DFT-based spectral moment estimators for spacebourne doppler precipitation radar
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precipitation radar TRMM GPM CAMEX-4↗
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DFT-based spectral moments estimators for spaceborne Doppler precipitation radar
In this paper an in-depth analysis on the performance of the Fourier analysis in estimating the first spectral moment of Doppler spectra of rain signals from a spaceborne radar is presented.
precipitation radar Doppler CAMEX-4↗
Discrete fourier transform (DFT) analysis for applications using iterative transform methods
According to various embodiments, a method is provided for determining aberration data for an optical system. The method comprises collecting a data signal, and generating a pre-transformation algorithm. The data is pre-transformed by multiplying the data with the pre-transformation algorithm. A discrete Fourier transform of the pre-transformed data is performed in an iterative loop. The method further comprises back-transforming the data to generate aberration data.
Dean, Bruce H.↗
An Ongoing Quantum Chemistry Study of Molecules with Potential for Molecular Quantum Communications Using Density Functional Theory (DFT) and Other Techniques
Molecular quantum communications (the term here being used to define the transfer of information using the movement of quantum states between molecules or between molecules and a sensing environment that can be queried) can be achieved with a wide range of phenomena. Although there are excellent materials databases such as the Open Quantum Materials Database (http://oqmd.org/analysis/gclp/) and the Materials Project (https://materialsproject.org/), there is no centralized database of materials correlated to their quantum communications possibilities.
Harry Shaw↗
Discrete Fourier Transform Analysis in a Complex Vector Space
Alternative computational strategies for the Discrete Fourier Transform (DFT) have been developed using analysis of geometric manifolds. This approach provides a general framework for performing DFT calculations, and suggests a more efficient implementation of the DFT for applications using iterative transform methods, particularly phase retrieval. The DFT can thus be implemented using fewer operations when compared to the usual DFT counterpart. The software decreases the run time of the DFT in certain applications such as phase retrieval that iteratively call the DFT function. The algorithm exploits a special computational approach based on analysis of the DFT as a transformation in a complex vector space. As such, this approach has the potential to realize a DFT computation that approaches N operations versus Nlog(N) operations for the equivalent Fast Fourier Transform (FFT) calculation.
Dean, Bruce H.↗
Polyphase-discrete Fourier transform spectrum analysis for the Search for Extraterrestrial Intelligence sky survey
The sensitivity of a matched filter-detection system to a finite-duration continuous wave (CW) tone is compared with the sensitivities of a windowed discrete Fourier transform (DFT) system and an ideal bandpass filter-bank system. These comparisons are made in the context of the NASA Search for Extraterrestrial Intelligence (SETI) microwave observing project (MOP) sky survey. A review of the theory of polyphase-DFT filter banks and its relationship to the well-known windowed-DFT process is presented. The polyphase-DFT system approximates the ideal bandpass filter bank by using as few as eight filter taps per polyphase branch. An improvement in sensitivity of approx. 3 dB over a windowed-DFT system can be obtained by using the polyphase-DFT approach. Sidelobe rejection of the polyphase-DFT system is vastly superior to the windowed-DFT system, thereby improving its performance in the presence of radio frequency interference (RFI).
Zimmerman, G. A.↗
Machine Learning Approaches for Rare-Earth Silicate Environmental Barrier Coating Thermochemical and Thermomechanical Property Predictions
Environmental barrier coatings (EBCs) are a necessary enabling technology for the transition from superalloys to silicon carbide (SiC) ceramic matrix composites (CMCs) in gas turbine engines for increased efficiency and decreased fuel costs. SiC-based CMCs are prone to oxidation-based degradation in the engine hot section, and rare-earth (RE) silicates are promising candidates for EBCs due to their close thermal expansion match to the composite substrate and oxidation resistance. However, the design of EBCs is hindered by the large chemical space of candidate materials and the difficulty in obtaining material properties for engineering optimization. This is especially difficult as research continues into mixed-cation or “high-entropy” RE silicates. First-principles computational methods such as density functional theory (DFT) are highly effective at calculating material properties to guide coating design but are limited by their computational cost. Atomistic simulations have the potential to both accelerate property calculations and expand the properties able to be calculated due to their lower computational compared to DFT. However, they require interatomic potentials (IAPs) specific to the material system of interest, and, to our knowledge, there are no suitable IAPs for RE silicates. Machine learning (ML) is a promising technique to accelerate material property predictions indirectly by generating IAPs for atomistic simulations or via direct prediction. In this work, we present two ML approaches to accelerate the calculation of RE silicate properties relevant to EBC design: 1) a ML-derived interatomic potential (IAP) for atomistic simulations of yttrium disilicate (Y2Si2O7) from DFT training data, and 2) a neural network (NN) model to directly predict thermochemical properties of RE silicates and oxides directly from easily obtainable unit cell parameters. Classical MD simulations using the IAP yield lattice properties and bond lengths in good agreement with both DFT and experimental results from x-ray diffraction. Thermodynamic properties calculated using the finite-displacement phonon method and quasi-harmonic approximation were orders of magnitude faster than DFT with good agreement to the DFT results. The IAP was also used to calculate properties such as coefficient of thermal expansion (CTE) that require large simulation supercells and are therefore difficult with DFT. The IAP correctly predicted the anisotropic nature of the CTE in three different phases of Y2Si2O7. The NN model predicts constant pressure heat capacity, Cp, orders of magnitude faster than DFT calculations, which can enable its use as a surrogate model for multiscale simulations. The two methods presented in this work demonstrate the utility of ML for accelerating the prediction of RE silicate properties, which can in turn accelerate EBC design and optimization.
machine learning↗
A Comparison of Density Functional Theory with Ab initio Approaches for Systems Involving First Transition Row Metals
Density functional theory (DFT) is found to give a better description of the geometries and vibrational frequencies of FeL and FeL(sup +) systems than second order Moller Plesset perturbation theory (MP2). Namely, the DFT correctly predicts the shift in the CO vibrational frequency between free CO and the Sigma(sup -) state of FeCO and yields a good result for the Fe-C distance in the quartet states of FeCH4(+) 4 These are properties where the MP2 results are unsatisfactory. Thus DFT appears to be an excellent approach for optimizing the geometries and computing the zero-point energies of systems containing first transition row atoms. Because the DFT approach is biased in favor of the 3d(exp 7) occupation, whereas the more traditional approaches are biased in favor of the 3d(exp 6) occupation, differences are found in the relative ordering of states. It is shown that if the dissociation is computed to the most appropriate atomic asymptote and corrected to the ground state asymptote using the experimental separations, the DFT results are in good agreement with high levels of theory. The energetics at the DFT level are much superior to the MP2 and in most cases in good agreement with high levels of theory.
Ricca, Alessandra↗
A Frequency Analysis Approach for Categorizing Air Traffic Behavior
A method of analyzing National Air Space (NAS) air traffic that uses the Discrete Fourier Transform (DFT) is presented. The DFT is used to transform time domain traffic count data into the frequency domain where the sources of traffic in air spaces can be identified and characterized more easily. It is shown in simulation that individual traffic flows within Air Route Traffic Control Centers can be distinguished by their periodicity in the DFT plot. Next, three Traffic Management Initiatives (playbook rerouting, metered flows, and Ground Delay Programs) are implemented in simulations and their signature effects on the traffic are identified using the DFT. Finally, historical flight data is studied and the DFT is applied to sector traffic count data. It is found that in many cases, variations in traffic due to rerouting and convective weather disturbances are better highlighted in the frequency domain than in the original time domain data. Initial results of the DFT show it has potential as a tool for measuring and/or predicting NAS behavior for daily tactical planning and control purposes.
fourier transform↗
Application of Density Functional Theory to Systems Containing Metal Atoms
The accuracy of density functional theory (DFT) for problems involving metal atoms is considered. The DFT results are compared with experiment as well as results obtained using the coupled cluster approach. The comparisons include geometries, frequencies, and bond energies. The systems considered include MO2, M(OH)+(sub n), MNO+, and MCO+(sub 2). The DFT works well for frequencies and geometries, even in cases with symmetry breaking; however, some examples have been found where the symmetry breaking is quite severe and the DFT methods do not work well. The calculation of bond energies is more difficult and examples of the successes as well as failures of DFT will be given.
Bauschlicher, Charles W., Jr.↗
Application of Density Functional Theory to Systems Containing Metal Atoms
The accuracy of density functional theory (DFT) for problems involving metal atoms is considered. The DFT results are compared with experiment as well as results obtained using the coupled cluster approach. The comparisons include geometries, frequencies, and bond energies. The systems considered include MO2, M(OH)+n, MNO+, and MCO+2. The DFT works well for frequencies and geometries, even in case with symmetry breaking; however, some examples have been found where the symmetry breaking is quite severe and the DFT methods do not work well. The calculation of bond energies is more difficult and examples of successes as well as failures of DFT will be given.
Bauschlicher, Charles W., Jr.↗
Theoretical Prediction of Thermal Expansion Anisotropy for Y 2 Si 2 O 7 Environmental Barrier Coatings Using a Deep Neural Network Potential and Comparison to Experiment
Environmental barrier coatings (EBCs) are an enabling technology for silicon carbide (SiC)-based ceramic matrix composites (CMCs) in extreme environments such as gas turbine engines. However, development of new coating systems is hindered by the large design space and difficulty in predicting properties for these materials. Density Functional Theory (DFT) has successfully been used to model and predict some thermodynamic and thermo-mechanical properties of high-temperature ceramics for EBCs, although these calculations are challenging due to their high computational costs. In this work, we use machine learning to train a deep neural network potential (DNP) for Y 2 Si 2 O 7 , which is then applied to calculate thermodynamic and thermo-mechanical properties at near-DFT accuracy much faster and using less computational resources than DFT. We use this DNP to predict phonon-based thermodynamic properties of Y 2 Si 2 O 7 with good agreement to DFT and experiments. We also utilize the DNP to calculate the anisotropic, lattice direction-dependent coefficients of thermal expansion (CTEs) for Y 2 Si 2 O 7 . Molecular dynamics trajectories using the DNP correctly demonstrate accurate prediction of the anisotropy of the CTE in good agreement with diffraction experiments. In the future, this DNP could be applied to accelerate additional property calculations for Y 2 Si 2 O 7 compared to DFT or experiments.
rare earth silicates↗
Implementation of real-time digital signal processing systems
Special purpose hardware implementation of DFT Computers and digital filters is considered in the light of newly introduced algorithms and IC devices. Recent work by Winograd on high-speed convolution techniques for computing short length DFT's, has motivated the development of more efficient algorithms, compared to the FFT, for evaluating the transform of longer sequences. Among these, prime factor algorithms appear suitable for special purpose hardware implementations. Architectural considerations in designing DFT computers based on these algorithms are discussed. With the availability of monolithic multiplier-accumulators, a direct implementation of IIR and FIR filters, using random access memories in place of shift registers, appears attractive. The memory addressing scheme involved in such implementations is discussed. A simple counter set-up to address the data memory in the realization of FIR filters is also described. The combination of a set of simple filters (weighting network) and a DFT computer is shown to realize a bank of uniform bandpass filters. The usefulness of this concept in arriving at a modular design for a million channel spectrum analyzer, based on microprocessors, is discussed.
Narasimha, M.↗
Discrete Fourier transforms of nonuniformly spaced data
Time series or spatial series of measurements taken with nonuniform spacings have failed to yield fully to analysis using the Discrete Fourier Transform (DFT). This is due to the fact that the formal DFT is the convolution of the transform of the signal with the transform of the nonuniform spacings. Two original methods are presented for deconvolving such transforms for signals containing significant noise. The first method solves a set of linear equations relating the observed data to values defined at uniform grid points, and then obtains the desired transform as the DFT of the uniform interpolates. The second method solves a set of linear equations relating the real and imaginary components of the formal DFT directly to those of the desired transform. The results of numerical experiments with noisy data are presented in order to demonstrate the capabilities and limitations of the methods.
Swan, P. R.↗
Formation of Carbon Nanotube Based Gears: Quantum Chemistry and Molecular Mechanics Study of the Electrophilic Addition of o-Benzyne to Fullerenes, Graphene, and Nanotubes
Considerable progress has been made in recent years in chemical functionalization of fullerene molecules. In some cases, the predominant reaction products are different from those obtained (using the same reactants) from polycyclic aromatic hydrocarbons (PAHs). One such example is the cycloaddition of o-benzyne to C60. It is well established that benzyne adds across one of the rings in naphthalene, anthracene and other PAHs forming the [2+4] cycloaddition product (benzobicyclo[2.2.2.]-octatriene with naphthalene and triptycene with anthracene). However, Hoke et al demonstrated that the only reaction path for o-benzyne with C60 leads to the [2+2] cycloaddition product in which benzyne adds across one of the interpentagonal bonds (forming a cyclobutene ring in the process). Either reaction product results in a loss of aromaticity and distortion of the PAH or fullerene substrate, and in a loss of strain in the benzyne. It is not clear, however, why different products are preferred in these cases. In the current paper, we consider the stability of benzyne-nanotube adducts and the ability of Brenner's potential energy model to describe the structure and stability of these adducts. The Brenner potential has been widely used for describing diamondoid and graphitic carbon. Recently it has also been used for molecular mechanics and molecular dynamics simulations of fullerenes and nanotubes. However, it has not been tested for the case of functionalized fullerenes (especially with highly strained geometries). We use the Brenner potential for our companion nanogear simulations and believe that it should be calibrated to insure that those simulations are physically reasonable. In the present work, Density Functional theory (DFT) calculations are used to determine the preferred geometric structures and energetics for this calibration. The DFT method is a kind of ab initio quantum chemistry method for determining the electronic structure of molecules. For a given basis set expansion, it is comparable in accuracy to the MP2 method (better than Hartree Fock, but less accurate than more extensive electron correlation methods such as MP4 or CCSD). However, for systems with large numbers of basis functions it more efficient than any other methods that include electron correlation effects. In this presentation we show the results of DFT calculations for the reaction of benzyne with naphthalene, C60, and nanotube models. We compare energies for [2+2] and [2+4] cycloaddition products. The preferred products for the naphthalene and C60 reactions have been determined by experiment and, thus, these cases serve as a validation of our quantum chemical approach. We also compare the DFT and Brenner potential results. Finally we can predict the likelihood of reaction between benzyne and nanotubes.
Jaffe, Richard↗
A Discussion of Using a Reconfigurable Processor to Implement the Discrete Fourier Transform
This paper presents the design and implementation of the Discrete Fourier Transform (DFT) algorithm on a reconfigurable processor system. While highly applicable to many engineering problems, the DFT is an extremely computationally intensive algorithm. Consequently, the eventual goal of this work is to enhance the execution of a floating-point precision DFT algorithm by off loading the algorithm from the computing system. This computing system, within the context of this research, is a typical high performance desktop computer with an may of field programmable gate arrays (FPGAs). FPGAs are hardware devices that are configured by software to execute an algorithm. If it is desired to change the algorithm, the software is changed to reflect the modification, then download to the FPGA, which is then itself modified. This paper will discuss methodology for developing the DFT algorithm to be implemented on the FPGA. We will discuss the algorithm, the FPGA code effort, and the results to date.
White, Michael J.↗
A Discussion of the Discrete Fourier Transform Execution on a Typical Desktop PC
This paper will discuss and compare the execution times of three examples of the Discrete Fourier Transform (DFT). The first two examples will demonstrate the direct implementation of the algorithm. In the first example, the Fourier coefficients are generated at the execution of the DFT. In the second example, the coefficients are generated prior to execution and the DFT coefficients are indexed at execution. The last example will demonstrate the Cooley- Tukey algorithm, better known as the Fast Fourier Transform. All examples were written in C executed on a PC using a Pentium 4 running at 1.7 Ghz. As a function of N, the total complex data size, the direct implementation DFT executes, as expected at order of N2 and the FFT executes at order of N log2 N. At N=16K, there is an increase in processing time beyond what is expected. This is not caused by implementation but is a consequence of the effect that machine architecture and memory hierarchy has on implementation. This paper will include a brief overview of digital signal processing, along with a discussion of contemporary work with discrete Fourier processing.
White, Michael J.↗
A fast D.F.T. algorithm using complex integer transforms
Winograd (1976) has developed a new class of algorithms which depend heavily on the computation of a cyclic convolution for computing the conventional DFT (discrete Fourier transform); this new algorithm, for a few hundred transform points, requires substantially fewer multiplications than the conventional FFT algorithm. Reed and Truong have defined a special class of finite Fourier-like transforms over GF(q squared), where q = 2 to the p power minus 1 is a Mersenne prime for p = 2, 3, 5, 7, 13, 17, 19, 31, 61. In the present paper it is shown that Winograd's algorithm can be combined with the aforementioned Fourier-like transform to yield a new algorithm for computing the DFT. A fast method for accurately computing the DFT of a sequence of complex numbers of very long transform-lengths is thus obtained.
Reed, I. S.↗