, the location of each pixel is computed. Mosaics are made of these images and stored as digital databases. Completed Sinusoidal databases may be used for digital analysis and registration with other spatial data. They may also be reproduced as published image maps by digitally transforming them to appropriate map projections.
A technique devised using a vector transformation of LANDSAT digital data to indicate when vegetation is undergoing moisture stress is described. A relation established between the remote sensing-based criterion (the Green Index Number) and a ground-based criterion (Crop Moisture Index) is discussed.
A method is developed for relating scene digital counts among several images of the same scene by identifying radiometric control sets with mean reflectances that are basically constant. The average digital-count values of the control sets are utilized to compute linear transforms that relate digital count values between images. Two Landsat TM images are studied by means of the technique using simulations of a wide range of atmospheric conditions. In the visible and near-IR bands the algorithm effectively adjusts the surface reflectance for the effects of relative atmospheric differences to within 1 percent. The proposed method is found to be an effective relative correction procedure that can be used when atmospheric optical-depth data and calibration coefficients are not available.
One of the main heritage tools used in scientific and engineering data spectrum analysis is the Fourier Integral Transform and its high performance digital equivalent - the Fast Fourier Transform (FFT). The FFT is particularly useful in two-dimensional (2-D) image processing (FFT2) within optical systems control. However, timing constraints of a fast optics closed control loop would require a supercomputer to run the software implementation of the FFT2 and its inverse, as well as other image processing representative algorithm, such as numerical image folding and fringe feature extraction. A laboratory supercomputer is not always available even for ground operations and is not feasible for a night project. However, the computationally intensive algorithms still warrant alternative implementation using reconfigurable computing technologies (RC) such as Digital Signal Processors (DSP) and Field Programmable Gate Arrays (FPGA), which provide low cost compact super-computing capabilities. We present a new RC hardware implementation and utilization architecture that significantly reduces the computational complexity of a few basic image-processing algorithm, such as FFT2, image folding and phase diversity for the NASA Solar Viewing Interferometer Prototype (SVIP) using a cluster of DSPs and FPGAs. The DSP cluster utilization architecture also assures avoidance of a single point of failure, while using commercially available hardware. This, combined with the control algorithms pre-hardware optimization, or the first time allows construction of image-based 800 Hertz (Hz) optics closed control loops on-board a spacecraft, based on the SVIP ground instrument. That spacecraft is the proposed Earth Atmosphere Solar Occultation Imager (EASI) to study greenhouse gases CO2, C2H, H2O, O3, O2, N2O from Lagrange-2 point in space. This paper provides an advanced insight into a new type of science capabilities for future space exploration missions based on on-board image processing for control and for robotics missions using vision sensors. It presents a top-level description of technologies required for the design and construction of SVIP and EASI and to advance the spatial-spectral imaging and large-scale space interferometry science and engineering.
One of the main heritage tools used in scientific and engineering data spectrum analysis is the Fourier Integral Transform and its high performance digital equivalent - the Fast Fourier Transform (FFT). The Fourier view of nonlinear mechanics that had existed for a long time, and the associated FFT (fairly recent development), carry strong a-priori assumptions about the source data, such as linearity and of being stationary. Natural phenomena measurements are essentially nonlinear and nonstationary. A very recent development at the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC), known as the Hilbert-Huang Transform (HHT) proposes a novel approach to the solution for the nonlinear class of spectrum analysis problems. Using the Empirical Mode Decomposition (EMD) followed by the Hilbert Transform of the empirical decomposition data (HT), the HHT allows spectrum analysis of nonlinear and nonstationary data by using an engineering a-posteriori data processing, based on the EMD algorithm. This results in a non-constrained decomposition of a source real value data vector into a finite set of Intrinsic Mode Functions (IMF) that can be further analyzed for spectrum interpretation by the classical Hilbert Transform. This paper describes phase one of the development of a new engineering tool, the HHT Data Processing System (HHTDPS). The HHTDPS allows applying the "T to a data vector in a fashion similar to the heritage FFT. It is a generic, low cost, high performance personal computer (PC) based system that implements the HHT computational algorithms in a user friendly, file driven environment. This paper also presents a quantitative analysis for a complex waveform data sample, a summary of technology commercialization efforts and the lessons learned from this new technology development.
One of the main heritage tools used in scientific and engineering data spectrum analysis is the Fourier Integral Transform and its high performance digital equivalent - the Fast Fourier Transform (FFT). Both carry strong a-priori assumptions about the source data, such as linearity, of being stationary, and of satisfying the Dirichlet conditions. A recent development at the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC), known as the Hilbert-Huang Transform (HHT), proposes a novel approach to the solution for the nonlinear class of spectrum analysis problems. Using a-posteriori data processing based on the Empirical Mode Decomposition (EMD) sifting process (algorithm), followed by the normalized Hilbert Transform of the decomposition data, the HHT allows spectrum analysis of nonlinear and nonstationary data. The EMD sifting process results in a non-constrained decomposition of a source real value data vector into a finite set of Intrinsic Mode Functions (IMF). These functions form a near orthogonal adaptive basis, a basis that is derived from the data. The IMFs can be further analyzed for spectrum interpretation by the classical Hilbert Transform. A new engineering spectrum analysis tool using HHT has been developed at NASA GSFC, the HHT Data Processing System (HHT-DPS). As the HHT-DPS has been successfully used and commercialized, new applications post additional questions about the theoretical basis behind the HHT and EMD algorithms. Why is the fastest changing component of a composite signal being sifted out first in the EMD sifting process? Why does the EMD sifting process seemingly converge and why does it converge rapidly? Does an IMF have a distinctive structure? Why are the IMFs near orthogonal? We address these questions and develop the initial theoretical background for the HHT. This will contribute to the developments of new HHT processing options, such as real-time and 2-D processing using Field Programmable Array (FPGA) computational resources, enhanced HHT synthesis, and broaden the scope of HHT applications for signal processing.
One of the main traditional tools used in scientific and engineering data spectral analysis is the Fourier Integral Transform and its high performance digital equivalent - the Fast Fourier Transform (FFT). Both carry strong a-priori assumptions about the source data, such as being linear and stationary, and of satisfying the Dirichlet conditions. A recent development at the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC), known as the Hilbert-Huang Transform (HHT), proposes a novel approach to the solution for the nonlinear class of spectral analysis problems. Using a-posteriori data processing based on the Empirical Mode Decomposition (EMD) sifting process (algorithm), followed by the normalized Hilbert Transform of the decomposed data, the HHT allows spectral analysis of nonlinear and nonstationary data. The EMD sifting process results in a non-constrained decomposition of a source real-value data vector into a finite set of Intrinsic Mode Functions (IMF). These functions form a nearly orthogonal derived from the data (adaptive) basis. The IMFs can be further analyzed for spectrum content by using the classical Hilbert Transform. A new engineering spectral analysis tool using HHT has been developed at NASA GSFC, the HHT Data Processing System (HHT-DPS). As the HHT-DPS has been successfully used and commercialized, new applications pose additional questions about the theoretical basis behind the HHT and EMD algorithms. Why is the fastest changing component of a composite signal being sifted out first in the EMD sifting process? Why does the EMD sifting process seemingly converge and why does it converge rapidly? Does an IMF have a distinctive structure? Why are the IMFs nearly orthogonal? We address these questions and develop the initial theoretical background for the HHT. This will contribute to the development of new HHT processing options, such as real-time and 2-D processing using Field Programmable Gate Array (FPGA) computational resources,
In the Large Area Crop Inventory Experiment a technique was devised using a vector transformation of Landsat digital data to indicate when vegetation is undergoing moisture stress. A relation was established between the remote-sensing-based criterion (the Green Index Number) and a ground-based criterion (Crop Moisture Index).
Digital Engineering is a transformative strategy that leverages an integrated model-based approach to improve communication, decision making, design understanding, and acquisition efficiency of system development. As modern systems are derived from pre-existing systems, harvesting expert knowledge from proven systems in a useful, model-based way will reduce the experiential learning and cognition required for new system development, contributing to a Digital Engineering transformation. Motivated by performance gains observed during a multi-year, sequential development activity, this survey reviews knowledge, architecture, and pattern literature to establish a framework for research of architectural methods for expert knowledge identification and description using Model Based System Engineering. The multi-year sequential development activity is offered as the experimental system of interest for this research. This work aims to enable a digital engineering strategy that improves concept phase decision making, accelerates knowledge acquisition from lessons learned repositories, and eases the burden of generational knowledge loss.
Digital Engineering is a transformative strategy that leverages an integrated model-based approach to improve communication, decision making, design understanding, and acquisition efficiency of system development. As modern systems are derived from pre-existing systems, harvesting tacit knowledge from existing systems in a useful, model-based way will reduce the experiential learning and cognition required for new system development, contributing to a Digital Engineering transformation. This study enables such a technique by demonstrating the use of architectural theory in expressing tacit knowledge from existing systems and presenting that knowledge according to the model-based view offered by the Functional Architecture of Systems methodology. By validating the functional information expressed by the design pattern, this work solidifies design patterns as a critical component of a technical architecture and proposes a functional architecture viewpoint for describing mined knowledge in a usable, model-based, way suitable for archival in a modern knowledge management system.
With present concern for ecological sustainability ever increasing, it is desirable to model the composition of Earth s upper atmosphere accurately with regards to certain helpful and harmful chemicals, such as greenhouse gases and ozone. The microwave limb sounder (MLS) is an instrument designed to map the global day-to-day concentrations of key atmospheric constituents continuously. One important component in MLS is the spectrometer, which processes the raw data provided by the receivers into frequency-domain information that cannot only be transmitted more efficiently, but also processed directly once received. The present-generation spectrometer is fully analog. The goal is to include a fully digital spectrometer in the next-generation sensor. In a digital spectrometer, incoming analog data must be converted into a digital format, processed through a Fourier transform, and finally accumulated to reduce the impact of input noise. While the final design will be placed on an application specific integrated circuit (ASIC), the building of these chips is prohibitively expensive. To that end, this design was constructed on a field-programmable gate array (FPGA). A family of state-of-the-art digital Fourier transform spectrometers has been developed, with a combination of high bandwidth and fine resolution. Analog signals consisting of radiation emitted by constituents in planetary atmospheres or galactic sources are downconverted and subsequently digitized by a pair of interleaved analog-to-digital converters (ADCs). This 6-Gsps (gigasample per second) digital representation of the analog signal is then processed through an FPGA-based streaming fast Fourier transform (FFT). Digital spectrometers have many advantages over previously used analog spectrometers, especially in terms of accuracy and resolution, both of which are particularly important for the type of scientific questions to be addressed with next-generation radiometers.
A high pressure, high-temperature turbine test facility constructed for use in turbine cooling research is described. Several recently developed temperature and pressure measuring techniques are used in this facility. The measurement techniques, their status, previous applications and some results are discussed. Noncontact surface temperature measurements are made by optical methods. Radiation pyrometry principles combined with photoelectric scanning are used for rotating components and infrared photography for stationary components. Contact (direct) temperature and pressure measurements on rotating components are expected to be handled with an 80 channel rotary data package which mounts on and rotates with the turbine shaft at speeds up to 17,500 rpm. The data channels are time-division multiplexed and converted to digital words in the data package. A rotary transformer couples power and digital data to and from the shaft.
A high pressure, high-temperature turbine test facility is being constructed at the NASA Lewis Research Center for use in turbine cooling research. Several recently developed temperature and pressure measuring techniques will be used in this facility. This paper describes these measurement techniques, their status, previous applications and some results. Noncontact surface temperature measurements will be made by optical methods. Radiation pyrometry principles combined with photoelectric scanning will be used for rotating components and infrared photography for stationary components. Contact (direct) temperature and pressure measurements on rotating components will be handled with an 80-channel rotary data package which mounts on and rotates with the turbine shaft at speeds up to 17,500 rpm. The data channels are time-division multiplexed and converted to digital words in the data package. A rotary transformer couples power and digital data to and from the shaft.
The effects of the seasonal variation of illumination over digital processing of LANDSAT images are evaluated. Two sets of LANDSAT data referring to the orbit 150 and row 28 were selected with illumination parameters varying from 43 deg to 64 deg for azimuth and from 30 deg to 36 deg for solar elevation respectively. IMAGE-100 system permitted the digital processing of LANDSAT data. Original images were transformed by means of digital filtering so as to enhance their spatial features. The resulting images were used to obtain an unsupervised classification of relief units. Topographic variables (declivity, altitude, relief range and slope length) were used to identify the true relief units existing on the ground. The LANDSAT over pass data show that digital processing is highly affected by illumination geometry, and there is no correspondence between relief units as defined by spectral features and those resulting from topographic features.
An apparatus for image processing comprising a camera for receiving an original visual image and transforming the original visual image into an analog image, a first converter for transforming the analog image of the camera to a digital image, a processor having a single flow architecture for receiving the digital image and producing, with a single algorithm, an output image, a second converter for transforming the digital image of the processor to an analog image, and a viewer for receiving the analog image, transforming the analog image into a transformed visual image for observing the transformations applied to the original visual image. The processor comprises one or more subprocessors for the parallel reception of a digital image for producing an output matrix of the transformed visual image. More particularly, the processor comprises a plurality of subprocessors for receiving in parallel and transforming the digital image for producing a matrix of the transformed visual image, and an output interface means for receiving the respective portions of the transformed visual image from the respective subprocessor for producing an output matrix of the transformed visual image.
The paper reports the two observing programs conducted to compare two techniques which have been proposed as methods for performing the requisite Fourier transformations in very large multichannel spectrum analysers (MCSA): the direct digital FFT and optical transform processor. The details of the observations at NRAO utilizing a direct digital FFT are given. A description of the NAIC, Arecibo observations utilizing an optical processor at the Environmental Research Institute of Michigan (ERIM) and a microdensitometer at Electromagnetics System Laboratories (ESL) is presented. For both observing programs, statistical analysis of the power spectra produced by the nonreal-time MCSAs (or post-processing) was accomplished.
Speed requirements have been, and will continue to be, a major consideration in the design of hardware to implement digital signal processing functions like digital filters and transforms like the DFT and DCT. The conventional approach is to increase speed by adding hardware and increasing chip area. The real challenge is to save chip area while still maintaining high speed performance. The approach we propose is based on the distributed arithmetic implementation (DA) of digital filters. The improvement is based on two observations. Firstly, a single memory element can replace several identical memory elements in a fully parallel DA implementation. Secondly, truncation or rounding may be introduced into the computation at strategic points without increasing error unduly. Both of these approaches can be used to attain area savings without impairing speed of operation.