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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 91 records · Page 5
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NASA NTRS1979

Faster fourier transformation: The algorithm of S. Winograd

The new DFT algorithm of S. Winograd is developed and presented in detail. This is an algorithm which uses about 1/5 of the number of multiplications used by the Cooley-Tukey algorithm and is applicable to any order which is a product of relatively prime factors from the following list: 2,3,4,5,7,8,9,16. The algorithm is presented in terms of a series of tableaus which are convenient, compact, graphical representations of the sequence of arithmetic operations in the corresponding parts of the algorithm. Using these in conjunction with included Tables makes it relatively easy to apply the algorithm and evaluate its performance.

Zohar, S.↗
NASA NTRS1979

A new hybrid algorithm for computing a fast discrete Fourier transform

In this paper for certain long transform lengths, Winograd's algorithm for computing the discrete Fourier transform (DFT) is extended considerably. This is accomplished by performing the cyclic convolution, required by Winograd's method, with the Mersenne prime number-theoretic transform developed originally by Rader. This new algorithm requires fewer multiplications than either the standard fast Fourier transform (FFT) or Winograd's more conventional algorithm. However, more additions are required.

Reed, I. S.↗
NASA NTRS1979

A prescription of Winograd's discrete Fourier transform algorithm

A detailed and complete description of Winograd's discrete Fourier transform algorithm (DFT) is presented omitting all proofs and derivations. The algorithm begins with the transfer of data from the input vector array to the working array where the actual transformation takes place, otherwise known as input scrambling and output unscrambling. The third array holds constraints required in the transformation stage that are evaluated in the precomputation stage. The algorithm is made up of several FORTRAN subroutines which are not to be confused with practical software algorithmic implementation since they are designed for clarity and not for speed.

Zohar, S.↗
NASA NTRS1980

Low power, compact charge coupled device signal processing system

A variety of charged coupled devices (CCDs) for performing programmable correlation for preprocessing environmental sensor data preparatory to its transmission to the ground were developed. A total of two separate ICs were developed and a third was evaluated. The first IC was a CCD chirp z transform IC capable of performing a 32 point DFT at frequencies to 1 MHz. All on chip circuitry operated as designed with the exception of the limited dynamic range caused by a fixed pattern noise due to interactions between the digital and analog circuits. The second IC developed was a 64 stage CCD analog/analog correlator for performing time domain correlation. Multiplier errors were found to be less than 1 percent at designed signal levels and less than 0.3 percent at the measured smaller levels. A prototype IC for performing time domain correlation was also evaluated.

Bosshart, P. W.↗
NASA NTRS1980

An experimental distributed microprocessor implementation with a shared memory communications and control medium

The distributed processing concept is defined in terms of control primitives, variables, and structures and their use in performing a decomposed discrete Fourier transform (DET) application function. The design assumes interprocessor communications to be anonymous. In this scheme, all processors can access an entire common database by employing control primitives. Access to selected areas within the common database is random, enforced by a hardware lock, and determined by task and subtask pointers. This enables the number of processors to be varied in the configuration without any modifications to the control structure. Decompositional elements of the DFT application function in terms of tasks and subtasks are also described. The experimental hardware configuration consists of IMSAI 8080 chassis which are independent, 8 bit microcomputer units. These chassis are linked together to form a multiple processing system by means of a shared memory facility. This facility consists of hardware which provides a bus structure to enable up to six microcomputers to be interconnected. It provides polling and arbitration logic so that only one processor has access to shared memory at any one time.

Mejzak, R. S.↗
NASA NTRS1982

LSI/VLSI design for testability analysis and general approach

The incorporation of testability characteristics into large scale digital design is not only necessary for, but also pertinent to effective device testing and enhancement of device reliability. There are at least three major DFT techniques, namely, the self checking, the LSSD, and the partitioning techniques, each of which can be incorporated into a logic design to achieve a specific set of testability and reliability requirements. Detailed analysis of the design theory, implementation, fault coverage, hardware requirements, application limitations, etc., of each of these techniques are also presented.

Lam, A. Y.↗
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

Maintenance of Time and Frequency in the DSN Using the Global Positioning System

The Deep Space Network must maintain time and frequency within specified limits in order to accurately track the spacecraft engaged in deep space exploration. The DSN has three tracking complexes, located approximately equidistantly around the Earth. Various methods are used to coordinate the clocks among the three complexes. These methods include Loran-C, TV Line 10, very long baseline interferometry (VLBI), and the Global Positioning System (GPS). The GPS is becoming increasingly important because of the accuracy, precision, and rapid availability of the data; GPS receivers have been installed at each of the DSN complexes and are used to obtain daily time offsets between the master clock at each site and UTC(USNO/NBS). Calculations are made to obtain frequency offsets and Allan variances. These data are analyzed and used to monitor the performance of the hydrogen masers that provide the reference frequencies for the DSN frequency and timing system (DFT). A brief history of the GPS timing receivers in the DSN, a description of the data and information flow, data on the performance of the DSN master clocks and GPS measurement system, and a description of hydrogen maser frequency steering using these data are presented.

Clements, P. A.↗
NASA NTRS1984

Maintenance of time and frequency in the Jet Propulsion Laboratory's Deep Space Network using the Global Positioning System

The Deep Space Network (DSN), managed by the Jet Propulsion Laboratory for NASA, must maintain time and frequency within specified limits in order to accurately track the spacecraft engaged in deep space exploration. Various methods are used to coordinate the clocks among the three tracking complexes. These methods include Loran-C, TV Line 10, Very Long Baseline Interferometry (VLBI), and the Global Positioning System (GPS). Calculations are made to obtain frequency offsets and Allan variances. These data are analyzed and used to monitor the performance of the hydrogen masers that provide the reference frequencies for the DSN Frequency and Timing System (DFT). Areas of discussion are: (1) a brief history of the GPS timing receivers in the DSN, (2) a description of the data and information flow, (3) data on the performance of the DSN master clocks and GPS measurement system, and (4) a description of hydrogen maser frequency steering using these data.

Clements, P. A.↗
NASA NTRS1986

Some approaches to substructure coupling with damping

Time-domain and frequency-domain methods for coupling substructures with general linear damping are discussed. A time-domain method is presented which employs a state variable representation of each substructure. Also presented is a method which employs frequency-domain coupling together with DFT and FFT transformations to obtain transient response solutions.

Craig, R. R., Jr.↗
NASA NTRS1988

Local buckling and crippling of composite stiffener sections

Local buckling, postbuckling, and crippling (failure) of channel, zee, and I- and J-section stiffeners made of AS4/3502 graphite-epoxy unidirectional tape are studied by experiment and analysis. Thirty-six stiffener specimens were tested statically to failure in axial compression as intermediate length columns. Web width is 1.25 inches for all specimens, and the flange width-to-thickness ratio ranges from 7 to 28 for the specimens tested. The radius of the stiffener corners is either 0.125 or 0.250 inches. A sixteen-ply orthotropic layup, an eight-ply quasi-isotropic layup, and a sixteen-ply quasi-isotropic layup are examined. Geometrically nonlinear analyses of five specimens were performed with the STAGS finite element code. Analytical results are compared to experimental data. Inplane stresses from STAGS are used to conduct a plane stress failure analysis of these specimens. Also, the development of interlaminar stress equations from equilibrium for classical laminated plate theory is presented. An algorithm to compute high order displacement derivatives required by these equations based on the Discrete Fourier Transform (DFT) is discussed.

Bonanni, David L.↗
NASA NTRS1991

The behavior of quantization spectra as a function of signal-to-noise ratio

An expression for the spectrum of quantization error in a discrete-time system whose input is a sinusoid plus white Gaussian noise is derived. This quantization spectrum consists of two components: a white-noise floor and spurious harmonics. The dithering effect of the input Gaussian noise in both components of the spectrum is considered. Quantitative results in a discrete Fourier transform (DFT) example show the behavior of spurious harmonics as a function of the signal-to-noise ratio (SNR). These results have strong implications for digital reception and signal analysis systems. At low SNRs, spurious harmonics decay exponentially on a log-log scale, and the resulting spectrum is white. As the SNR increases, the spurious harmonics figure prominently in the output spectrum. A useful expression is given that roughly bounds the magnitude of a spurious harmonic as a function of the SNR.

Flanagan, M. J.↗
NASA NTRS1991

The fractional Fourier transform and applications

This paper describes the 'fractional Fourier transform', which admits computation by an algorithm that has complexity proportional to the fast Fourier transform algorithm. Whereas the discrete Fourier transform (DFT) is based on integral roots of unity e exp -2(pi)i/n, the fractional Fourier transform is based on fractional roots of unity e exp -2(pi)i(alpha), where alpha is arbitrary. The fractional Fourier transform and the corresponding fast algorithm are useful for such applications as computing DFTs of sequences with prime lengths, computing DFTs of sparse sequences, analyzing sequences with noninteger periodicities, performing high-resolution trigonometric interpolation, detecting lines in noisy images, and detecting signals with linearly drifting frequencies. In many cases, the resulting algorithms are faster by arbitrarily large factors than conventional techniques.

Bailey, David H.↗
NASA NTRS1992

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.↗
NASA NTRS1991

An improved distributed arithmetic architecture

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.

Guo, X.↗
NASA NTRS1994

Blocking reduction of Landsat Thematic Mapper JPEG browse images using optimal PSNR estimated spectra adaptive postfiltering

Two representative sample images of Band 4 of the Landsat Thematic Mapper are compressed with the JPEG algorithm at 8:1, 16:1 and 24:1 Compression Ratios for experimental browsing purposes. We then apply the Optimal PSNR Estimated Spectra Adaptive Postfiltering (ESAP) algorithm to reduce the DCT blocking distortion. ESAP reduces the blocking distortion while preserving most of the image's edge information by adaptively postfiltering the decoded image using the block's spectral information already obtainable from each block's DCT coefficients. The algorithm iteratively applied a one dimensional log-sigmoid weighting function to the separable interpolated local block estimated spectra of the decoded image until it converges to the optimal PSNR with respect to the original using a 2-D steepest ascent search. Convergence is obtained in a few iterations for integer parameters. The optimal logsig parameters are transmitted to the decoder as a negligible byte of overhead data. A unique maxima is guaranteed due to the 2-D asymptotic exponential overshoot shape of the surface generated by the algorithm. ESAP is based on a DFT analysis of the DCT basis functions. It is implemented with pixel-by-pixel spatially adaptive separable FIR postfilters. PSNR objective improvements between 0.4 to 0.8 dB are shown together with their corresponding optimal PSNR adaptive postfiltered images.

Linares, Irving↗
NASA NTRS1994

FFT Computation with Systolic Arrays, A New Architecture

The use of the Cooley-Tukey algorithm for computing the l-d FFT lends itself to a particular matrix factorization which suggests direct implementation by linearly-connected systolic arrays. Here we present a new systolic architecture that embodies this algorithm. This implementation requires a smaller number of processors and a smaller number of memory cells than other recent implementations, as well as having all the advantages of systolic arrays. For the implementation of the decimation-in-frequency case, word-serial data input allows continuous real-time operation without the need of a serial-to-parallel conversion device. No control or data stream switching is necessary. Computer simulation of this architecture was done in the context of a 1024 point DFT with a fixed point processor, and CMOS processor implementation has started.

Boriakoff, Valentin↗
NASA NTRS1995

Theoretical Study of Fe(CO)n-

The structures and CO binding energies are computed for Fe(CO)n- using a hybrid density functional theory (DFT) approach. The structures and ground states can be explained in terms of maximizing the Fe to CO 2pi* donation and minimizing Fe-CO 5 sigma repulsion. The trends in the CO binding energies for Fe(CO)n- and the differences between the trends for Fe(CO)n- and Fe(CO)n are also explained. For Fe(CO)n-, the second, third, and fourth CO bonding energies are in good agreement with experiment, while the first is too small. The first CO binding is also too small using the coupled cluster singles and doubles approach including a perturbation estimate of the connected triple excitations.

Ricca, Alessandra↗