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NASA NTRS1983

A parallel architecture for digital filtering using Fermat number transforms

In this correspondence, a parallel architecture is developed to compute the linear convolution of two sequences of arbitrary lengths using the Fermat number transform (FNT). In particular, a pipeline structure is designed to compute a 128-point FNT. In this FNT, only additions and bit rotations are required. The overlap-save method is generalized for the FNT to realize a digital filter of arbitrary length. The generalized overlap-save method alleviates the usual dynamic range limitation of FNT's of long transform lengths. A parallel architecture is developed to realize this type of overlap-save method using one FNT and several inverse FNT's of 128 points. Its architecture is regular, simple, and flexible, and therefore naturally suitable for VLSI implementation.

Truong, T. K.↗

NASA NTRS1984

Application of nonlinear transformations to automatic flight control

The theory of transformations of nonlinear systems to linear ones is applied to the design of an automatic flight controller for the UH-1H helicopter. The helicopter mathematical model is described and it is shown to satisfy the necessary and sufficient conditions for transformability. The mapping is constructed, taking the nonlinear model to canonical form. The performance of the automatic control system in a detailed simulation on the flight computer is summarized.

Meyer, G.↗

NASA NTRS1984

Digital SAR processing using a fast polynomial transform

A new digital processing algorithm based on the fast polynomial transform is developed for producing images from Synthetic Aperture Radar data. This algorithm enables the computation of the two dimensional cyclic correlation of the raw echo data with the impulse response of a point target, thereby reducing distortions inherent in one dimensional transforms. This SAR processing technique was evaluated on a general-purpose computer and an actual Seasat SAR image was produced. However, regular production runs will require a dedicated facility. It is expected that such a new SAR processing algorithm could provide the basis for a real-time SAR correlator implementation in the Deep Space Network. Previously announced in STAR as N82-11295

Truong, T. K.↗

NASA NTRS1984

A physically-based transformation of Thematic Mapper data The TM tasseled cap

In an extension of previous simulation studies, a transformation of actual TM data in the six reflective bands is described which achieves three objectives: a fundamental view of TM data structures is presented, the vast majority of data variability is concentrated in a few (three) features, and the defined features can be directly associated with physical scene characteristics. The underlying TM data structure, based on three TM scenes as well as simulated data, is described, as are the general spectral characteristics of agricultural crops and other scene classes in the transformed data space.

Crist, E. P.↗

NASA NTRS1984

Analysis and application of Fourier transform spectroscopy in atmospheric remote sensing

An analysis method for Fourier transform spectroscopy is summarized with applications to various types of distortion in atmospheric absorption spectra. This analysis method includes the fast Fourier transform method for simulating the interferometric spectrum and the nonlinear least-squares method for retrieving the information from a measured spectrum. It is shown that spectral distortions can be simulated quite well and that the correct information can be retrieved from a distorted spectrum by this analysis technique.

Park, J. H.↗

NASA NTRS1984

Spectral characteristics and meridional variations of energy transformations during the first and second special observation periods of FGGE

The global features and meridional spectral energy transformation variations of the first and second special observation periods of the First Global GARP Experiment (FGGE) are investigated, together with the latitudinal distribution of the kinetic energy balance. Specific seasonal characteristics are shown by the spectral distributions of the global transformations between (1) zonal mean and eddy components of the available potential energy, (2) the zonal mean and eddy components of the kinetic energy, and (3) the available potential energy and the kinetic energy. Maximum kinetic energy production is found to occur at subtropical latitudes, with a secondary maximum at higher middle latitudes. Between these two regions, there is another region characterized by the adiabatic destruction of kinetic energy above the lower troposphere.

Kung, E. C.↗

NASA NTRS1986

Geometric Representations for Discrete Fourier Transforms

Simple geometric representations show symmetry and periodicity of discrete Fourier transforms (DFT's). Help in visualizing requirements for storing and manipulating transform value in computations. Representations useful in any number of dimensions, but particularly in one-, two-, and three-dimensional cases often encountered in practice.

Cambell, C. W.↗

NASA NTRS1985

High voltage isolation transformer

A high voltage isolation transformer is provided with primary and secondary coils separated by discrete electrostatic shields from the surfaces of insulating spools on which the coils are wound. The electrostatic shields are formed by coatings of a compound with a low electrical conductivity which completely encase the coils and adhere to the surfaces of the insulating spools adjacent to the coils. Coatings of the compound also line axial bores of the spools, thereby forming electrostatic shields separating the spools from legs of a ferromagnetic core extending through the bores. The transformer is able to isolate a high constant potential applied to one of its coils, without the occurrence of sparking or corona, by coupling the coatings, lining the axial bores to the ferromagnetic core and by coupling one terminal of each coil to the respective coating encasing the coil.

Clatterbuck, C. H.↗

NASA NTRS1985

A separable two-dimensional discrete Hartley transform

Bracewell has proposed the Discrete Hartley Transform (DHT) as a substitute for the Discrete Fourier Transform (DFT), particularly as a means of convolution. Here, it is shown that the most natural extension of the DHT to two dimensions fails to be separate in the two dimensions, and is therefore inefficient. An alternative separable form is considered, corresponding convolution theorem is derived. That the DHT is unlikely to provide faster convolution than the DFT is also discussed.

Watson, A. B.↗

NASA NTRS1985

Three-dimensional radiative transfer using a Fourier-transform matrix-operator method

The three-dimensional equation of transfer for a scattering medium with planar geometry is solved by using a spatial Fourier transform and extending matrix-operator techniques developed previously for the one-dimensional equation. Doubling and adding algorithms were derived by means of an interaction principle for computing the Fourier-transformed radiation field. The resulting expressions fully describe the radiative transfer process in a scattering medium, inhomogeneous in the x-, y- and z-directions, illuminated from above by an arbitrarily general intensity field and bounded from below by a surface with completely general reflection properties.

Martonchik, J. V.↗

NASA NTRS1986

Fourier transform techniques for the evaluation of the Thematic Mapper line spread function

An endeavor was made to use Fourier transform techniques to estimate the line spread function (LSF) of the Thematic Mapper (TM) from processed data. Data near the boundary of small fields from TM scenes were sampled, fitted to a theoretical curve, lowpass filtered, and then deconvolved to obtain the LSF. Lowpass filtering improved the truncation effect and eliminated the discontinuity at both ends of the data sequence.The selection of the cutoff frequency and the order of a lowpass filter is based on a newly defined criterion which tests the distortion of the processed edge by comparing it with the original edge. A parameter of the LSF, the equivalent width, is used to compare these LSF's deconvolved from sampled edge data with those evaluated by the derivative techniques. The calculated equivalent widths using the Fourier transform techniques for infrared bands are very close to TM design specifications.

Carnahan, W. H.↗

NASA NTRS1987

Transformation Aids Crop Analysis From Spectral Data

Crop analysis aided by mathematical transformation that optimizes perspective of six-dimensional, six-band, spectral data taken from spacecraft or aircraft. Transformation applied to any temperatureclimate vegetated scene, providing direct view of regions of data concentration resulting from band correlations and fundamental reflectance properties of scene classes. Almost all of data variability captured in three spectral features, thus reducing by factor of 2 number of spectral features carried, incurring minimal loss of important information. Three-dimensional representation with two principal planes retains about 95 percent of six-dimensional spectral data used to distinguish among scenes containing green plants and bare soil with varying degrees of moisture.

Crist, E. P.↗

NASA NTRS1987

Fast-Polynomial-Transform Program

Computer program uses fast-polynomial-transformation (FPT) algorithm applicable to two-dimensional mathematical convolutions. Two-dimensional cyclic convolutions converted to one-dimensional convolutions in polynomial rings. Program decomposes cyclic polynomials into polynomial convolutions of same length. Only FPT's and fast Fourier transforms of same length required. Modular approach saves computional resources. Program written in C.

Truong, T. K.↗

NASA NTRS1986

A Fourier transform telescope for sub-arcsecond imaging of X-rays and gamma rays

This paper describes a Fourier transform telescope designed to image solar flare X-rays and gamma rays at energies up to 1 MeV with arcsec resolution. The imaging technique makes use of a bigrid collimator divided into a number of smaller areas called subcollimators. The grids in each subcollimator consist of a set of linear apertures so configured that each subcollimator provides a measurement of a single Fourier component of the angular distribution of the source. The imaging concept is therefore a mathematical analog to aperture synthesis in radio astronomy. For X-ray and gamma-ray astronomy, this approach has significant advantages in terms of relaxed requirements for astronomy, this approach has significant advantages in terms of relaxed requirements for position sensitivity in the detector and for control of grid alignment in the large scale telescope structure. The concept of the Fourier transform telescope will be illustrated with numerical parameters of a version now under study for the Pinhole/Occulter Facility.

Crannell, C. J.↗

NASA NTRS1987

A laboratory demonstration of high-resolution hard X-ray and gamma-ray imaging using Fourier-transform techniques

A laboratory imaging system has been developed to study the use of Fourier-transform techniques in high-resolution hard X-ray and gamma-ray imaging, with particular emphasis on possible applications to high-energy astronomy. Considerations for the design of a Fourier-transform imager and the instrumentation used in the laboratory studies is described. Several analysis methods for image reconstruction are discussed including the CLEAN algorithm and maximum entropy methods. Images obtained using these methods are presented.

Palmer, David↗

NASA NTRS1986

Separable two-dimensional discrete Hartley transform

Watson, Andrew B.↗

NASA NTRS1987

Changes in measured vector magnetic fields when transformed into heliographic coordinates

The changes that occur in measured magnetic fields when they are transformed into a heliographic coordinate system are investigated. To carry out this investigation, measurements of the vector magnetic field of an active region that was observed at 1/3 the solar radius from disk center are taken, and the observed field is transformed into heliographic coordinates. Differences in the calculated potential field that occur when the heliographic normal component of the field is used as the boundary condition rather than the observed line-of-sight component are also examined. The results of this analysis show: (1) that the observed fields of sunspots more closely resemble the generally accepted picture of the distribution of umbral fields if they are displayed in heliographic coordinates; (2) that the differences in the potential calculations are less than 200 G in field strength and 20 deg in field azimuth outside sunspots; and (3) that differences in the two potential calculations in the sunspot areas are no more than 400 G in field strength but range from 60 to 80 deg in field azimuth in localized umbral areas.

Hagyard, M. J.↗

NASA NTRS1987

Interferogram analysis using Fourier transform techniques

A method of interferogram analysis is described in which Fourier transform techniques are used to map the complex fringe visibility in several types of interferograms. Algorithms are developed for estimation of both the amplitude and the phase of the fringes (yielding the modulus and the phase of the holographically recorded object Fourier transform). The algorithms were applied to the reduction of interferometric seeing measurements (i.e., the estimation of the fringe amplitude only), and the reduction of interferometric tests (i.e., estimation of the fringe phase only). The method was used to analyze scatter-plate interferograms obtained at NOAO.

Roddier, Claude↗