It is well known that the magnitudes of the coefficients of the discrete Fourier transform (DFT) are invariant under certain operations on the input data. In this paper, the effects of rearranging the elements of an input data on its DFT are studied. In the one-dimensional case, the effects of permuting the elements of a finite sequence of length N on its discrete Fourier transform (DFT) coefficients are investigated. The permutations that leave the unordered collection of Fourier coefficients and their magnitudes invariant are completely characterized. Conditions under which two different permutations give the same DFT coefficient magnitudes are given. The characterizations are based on the automorphism group of the additive group ZN of integers modulo N and the group of translations of ZN. As an application of the results presented, a generalization of the theorem characterizing all permutations that commute with the discrete Fourier transform is given. Numerical examples illustrate the obtained results. Possible generalizations and open problems are discussed. In higher dimensions, results on the effects of certain geometric transformations of an input data array on its DFT are given and illustrated with an example.
This paper presents a universal approximation of the unit circle by a polygon that can be used in signal processing algorithms. Optimal choice of the values of three parameters of this approximation allows one to obtain a high accuracy of approximation. The approximation described in the paper has a universal character and can be used in many signal processing algorithms, such as DFT, that use the mathematical form of the unit circle. One of the applications of the described approximation is the DFT linear interpolation method (LIDFT). Applying the results of the presented paper to improve the LIDFT method allows one to significantly decrease the errors in estimating the amplitudes and frequencies of multifrequency signal components. The paper presents the derived formulas, an analysis of the approximation accuracy and the region of best values for the approximation parameters.
To improve the estimation of active power, the possibility of estimating the amplitude square of a signal component using the interpolation of the squared amplitude discrete Fourier transform (DFT) coefficients is presented. As with an energy-based approach, the amplitude square can be estimated with the squared amplitude DFT coefficients around the component peak and a suitable interpolation algorithm. The use of the Hann window, for which the frequency spectrum is well known, and the three largest local amplitude DFT coefficients gives lower systematic errors in squared interpolated approach or in better interpolated squared approach than the energy-based approach, although the frequency has to be estimated in the first step. All investigated algorithms have almost the same noise propagation and the standard deviations are about two times larger than the Cramér-Rao lower bound.
The half-metallic, mechanical, and transport properties of the quaternary Heusler compound of PdZrTiAl is discussed under hydrostatic pressures in the range of –11.4 GPa to 18.4 GPa in the framework of the density functional theory (DFT) and Boltzmann quasi-classical theory using the generalization gradient approximation (GGA). By applying the stress, the band gap in the minor spin increases so that the lowest band is obtained 0.25 eV at the pressure of –11.4 GPa while the maximum gap is calculated 0.9 eV at the pressure of 18.4 GPa. In all positive and negative pressures, the PdZrTiAl composition exhibits a half-metallic behavior 100% spin polarization at the Fermi level. It is also found that applying stress increases the Seebeck coefficient in both spin directions. In the minority spin, the n-type PdZrTiAl, the power factor (PF) for all the cases is greater in the equilibrium state than the strain and stress conditions whereas in the majority spin, the PF value of the stress state is greater than the other two. The non-dimensional figure of merit (ZT) is significant and is about one in spin down in the room temperature for the all pressure states that it remains on this value by applying pressure. The obtained elastic constants indicate that the PdZrTiAl crystalline structure has a mechanical stability. Based on the Yong (E), Bulk (B) and shear (G) modulus and Poisson (n) ratio, the brittle-ductile behavior of this compound has been investigated under pressure. The results indicate that PdZrTiAl has a ductile nature and it is a stiffness compound in which elastic and mechanical instability increases by applying strain.
Power systems that are highly loaded, especially by a stochastic supply of renewables and the presence of storages, require dynamic measurements for their optimal control. Phasor measurement units (PMUs) can be used to capture electrical parameters of a power system. Standards on the PMU dynamic performance have been modified to incorporate their new dynamic mode of operation. This paper examines the PMU dynamic performance and proposes essential algorithms for measurement accuracy verification. Measurements of dynamic input signals, which vary in amplitude or frequency, were taken during automated tests of two PMUs. The test results are presented and expounded with further recommendation for the performance requirements. This paper also presents and examines applied testing procedures with relevance to the specifications of the IEEE Standard for Synchrophasor C37.118.1™-2011 and its amendment C37.118.1a™-2014.
This paper presents the general solution of the least-squares approximation of the frequency characteristic of the data window by linear functions combined with zero padding technique. The approximation characteristic can be discontinuous or continuous, what depends on the value of one approximation parameter. The approximation solution has an analytical form and therefore the results have universal character. The paper presents derived formulas, analysis of approximation accuracy, the exemplary characteristics and conclusions, which confirm high accuracy of the approximation. The presented solution is applicable to estimating methods, like the LIDFT method, visualizations, etc.
This overview paper presents and compares different methods traditionally used for estimating damped sinusoid parameters. Firstly, direct nonlinear least squares fitting the signal model in the time and frequency domains are described. Next, possible applications of the Hilbert transform for signal demodulation are presented. Then, a wide range of autoregressive modelling methods, valid for damped sinusoids, are discussed, in which frequency and damping are estimated from calculated signal linear self-prediction coefficients. These methods aim at solving, directly or using least squares, a matrix linear equation in which signal or its autocorrelation function samples are used. The Prony, Steiglitz-McBride, Kumaresan-Tufts, Total Least Squares, Matrix Pencil, Yule-Walker and Pisarenko methods are taken into account. Finally, the interpolated discrete Fourier transform is presented with examples of Bertocco, Yoshida, and Agrež algorithms. The Matlab codes of all the discussed methods are given. The second part of the paper presents simulation results, compared with the Cramér-Rao lower bound and commented. All tested methods are compared with respect to their accuracy (systematic errors), noise robustness, required signal length, and computational complexity.
This paper derives analytical formulas for the systematic errors of the linear interpolated DFT (LIDFT) method when used to estimating multifrequency signal parameters and verifies this analysis using Monte-Carlo simulations. The analysis is performed on the version of the LIDFT method based on optimal approximation of the unit circle by a polygon using a pair of windows. The analytical formulas derived here take the systematic errors in the estimation of amplitude and frequency of component oscillations in the multifrequency signal as the sum of basic errors and the errors caused by each of the component oscillations. Additional formulas are also included to analyze particular quantities such as a signal consisting of two complex oscillations, and the analyses are verified using Monte-Carlo simulations.
In this article, synthesis, electronic and optical properties of an N-cyclohexyl-acrylamide (NCA) molecule are described based on different solvent environments and supported by theoretical calculations. Theoretical calculations have been carried out using a density function theory (DFT). Temperature dependence of the sample electrical resistance has been obtained by a four-point probe technique. Experimental and semi-theoretical parameters such as optical density, transmittance, optical band gap, refractive index of the NCA for different solvents were obtained. Both optical values and electrical resistance values have shown that NCA is a semiconductor material. The values of HOMO and LUMO energy levels of the headline molecule indicate that it can be used as the electron transfer material in OLEDs. All results obtained confirm that the NCA is a candidate molecule for OLED and optoelectronic applications.
The electronic, optical and thermoelectric properties of zirconia-based MgZrO3 oxide have been studied theoretically at a variant pressure up to 25 GPa. Calculations for the formation energy and tolerance factor reveal the thermodynamic and structural stability of MgZrO3. To tune the indirect band gap from to a direct band gap, the optimized structure of MgZrO3 has been subjected to external pressure up to 25 GPa. The optical properties have been discussed in the form of dielectric constant and refraction that brief us about the dispersion, polarization, absorption, and transparency of the MgZrO3. In the end, the thermoelectric parameters have been analyzed at variant pressure against the chemical potential and temperature. The narrow band gap and high absorption in the ultraviolet region increase the demand of the studied oxide for energy harvesting device applications.
Quality of energy produced in renewable energy systems has to be at the high level specified by respective standards and directives. One of the most important factors affecting quality is the estimation accuracy of grid signal parameters. This paper presents a method of a very fast and accurate amplitude and phase grid signal estimation using the Fast Fourier Transform procedure and maximum decay side-lobes windows. The most important features of the method are elimination of the impact associated with the conjugate’s component on the results and its straightforward implementation. Moreover, the measurement time is very short ‒ even far less than one period of the grid signal. The influence of harmonics on the results is reduced by using a bandpass pre-filter. Even using a 40 dB FIR pre-filter for the grid signal with THD ≈ 38%, SNR ≈ 53 dB and a 20‒30% slow decay exponential drift the maximum estimation errors in a real-time DSP system for 512 samples are approximately 1% for the amplitude and approximately 8.5・10‒2 rad for the phase, respectively. The errors are smaller by several orders of magnitude with using more accurate pre-filters.
This study is based on the investigation of AlSb layer thickness effect on heavy−hole light−hole (HH−LH) splitting and band gap energies in a recently developed N−structure based on InAs/AlSb/GaSb type II superlattice (T2SL) p−i−n photodetector.eFirst principle calculations were carried out tailoring the band gap and HH−LH splitting energies for two possible interface transition alloys of InSb and AlAs between InAs and AlSb interfaces in the superlattice. Results show that AlSb and InAs−GaSb layer thicknesses enable to control HH−LH splitting energies to desired values for Auger recombination process where AlSb/GaSb total layer thickness is equal to InAs layers for the structures with InSb and AlAs interfaces