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All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Quantum Fourier transform revisited

Summary The fast Fourier transform (FFT) is one of the most successful numerical algorithms of the 20th century and has found numerous applications in many branches of computational science and engineering. The FFT algorithm can be derived from a particular matrix decomposition of the discrete Fourier transform (DFT) matrix. In this paper, we show that the quantum Fourier transform (QFT) can be derived by further decomposing the diagonal factors of the FFT matrix decomposition into products of matrices with Kronecker product structure. We analyze the implication of this Kronecker product structure on the discrete Fourier transform of rank‐1 tensors on a classical computer. We also explain why such a structure can take advantage of an important quantum computer feature that enables the QFT algorithm to attain an exponential speedup on a quantum computer over the FFT algorithm on a classical computer. Further, the connection between the matrix decomposition of the DFT matrix and a quantum circuit is made. We also discuss a natural extension of a radix‐2 QFT decomposition to a radix‐ d QFT decomposition. No prior knowledge of quantum computing is required to understand what is presented in this paper. Yet, we believe this paper may help readers to gain some rudimentary understanding of the nature of quantum computing from a matrix computation point of view.

Camps, Daan↗
DOE OSTI2021

Improved motional Stark effect signal processing using fast Fourier transform spectral analysis

A Fast Fourier Transform (FFT) based method has been developed, which improves the frequency response of the Motional Stark Effect (MSE) system by about a factor of 10 over the conventional analog lock-in method. The method uses fits to rigorously derived analytic expressions for the FFT spectral components of the MSE signal to accurately obtain the amplitudes and phases of the 2f1 and 2f2 photo-elastic modulator (PEM) frequencies that encode the polarization angle. Since no frequency filtering is used in the FFT method, the frequency response is limited by fundamental measurement properties: the frequency response of the detector, photon statistics, sample rate, and the ability to resolve the spectral components. In contrast, the frequency response of the analog lock-in is limited by a low pass filter with a cutoff of around 500 Hz. In the case of the DIII-D MSE system, the output of the photo-multiplier tube detector was sampled at 500 kHz and FFTs with as few as 100 points were used to obtain the amplitudes of the 2f1 and 2f2 PEM frequency components. This corresponds to a frequency response of 5 kHz, about ten times faster than the analog lock-in amplifier system. Details of the FFT method will be presented and compared to those of the analog lock-in system.

Makowski, M. A.↗
DOE OSTI2024

Rotational Millimeter-Wave Shoe Scanner Using the Discrete Fourier Transform for Backprojection-Based Image Reconstruction

An active 3D microwave / millimeter-wave shoe scanner was previously developed at the Pacific Northwest National Laboratory (PNNL) using two linear arrays scanned over a rectilinear aperture. The radar system chirps a frequency sweep from 10-40 GHz. These frequencies allow imaging through optically opaque material such as leather, rubber, plastics, and other dielectrics. The system was designed to detect concealed items in the soles of shoes while allowing people to leave their shoes on through a security checkpoint. To shrink the footprint of the system, a new iteration of the design has been developed that scans the two linear arrays over a circular aperture. This new footprint opens the possibility of it being installed in the floor of a cylindrical millimeter-wave body scanner. The backprojection-based multilayer dielectric image reconstruction developed at PNNL can easily handle arbitrary spatial sampling, accommodating the new rotational shoe scanner design. Commonly, the fast Fourier transform (FFT) is used to efficiently compute the range response from the data collected by the system as a preprocessing step to the backprojection algorithm. It was found that converting to range using the discrete Fourier transform (DFT) directly has some advantages over the FFT. For example, nonlinear and non-uniform frequency sweeps can easily be compensated for during the computation of the DFT and only the range bins of interest need to be computed and their spacing can be chosen arbitrarily. Because the range conversion step of the image reconstruction is the fastest part of the process there is very little speed penalty for using the DFT over the FFT and it can even increase the speed of image reconstruction when the ranges of interest are fewer than the total span that is calculated in the FFT.

Millimeter-wave imaging, microwave imaging, shoe s↗
DOE OSTI2022

Benchmarking a Proof-of-Concept Performance Portable SYCL-based Fast Fourier Transformation Library

ABSTRACT In this paper, we present an early version of a SYCL-based FFT library, capable of running on all major vendor hardware, including CPUs and GPUs from AMD, ARM, Intel and NVIDIA. The current limitations of our library is it supports single-dimension FFTs up to 211 in length and base-2 input sequences. Although preliminary, the aim of this work is to seed further developments for a rich set of features for calculating FFTs. The library has the advantage over existing portable FFT libraries in that it is single-source, and there- fore removes the complexities that arise due to abundant use of pre-processor macros and auto-generated kernels to target different architectures. We exercise two SYCL-enabled compilers, Codeplay ComputeCpp and Intel's open-source LLVM project, to evaluate performance portability of our SYCL-based FFT on various hetero- geneous architectures.We provide studies comparing our portable library with highly optimized vendor-specific FFT libraries, and discuss potential sources hindering performance.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Vectors of Efficiency in Hybrid Poplar Genotype Testing

Abstract The Natural Resources Research Institute Hybrid Poplar Program breeds and tests genetically improved clones for bio-mass production and environmental services. The testing process progresses from Nursery Progeny Tests (NPT) to Family Field Trials (FFT) to Clone Trials (CT) to Yield Blocks (YB), with limited replication of many clones in FFT and CT and a limited number of highly selected clones set out in monoclonal blocks (YB) to approximate the conditions of commercial plantations. We used correlation vectors, R 2 (coefficient of determination) and r s (Spearman’s Coefficient) for growth (DBH 2 ) and McFadden’s Pseudo R 2 for canker severity score, to determine where testing times could be altered (age – age correlations) and whole testing steps eliminated. FFT can be shortened from 5 years to 4 years. In CT, rank correlations between age 5 (half-rotation) and age 9/10 (full rotation) were significant (R 2 = 0.39 – 0.72), but age 5 selection missed 44 % of the top ten clones at age 9/10. Clone rank in CT at full, but not half, rotation was correlated with rank at full rotation in YB. Choosing clones at 9 years in CT adds 4 years but allows possible elimination of YB for clone selection. Both FFT and CT are necessary. Canker abundance and severity in CT at full rotation cannot be determined at earlier ages. An aggressive strategy saves 6 years of testing.

Forestry↗
NASA NTRS1978

Fixed-point error analysis of Winograd Fourier transform algorithms

The quantization error introduced by the Winograd Fourier transform algorithm (WFTA) when implemented in fixed-point arithmetic is studied and compared with that of the fast Fourier transform (FFT). The effect of ordering the computational modules and the relative contributions of data quantization error and coefficient quantization error are determined. In addition, the quantization error introduced by the Good-Winograd (GW) algorithm, which uses Good's prime-factor decomposition for the discrete Fourier transform (DFT) together with Winograd's short length DFT algorithms, is studied. Error introduced by the WFTA is, in all cases, worse than that of the FFT. In general, the WFTA requires one or two more bits for data representation to give an error similar to that of the FFT. Error introduced by the GW algorithm is approximately the same as that of the FFT.

Patterson, R. W.↗
NASA NTRS1986

On the electromagnetic scattering from infinite rectangular grids with finite conductivity

A variety of methods can be used in constructing solutions to the problem of mesh scattering. However, each of these methods has certain drawbacks. The present paper is concerned with a new technique which is valid for all spacings. The new method involved, called the fast Fourier transform-conjugate gradient method (FFT-CGM), represents an iterative technique which employs the conjugate gradient method to improve upon each iterate, utilizing the fast Fourier transform. The FFT-CGM method provides a new accurate model which can be extended and applied to the more difficult problems of woven mesh surfaces. The formulation of the FFT-conjugate gradient method for aperture fields and current densities for a planar periodic structure is considered along with singular operators, the formulation of the FFT-CG method for thin wires with finite conductivity, and reflection coefficients.

Christodoulou, C. G.↗
NASA NTRS1988

Fast Fourier Transform algorithm design and tradeoffs

The Fast Fourier Transform (FFT) is a mainstay of certain numerical techniques for solving fluid dynamics problems. The Connection Machine CM-2 is the target for an investigation into the design of multidimensional Single Instruction Stream/Multiple Data (SIMD) parallel FFT algorithms for high performance. Critical algorithm design issues are discussed, necessary machine performance measurements are identified and made, and the performance of the developed FFT programs are measured. Fast Fourier Transform programs are compared to the currently best Cray-2 FFT program.

Kamin, Ray A., III↗
NASA NTRS1990

Propane spectral resolution enhancement by the maximum entropy method

The Burg algorithm for maximum entropy power spectral density estimation is applied to a time series of data obtained from a Michelson interferometer and compared with a standard FFT estimate for resolution capability. The propane transmittance spectrum was estimated by use of the FFT with a 2 to the 18th data sample interferogram, giving a maximum unapodized resolution of 0.06/cm. This estimate was then interpolated by zero filling an additional 2 to the 18th points, and the final resolution was taken to be 0.06/cm. Comparison of the maximum entropy method (MEM) estimate with the FFT was made over a 45/cm region of the spectrum for several increasing record lengths of interferogram data beginning at 2 to the 10th. It is found that over this region the MEM estimate with 2 to the 16th data samples is in close agreement with the FFT estimate using 2 to the 18th samples.

Bonavito, N. L.↗
NASA NTRS1989

Ordered fast fourier transforms on a massively parallel hypercube multiprocessor

Design alternatives for ordered Fast Fourier Transformation (FFT) algorithms were examined on massively parallel hypercube multiprocessors such as the Connection Machine. Particular emphasis is placed on reducing communication which is known to dominate the overall computing time. To this end, the order and computational phases of the FFT were combined, and the sequence to processor maps that reduce communication were used. The class of ordered transforms is expanded to include any FFT in which the order of the transform is the same as that of the input sequence. Two such orderings are examined, namely, standard-order and A-order which can be implemented with equal ease on the Connection Machine where orderings are determined by geometries and priorities. If the sequence has N = 2 exp r elements and the hypercube has P = 2 exp d processors, then a standard-order FFT can be implemented with d + r/2 + 1 parallel transmissions. An A-order sequence can be transformed with 2d - r/2 parallel transmissions which is r - d + 1 fewer than the standard order. A parallel method for computing the trigonometric coefficients is presented that does not use trigonometric functions or interprocessor communication. A performance of 0.9 GFLOPS was obtained for an A-order transform on the Connection Machine.

Tong, Charles↗
NASA NTRS1994

Applications Performance on NAS Intel Paragon XP/S - 15#

The Numerical Aerodynamic Simulation (NAS) Systems Division received an Intel Touchstone Sigma prototype model Paragon XP/S- 15 in February, 1993. The i860 XP microprocessor with an integrated floating point unit and operating in dual -instruction mode gives peak performance of 75 million floating point operations (NIFLOPS) per second for 64 bit floating point arithmetic. It is used in the Paragon XP/S-15 which has been installed at NAS, NASA Ames Research Center. The NAS Paragon has 208 nodes and its peak performance is 15.6 GFLOPS. Here, we will report on early experience using the Paragon XP/S- 15. We have tested its performance using both kernels and applications of interest to NAS. We have measured the performance of BLAS 1, 2 and 3 both assembly-coded and Fortran coded on NAS Paragon XP/S- 15. Furthermore, we have investigated the performance of a single node one-dimensional FFT, a distributed two-dimensional FFT and a distributed three-dimensional FFT Finally, we measured the performance of NAS Parallel Benchmarks (NPB) on the Paragon and compare it with the performance obtained on other highly parallel machines, such as CM-5, CRAY T3D, IBM SP I, etc. In particular, we investigated the following issues, which can strongly affect the performance of the Paragon: a. Impact of the operating system: Intel currently uses as a default an operating system OSF/1 AD from the Open Software Foundation. The paging of Open Software Foundation (OSF) server at 22 MB to make more memory available for the application degrades the performance. We found that when the limit of 26 NIB per node out of 32 MB available is reached, the application is paged out of main memory using virtual memory. When the application starts paging, the performance is considerably reduced. We found that dynamic memory allocation can help applications performance under certain circumstances. b. Impact of data cache on the i860/XP: We measured the performance of the BLAS both assembly coded and Fortran coded. We found that the measured performance of assembly-coded BLAS is much less than what memory bandwidth limitation would predict. The influence of data cache on different sizes of vectors is also investigated using one-dimensional FFTs. c. Impact of processor layout: There are several different ways processors can be laid out within the two-dimensional grid of processors on the Paragon. We have used the FFT example to investigate performance differences based on processors layout.

Saini, Subhash↗
DOE OSTI2025

A Green’s function fast multipole method for computation of micromechanical fields in heterogeneous materials

Computation of micromechanical fields in heterogeneous materials is usually performed using either the finite element method or the Green’s function method based on FFTs. The finite element method allows for accurate discretization and for non-periodic boundary conditions but is computationally expensive. On the other hand, the FFT-based method is computationally efficient but requires discretization on a regular grid of hexahedral voxels. In this paper, a Green’s function method allowing for accurate discretization using tetrahedral elements and for non-periodic boundary conditions is proposed. The convolution is computed using the fast multipole method, which provides good accuracy even for low-order expansion due to the fast decay of interactions between elements. The proposed Green’s function fast multipole method is verified by comparison with analytical and FFT-based solutions. Furthermore, the computational time is analyzed and compared to the FFT-based method for non-periodic convolution. Finally, effective properties of an elastic polycrystalline microstructure containing thin intergranular cracks are computed and analyzed.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Investigation of thermal hydraulic behavior of the High Temperature Test Facility's lower plenum via large eddy simulation

A high-fidelity computational fluid dynamics (CFD) analysis was performed using the Large Eddy Simulation (LES) model for the lower plenum of the High–Temperature Test Facility (HTTF), a ¼ scale test facility of the modular high temperature gas-cooled reactor (MHTGR) managed by Oregon State University. In most next–generation nuclear reactors, thermal stress due to thermal striping is one of the risks to be curiously considered. This is also true for HTGRs, especially since the exhaust helium gas temperature is high. In order to evaluate these risks and performance, organizations in the United States led by the OECD NEA are conducting a thermal hydraulic code benchmark for HTGR, and the test facility used for this benchmark is HTTF. HTTF can perform experiments in both normal and accident situations and provide high-quality experimental data. However, it is difficult to provide sufficient data for benchmarking through experiments, and there is a problem with the reliability of CFD analysis results based on Reynolds–averaged Navier–Stokes to analyze thermal hydraulic behavior without verification. To solve this problem, high-fidelity 3-D CFD analysis was performed using the LES model for HTTF. It was also verified that the LES model can properly simulate this jet mixing phenomenon via a unit cell test that provides experimental information. As a result of CFD analysis, the lower the dependency of the sub-grid scale model, the closer to the actual analysis result. In the case of unit cell test CFD analysis and HTTF CFD analysis, the volume-averaged sub-grid scale model dependency was calculated to be 13.0% and 9.16%, respectively. As a result of HTTF analysis, quantitative data of the fluid inside the HTTF lower plenum was provided in this paper. As a result of qualitative analysis, the temperature was highest at the center of the lower plenum, while the temperature fluctuation was highest near the edge of the lower plenum wall. The power spectral density of temperature was analyzed via fast Fourier transform (FFT) for specific points on the center and side of the lower plenum. FFT results did not reveal specific frequency-dominant temperature fluctuations in the center part. It was confirmed that the temperature power spectral density (PSD) at the top increased from the center to the wake. The vortex was visualized using the well-known scalar Q-criterion, and as a result, the closer to the outlet duct, the greater the influence of the mainstream, so that the inflow jet vortex was dissipated and mixed at the top of the lower plenum. Additionally, FFT analysis was performed on the support structure near the corner of the lower plenum with large temperature fluctuations, and as a result, it was confirmed that the temperature fluctuation of the flow did not have a significant effect near the corner wall. In addition, the vortices generated from the lower plenum to the outlet duct were identified in this paper. It is considered that the quantitative and qualitative results presented in this paper will serve as reference data for the benchmark.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Characterization of the Fast-Neutron Irradiator and the Fast-Flux Tube Irradiation Fixtures at the Pennsylvania State Breazeale Reactor

Accurate knowledge of the neutron spectrum at a nuclear research reactor is a prerequisite for planning irradiation experiments, as well as for evaluating irradiation exposure results. The neutron-flux spectrum in the fast-neutron irradiator (FNI) and the fast-flux tube (FFT) irradiation fixtures at the Pennsylvania State Breazeale Reactor (PSBR) were characterized using the multi-foil neutron activation method. These irradiation fixtures make use of graded shielding to produce unique neutron fields. Multiple foil sets were irradiated in the fixtures with different exposure times and reactor powers to understand the stability over a wide range of operating conditions. Measured results were evaluated against a MCNP6 simulation to produce a measurement-informed neutron flux-energy spectrum for each fixture using STAYSL_PNNL. Simulated estimates of the FNI fixture, a newer fixture (~25 years old), demonstrated excellent agreement with measured results; the FFT did not. Thermal neutron measurements from the FFT suggest there is additional thermal leakage not captured in the simulation model. In conclusion, possible explanations for the discrepancy include burn-out or degradation (i.e., micro-cracking, gaps, etc.) in the boral and cadmium liners over the lifetime of the fixture (~40 years old).

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2024

CNN-Based Phase Fault Classification in Real and Simulated Power Systems Data

This study proposes a convolutional neural network (CNN)–based two-step phase fault detection and identification method to classify anomalies in the power grid signal. Specifically, the first step checks the fault’s existence and determines the need for the second step. Subsequently, in the case of anomalies in the power grid signal, the second step identifies the type of fault, including line-to-line, single-line-to-ground, double-line-to-ground, and triple-line. Accordingly, the CNN architecture is both designed for the classification layers and trained with simulated data. To provide maximum prediction accuracy with minimum processing time, this study investigates the combinations of various feature extraction (FE) techniques, such as fast Fourier transform (FFT), amplitude and phase (AP), auto-correlation function, power spectral density, and wavelet transform (WT). Consequently, simulated and real-world results demonstrate that the proposed two-step method outperforms conventional one-step techniques, with the best performance obtained by using the combination of AP-AP, AP-WT, FFT-AP, and FFT-WT–based FE methods.

Alaca, Ozgur↗
DOE OSTI2026

Data Driven Correlated Noise Simulation for the ICEBERG LArTPC

Accurate electronic-noise simulation is essential for low-energy physics in liquid-argon TPCs. More realistic noise modeling allows us to better tune reconstruction algorithms and more reliably assess and optimize signal-detection thresholds. We present a data-driven noise simulation framework developed for the ICEBERG test stand for DUNE that generates synthetic noise waveforms that reproduce both (i) the measured per-channel magnitude of the Fast Fourier Transform (FFT) and (ii) frequency-dependent channel-to-channel correlations observed in ICEBERG noise data. Using a dedicated noise-only dataset, we build a compact noise model containing per-channel FFT-magnitude targets together with a small set of band-wise cross-wire color matrices. White noise is generated in the frequency domain by drawing circular-symmetric complex Gaussian coefficients with random phases and scaling them to match the measured FFT-magnitude targets, and cross-wire correlations are subsequently imposed using the stored color matrices. The model and algorithm were integrated into the LArSoft + Wire-Cell Toolkit simulation chain and validated by comparing waveform structure, frequency-domain spectra, and band-limited correlation matrices from simulated noise and ICEBERG data. This approach can be extended to other LArTPC operating conditions.

Ghosh, Avik [Iowa State U.]↗
DOE OSTI2020

ICRF antenna matching systems with ferrite tuners for the Alcator C-Mod tokamak

Real-time fast ferrite tuning (FFT) has been successfully implemented on the ICRF antennas on Alcator C-Mod. The former prototypical FFT system on the E-port 2-strap antenna has been upgraded using new ferrite tuners. A new FFT system with two ferrite tuners and one fixed-length stub has been installed on the transmission line of the D-port 2-strap antenna. These two systems are able to achieve and maintain the reflected power to the transmitters to less than 1% in real time under almost all plasma conditions and help ensure reliable high power operation of the antennas. The loading insensitivity feature vs. plasma conditions of the innovative field-aligned (FA) 4-strap antenna on the J-port allows us to significantly improve the matching by installing a carefully designed stub on each of the two transmission lines. The reduction of the RF voltages in the transmission lines has enabled the J-port FA antenna to deliver 3.7 MW RF power to plasmas out of 4 MW source power. The matching on the J-port antenna can be further improved by adding a single ferrite tuner under real-time control on each transmission line and this scheme will be implemented in the near future.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1976

The fast decoding of Reed-Solomon codes using number theoretic transforms

It is shown that Reed-Solomon (RS) codes can be encoded and decoded by using a fast Fourier transform (FFT) algorithm over finite fields. The arithmetic utilized to perform these transforms requires only integer additions, circular shifts and a minimum number of integer multiplications. The computing time of this transform encoder-decoder for RS codes is less than the time of the standard method for RS codes. More generally, the field GF(q) is also considered, where q is a prime of the form K x 2 to the nth power + 1 and K and n are integers. GF(q) can be used to decode very long RS codes by an efficient FFT algorithm with an improvement in the number of symbols. It is shown that a radix-8 FFT algorithm over GF(q squared) can be utilized to encode and decode very long RS codes with a large number of symbols. For eight symbols in GF(q squared), this transform over GF(q squared) can be made simpler than any other known number theoretic transform with a similar capability. Of special interest is the decoding of a 16-tuple RS code with four errors.

Reed, I. S.↗