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At least 55 records · Page 3
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↗
NASA NTRS2007

Circuit and Method for Communication Over DC Power Line

A circuit and method for transmitting and receiving on-off-keyed (OOK) signals with fractional signal-to-noise ratios uses available high-temperature silicon- on-insulator (SOI) components to move computational, sensing, and actuation abilities closer to high-temperature or high-ionizing radiation environments such as vehicle engine compartments, deep-hole drilling environments, industrial control and monitoring of processes like smelting, and operations near nuclear reactors and in space. This device allows for the networking of multiple, like nodes to each other and to a central processor. It can do this with nothing more than the already in-situ power wiring of the system. The device s microprocessor allows it to make intelligent decisions within the vehicle operational loop and to effect control outputs to its associated actuators. The figure illustrates how each node converts digital serial data to OOK 18-kHz in transmit mode and vice-versa in receive mode; though operations at lower frequencies or up to a megahertz are within reason using this method and these parts. This innovation s technique modulates a DC power bus with millivolt-level signals through a MOSFET (metal oxide semiconductor field effect transistor) and resistor by OOK. It receives and demodulates this signal from the DC power bus through capacitive coupling at high temperature and in high ionizing radiation environments. The demodulation of the OOK signal is accomplished by using an asynchronous quadrature detection technique realized by a quasi-discrete Fourier transform through use of the quadrature components (0 and 90 phases) of the carrier frequency as generated by the microcontroller and as a function of the selected crystal frequency driving its oscillator. The detected signal is rectified using an absolute-value circuit containing no diodes (diodes being non-operational at high temperatures), and only operational amplifiers. The absolute values of the two phases of the received signal are then summed and hard limited (digitized) by comparing them to a reference level and are then input into a microprocessor as a serial bit stream. The quasi-discrete Fourier transform is performed in high-temperature components (operational amplifiers, analog switches, resistors, and capacitors). The demodulated signal is a serial data stream that is input to the UART (universal asynchronous receiver transmitter) receiver pin of the microprocessor. The OOK of the carrier frequency uses the output of the UART pin as an enabling signal that drives the gate of the MOSFET. Logic low bits enable the carrier frequency (realized by using the 0 phase signal from the microcontroller, though either phase may be used) to be DC-coupled to the power supply bus through a current-limiting resistor mounted between the MOSFET drain and the supply rail. The presence of logic lows on the power supply rail is realized by carrier bursts while logic highs are realized by the absence of bursts.

Krasowski, Michael J.↗
NASA NTRS1978

Far-field radiation patterns of aperture antennas by the Winograd Fourier transform algorithm

A more time-efficient algorithm for computing the discrete Fourier transform, the Winograd Fourier transform (WFT), is described. The WFT algorithm is compared with other transform algorithms. Results indicate that the WFT algorithm in antenna analysis appears to be a very successful application. Significant savings in cpu time will improve the computer turn around time and circumvent the need to resort to weekend runs.

Heisler, R.↗
DOE OSTI2022

Evaluating Methods for Measuring Grid Frequency in Low-Inertia Power Systems: Preprint

Accurate measurement of grid frequency is a critical component of reliable grid control. Traditionally, methods such as phase locked loops (PLLs) and discrete Fourier transforms (DFTs) have been used in inverters and phasor measurement units (PMUs) to measure frequency. However, as the percentage of inverter-based resources (IBRs) such as solar and wind has increased, these conventional frequency measurement methods are proving unable to guarantee reliable control in some cases. One challenge is measuring frequency during transient events, where there is a disruption in the steady state sinusoidal voltage. During these events, the underlying frequency of the grid may barely change, but measurement methods report a large spike in frequency due to the disrupted waveform. New methods must balance between suppressing spikes in frequency during faults, and providing fast, accurate, measurements in all other grid operation conditions, especially during events with high rate-of-change-of frequency (ROCOF), which are more prevalent in high-IBR power systems. This paper first surveys frequency measurement methods that have been proposed to reduce measurement errors during transient events. Then, both conventional and more novel frequency measurement methods are tested against an IEEE standard and industry recommendations, and their performance is evaluated for events simulated in PSCAD. Results quantify the trade-offs in performance during different grid conditions and lead to suggestions for the most appropriate frequency and ROCOF measurement methods for low inertia grids.

frequency↗
NASA NTRS1979

Programs for high-speed Fourier, Mellin and Fourier-Bessel transforms

Several FORTRAN program modules for performing one-dimensional and two-dimensional discrete Fourier transforms, Mellin, and Fourier-Bessel transforms are described along with programs that realize the algebra of high speed Fourier transforms on a computer. The programs can perform numerical harmonic analysis of functions, synthesize complex optical filters on a computer, and model holographic image processing methods.

Ikhabisimov, D. K.↗
NASA NTRS1978

A fast DFT algorithm using complex integer transforms

Winograd's algorithm for computing the discrete Fourier transform is extended considerably for certain large transform lengths. This is accomplished by performing the cyclic convolution, required by Winograd's method, by a fast transform over certain complex integer fields. This algorithm requires fewer multiplications than either the standard fast Fourier transform or Winograd's more conventional algorithms.

Reed, I. S.↗
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 NTRS1989

Studies in astronomical time series analysis. III - Fourier transforms, autocorrelation functions, and cross-correlation functions of unevenly spaced data

This paper develops techniques to evaluate the discrete Fourier transform (DFT), the autocorrelation function (ACF), and the cross-correlation function (CCF) of time series which are not evenly sampled. The series may consist of quantized point data (e.g., yes/no processes such as photon arrival). The DFT, which can be inverted to recover the original data and the sampling, is used to compute correlation functions by means of a procedure which is effectively, but not explicitly, an interpolation. The CCF can be computed for two time series not even sampled at the same set of times. Techniques for removing the distortion of the correlation functions caused by the sampling, determining the value of a constant component to the data, and treating unequally weighted data are also discussed. FORTRAN code for the Fourier transform algorithm and numerical examples of the techniques are given.

Scargle, Jeffrey D.↗
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 NTRS1986

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, Andrew B.↗
DOE OSTI2021

Alignment Method for Synchronized Phase Angle Measurement With Presence of Practical Time Shift

Synchronized Phase Angle Measurements (SPAMs) are widely used in power systems in the applications of situational awareness. However, the practical time shifts can lead to unexpected angle differences among Phasor Measurement Units (PMUs) manufactured from various vendors. Moreover, since most of PMUs calculate phase angle via Discrete Fourier Transform based approaches, this issue becomes even worse under the off-nominal frequency condition. To mitigate the impact of practical timing shift, this letter presents a fast method to rectify the SPAM for appropriate alignment. To verify the performance of the proposed method, laboratory and field tests have been conducted by implementing the method in PMUs and phasor data concentrators, respectively. The results demonstrate that the standard deviations of the phase angle differences have significantly decreased to 0.1$^{\circ }$ order with the adoption of the proposed method.

42 ENGINEERING↗
NASA NTRS2002

An Investigation into the Potential Application of Wavelets to Modal Testing and Analysis

The analysis of transient data of the type found in vibrating mechanical systems has been greatly improved through the use of modern techniques such as Fourier analysis. This is especially true when considered in conjunction with the development of the so-called Fast Fourier Transform algorithm by Cooley and the tremendous strides in computational power of the last several decades. The usefulness of the discrete Fourier Transform is its ability to transform sampled data from the "time-domain" to the "frequency domain," thereby allowing the analyst to decompose a signal into its frequency content. More recent developments have led to the wavelet transform. The strength of wavelet analysis is its ability to maintain both time and frequency information, thus making it an attractive candidate for the analysis of non-stationary signals. This report is an overview of wavelet theory and the potential use of the wavelet transform as an alternative to Fourier analysis in modal identification.

A. Fort Gwinn, Jr.↗
NASA NTRS1986

Short time Fourier analysis of the electromyogram - Fast movements and constant contraction

Short-time Fourier analysis was applied to surface electromyograms (EMG) recorded during rapid movements, and during isometric contractions at constant forces. A portion of the data to be transformed by multiplying the signal by a Hamming window was selected, and then the discrete Fourier transform was computed. Shifting the window along the data record, a new spectrum was computed each 10 ms. The transformed data were displayed in spectograms or 'voiceprints'. This short-time technique made it possible to see time-dependencies in the EMG that are normally averaged in the Fourier analysis of these signals. Spectra of EMGs during isometric contractions at constant force vary in the short (10-20 ms) term. Short-time spectra from EMGs recorded during rapid movements were much less variable. The windowing technique picked out the typical 'three-burst pattern' in EMG's from both wrist and head movements. Spectra during the bursts were more consistent than those during isometric contractions. Furthermore, there was a consistent shift in spectral statistics in the course of the three bursts. Both the center frequency and the variance of the spectral energy distribution grew from the first burst to the second burst in the same muscle. The analogy between EMGs and speech signals is extended to argue for future applicability of short-time spectral analysis of EMG.

Hannaford, Blake↗
NASA NTRS1980

System design for a million channel digital spectrum analyzer /MCSA/

The system design of a wideband (8 MHz) million-channel digital spectrum analyzer for use with a SETI receiver is presented. The analyzer makes use of a digital bandpass filter bank for transforming the wideband input signal into a specified number (120) of uniform narrowband output channels by the use of a Fourier transform digital processor combined with a prototype digital weighting network (finite impulse response filter). The output is then processed separately by 120 microprocessor-based discrete Fourier transform computers, each producing 8190 output channels of approximately 8 Hz bandwidth by the use of an 8190-point prime factor algorithm.

Peterson, A.↗
DOE OSTI2020

Experimental and theoretical evidence for hydrogen doping in polymer solution-processed indium gallium oxide

The field-effect electron mobility of aqueous solution-processed indium gallium oxide (IGO) thin-film transistors (TFTs) is significantly enhanced by polyvinyl alcohol (PVA) addition to the precursor solution, a >70-fold increase to 7.9 cm 2 /Vs. To understand the origin of this remarkable phenomenon, microstructure, electronic structure, and charge transport of IGO:PVA film are investigated by a battery of experimental and theoretical techniques, including In K-edge and Ga K-edge extended X-ray absorption fine structure (EXAFS); resonant soft X-ray scattering (R-SoXS); ultraviolet photoelectron spectroscopy (UPS); Fourier transform-infrared (FT-IR) spectroscopy; time-of-flight secondary-ion mass spectrometry (ToF-SIMS); composition-/processing-dependent TFT properties; high-resolution solid-state 1 H, 71 Ga, and 115 In NMR spectroscopy; and discrete Fourier transform (DFT) analysis with ab initio molecular dynamics (MD) liquid-quench simulations. The 71 Ga{ 1 H} rotational-echo double-resonance (REDOR) NMR and other data indicate that PVA achieves optimal H doping with a Ga···H distance of ~3.4 Å and conversion from six- to four-coordinate Ga, which together suppress deep trap defect localization. This reduces metal-oxide polyhedral distortion, thereby increasing the electron mobility. Finally, hydroxyl polymer doping thus offers a pathway for efficient H doping in green solvent-processed metal oxide films and the promise of high-performance, ultra-stable metal oxide semiconductor electronics with simple binary compositions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1978

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.↗
DOE OSTI2022

Direct measurement of storage and loss behavior in AFM force–distance experiments using the modified Fourier transformation

Force–distance curve experiments are commonly performed in atomic force microscopy (AFM) to obtain the viscoelastic characteristics of materials, such as the storage and loss moduli or compliances. The classic methods used to obtain these characteristics consist of fitting a viscoelastic material model to the experimentally obtained AFM data. Here, we demonstrate a new method that utilizes the modified discrete Fourier transform to approximate the storage and loss behavior of a material directly from the data, without the need for a fit. Additionally, one may still fit a model to the resulting storage and loss behavior if a parameterized description of the material is desired. In contrast to fitting the data to a model chosen a priori, departing from a model-free description of the material's frequency behavior guides the selection of the model, such that the user may choose the one that is most appropriate for the particular material under study. To this end, we also include modified Fourier domain descriptions of commonly used viscoelastic models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗