Discrete Fourier Transform Technique Research Articles

Hybridization of almost difference sets and DFT technique for concentric circular antenna array thinning

This paper introduces a hybrid methodology for minimizing the peak sidelobe level (PSLL) in concentric circular antenna arrays (CCAAs). Traditionally, the almost difference set (ADS) approach has been utilized for determining active element positions, but its effectiveness in PSLL reduction is limited. To address this limitation, the proposed methodology integrates the ADS approach with the discrete Fourier transform (DFT) technique. This integration optimizes excitation amplitudes for activated elements within the ADS-based thinned array, resulting in significant PSLL reduction. Simulation results across various case studies demonstrate that the hybrid ADS-DFT method achieves lower PSLL values than existing thinning techniques while maintaining high computational efficiency. Additionally, electromagnetic (EM) simulations validate the efficiency of the proposed method, considering mutual coupling effects.

Prospects for detecting proto-neutron star rotation and spin-down using supernova neutrinos

ABSTRACT After a successful supernova, a proto-neutron star (PNS) cools by emitting neutrinos on ∼1–100 s time-scales. Provided that there are neutrino emission ‘hotspots’ or ‘cold-spots’ on the surface of the rotating PNS, we can expect a periodic modulation in the number of neutrinos observable by detectors. We show that Fourier transform techniques can be used to determine the PNS rotation rate from the neutrino arrival times. Provided there is no spin-down, a 1-parameter Discrete Fourier Transform (DFT) is sufficient to determine the spin period of the PNS. If the PNS is born as a magnetar with polar magnetic field strength B0 ≳ 1015 G and is ‘slowly’ rotating with an initial spin period ≳100 ms, then it can spin-down to periods of the order of seconds during the cooling phase. We propose a modified DFT technique with three frequency parameters to detect spin-down. Due to lack of neutrino data from a nearby supernova except the ∼20 neutrinos detected from SN1987A, we use toy models and one physically motivated modulating function to generate neutrino arrival times. We use the false alarm rate (FAR) to quantify the significance of the Fourier power spectrum peaks. We show that PNS rotation and spin-down are detected with $\rm FAR\,\lt\, 2~{{\ \rm per\ cent}}$ (2σ) for periodic signal content $\rm M\gtrsim 13-15~{{\ \rm per\ cent}}$ if 5 × 103 neutrinos are detected in ∼3 s and with $\rm FAR\,\lt\, 1{{\ \rm per\ cent}}$ for $\rm M\,\ge 5{{\ \rm per\ cent}}$ if 5 × 104 neutrinos are detected in ∼3 s. Since we can expect ∼104−105 neutrino detections from a supernova at 10 kpc, detection of PNS rotation and spin-down is possible using the neutrinos from the next Galactic supernova.

Behavioral analysis of COVID-19 daily deaths in Sri Lanka

In December 2019, the world was unknowingly caught by coronavirus disease. Since it spread worldwide and the burden of this disease is very high, the whole world has tried to reduce the impact. Therefore, known scientific facts about future events are very useful for policymakers. Hence, this research contributes to a scientific and technological process to provide a method for controlling the movements of the general public by forecasting the future using Discrete Fourier Transform (DFT) technique. DFT technique can decompose a complex signal into simpler parts to facilitate the analysis. In this research, comparing the accuracy of the daily deaths and daily infected patient datasets, the daily deaths dataset was selected for the model. After that, the Sri Lankan COVID-19 daily deaths data subsequence was modelled as the DFT amplitude spectrum. Then by backward-transformation of significant harmonics predicts the near future of daily COVID-19 deaths. The results conclude that the proposed method can provide short-term forecasting of COVID-19 daily death data with sufficient accuracy. And these near-future predictions will help guide health planning and short-term policy changes.

Fast fourier transform based new pooling layer for deep learning

Abstract Convolution is considered most significant layer in deep learning because it can extract best features of data through the network but it may result in huge volume of data. This problem can be solved by using pooling. In this paper, A novel pooling method is proposed by using discrete Fourier transform (DFT), this method is used DFT technique to transform the data from spatial domain into frequency domain to preserve the most important information from the details coefficients, where the details information of the image is less significant, therefore it can be discarded to down sample the size of dimensions. Its effect will be great with advantage of reducing the eliminated details information as compared with other standard methods. After applying DFT, the most significant coefficients, which represent most important features are cropped while less important details will be discarded then the data are reconstructed by applying inverse DF, therefore the high quality of features are extracted, which solve the problem of losing significant information during the pooling layer. Different methods are proposed based on the scenario of using DFT. The proposed methods are tested by extracting pooled image then the original images were retrieved using only the pooled images. Then the retrieved images are compared with original images by using different measures such as SNR, correlation and SSIM. Then the proposed layers used for image classification for two different datasets. The results proved that the proposed methods outperformed standard methods, thus it can be used for deep learning application.

Improve correlation matrix of Discrete Fourier Transformation technique for finding the missing values of MRI images.

Missing values in the k-NN algorithm are a significant research concern, especially in low-grade tumours and CSF fluid, which are commonly identified in MRI scans. Missing values are usually ignored, but when data is mined, they can lead to bias and errors. In addition, the data is not missing at random. This study improves image accuracy, boosts the efficiency of missing k-NN hybrid values, and develops a research technique for detecting CSF fluid deposits in brain areas separated from non-tumor areas. We also offer a new method for detecting low-grade tumours or cerebrospinal fluid (CSF) formation in its early stages. In this study, we combine the hybrid K-Nearest Neighbor algorithm with the Discrete Fourier transform (DFT), as well as Time-Lagged analysis of four-dimensional (4D) MRI images. These dependencies exist in both space and time, but present techniques do not account for both sequential linkages and numerous types of missingness. To address this, we propose the DFLk-NN imputation method, which combines two imputation approaches based on a hybrid k-NN extension and the DFT to capture time-lag correlations both within and across variables. There are several types of missingness are enables the imputation of missing values across the variable even when all the data for a given time point is missing. The proposed method gives high accuracies of MRI datasets and retrieves the missing data in the images.

A RANS approach for transfer function plot based on discrete fourier transform

ABSTRACT Besides the other hydrodynamic phenomena, the ship design process includes also the accurate prediction of the motions in waves. In this paper, a Discrete Fourier Transform (DFT) based method is presented for calculations of ship motion transfer functions (TFs) by using Reynolds Averaged Navier Stokes (RANS) approach. The DTMB 5512 hull form is selected for the proof of the accuracy of the proposed method at the Froude number of 0.41 and head waves. Instead of sending regular waves separately to the model ship in a virtual towing tank, a wave energy spectrum is defined and the created long-crested irregular wave system is sent to the model ship. With the aid of the DFT technique, irregular vertical ship motions in the time domain are transformed into the frequency domain. With the proposed RANS method, it is reported that CPU time spent for CFD analyses are significantly dropped compared to traditional RANS TFs calculation processes.

Non-Extra Pixel Interpolation

A non-extra pixel interpolation NPI is introduced for efficient image upscaling purposes. The NPI algorithm uses extended-triangular and linear scaling functions to match the pixel coordinates. The triangular function uses a modulo-operator with only two variables representing image pixels and scaling ratio. Every two variables of the linear scaling function represent the source/destination image pixels and scaling ratio. The traditional ceil function is used to round off non-integer pixel coordinates. The circshift and padarray functions are used to circularly shift the elements in array output by [Formula: see text]-amount in each dimension and pad elements of the [Formula: see text]th columns/rows by g-padsize in the shifted array, respectively. The [Formula: see text], [Formula: see text] and [Formula: see text] values are determined with respect to integer scaling ratios by a vector of [Formula: see text]-elements. The Exactness, Peak Signal-to-Noise Ratio, Signal-to-Noise Ratio and Discrete Fourier Transform techniques were used for objective evaluation purposes. Experiments demonstrated comparable results as well as the need for further researches.

Precision analysis of turbulence phase screens and their influence on the simulation of Gaussian beam propagation in turbulent atmosphere.

The slip-step method is widely used in simulating optical wave propagation in turbulent atmosphere, which treats propagation and phase perturbations caused by turbulence separately and in discrete steps along the propagation axis. The phase perturbations are represented by a series of phase screens, and hence, the precision of the phase screen concerns the accuracy of the simulation. In this paper, we first discuss the precision and computational performance of phase screens generated by the subharmonic complemented discrete Fourier transformation (DFT) (DFT-SH) method, three kinds of randomized spectral sampling techniques (sparse spectrum (SS) technique, sparse spectrum technique with uniform wave vectors (SU), randomized DFT technique), and optimization-based (OB) method; then, the simulations are implemented with the phase screens generated by these methods. Some statistical quantities of the received optical field are calculated, such as beam wander variance, long-term beam radius, short-term beam radius, and on-axis scintillation index. The statistical results show that the undersampling of phase screen in the low-frequency region causes underestimation of the values of beam wander variance, long-term beam radius, and focused beam on-axis scintillation index because these quantities are sensitive to the large-scale inhomogeneities. However, the undersampling does not affect the predicted values of the short-term beam radius and collimated beam on-axis scintillation index because these quantities are insensitive to the large-scale inhomogeneities.

Comparison of four techniques for turbulent phase screens simulation.

In the study, we introduce a new technique, sparse spectrum with uniform wave vectors (SU), for generation of phase screen samples. In a manner similar to the known sparse spectrum (SS) technique, it uses a trigonometric series with random discrete spectral support. However, in contrast to the SS technique, random wave vectors are uniformly distributed on individual segments of the wave vector plane partition in the SU technique. We compare the accuracy and computational effectiveness of the SU technique with the subharmonics complemented discrete Fourier transform (DFT) technique, SS technique, and randomized DFT technique [ J. Opt. Soc. Am. B36, 3249 (2019)JOBPDE0740-322410.1364/JOSAB.36.003249]. The SU and SS techniques generate unbiased samples and indicate superior computational effectiveness for 1 MP and larger screens.

A fast numerical method for photomultiplier tube calibration

In this article, a new method is discussed for the calibration and monitoring of photomultiplier tubes (PMTs). This method is based on a Discrete Fourier Transform (DFT) and it is fast and general so that it can be used in cases where an analytical model of the PMT response is not available. The DFT approach is employed for the absolute calibration of the Hamamatsu R1408 photomultiplier tube. It should be noted that the R1408 PMTs do not show a sharp peak at the single photoelectron distribution and gain determination via conventional methods is often unattainable. Here, we show that the DFT technique, coupled with a gamma function model for the single photoelectron response, produces rigorous calibration results and it can be used for gain determination with a good accuracy.

Reduced Leakage Synchrophasor Estimation: Hilbert Transform Plus Interpolated DFT

Synchrophasor estimation is typically performed by means of spectral analysis based on the discrete Fourier transform (DFT). Traditional DFT approaches, though, suffer from several uncertainty contributions due to the stationarity assumption, spectral leakage effects, and the finite-grid resolution. This paper addresses these limitations, by proposing a joint application of the Hilbert transform (HT) and the interpolated DFT (IpDFT) technique. Specifically, the HT enables the suppression of the spectral leakage generated by the negative image of the tones under analysis, whereas the IpDFT limits the effects of spectrum granularity. In order to relax the constraint in terms of measurement reporting latency, the proposed estimator can adopt a window length of 40 ms and yet provides a noticeable estimation accuracy with a worst-case total vector error and frequency error equal to 0.02% and 4 mHz, respectively, in steady-state conditions. In this context, this paper discusses the most suitable setting of the algorithm parameters and their effect on spurious component rejection. Moreover, a thorough metrological characterization of the algorithm estimation accuracy and responsiveness with respect to the IEEE Std. C37.118.1 is carried out in order to detect the main uncertainty sources as well as possible room for enhancement. Finally, a comparison with two consolidated IpDFT approaches shows the actual performance enhancement provided by the proposed algorithm.

Range Resolution Enhancement using Root-MUSIC Analysis in CTFM Sonar for Bandwidth-limited Applications

ABSTRACT This paper presents a detailed study of the application of Root-MUSIC algorithm in the continuous-time frequency modulation (CTFM) system. Classically, CTFM-based sonars and radars use the Discrete Fourier transform (DFT) magnitude peaks to find the range of the received echoes. In applications where the medium does not support large signal bandwidth over the ranges of interest, the DFT technique cannot provide the required range resolution. A technique called dual demodulator continuous-time frequency modulation (DDCTFM) was proposed to overcome this limitation and provides greater range resolution. But we observe that there is a problem of phase mismatch in DDCTFM that does not increase the range resolution. This problem is explained in the paper. The super resolution Root-MUSIC algorithm is studied in this context to evaluate its efficacy in providing higher frequency resolution and corresponding range resolution in CTFM. Several detailed simulation experiments done in MATLAB to provide insight into its performance are reported in the paper. Also, lab experiments have been done to practically demonstrate the efficacy of using Root-MUSIC technique in CTFM. Based on the results obtained from the simulation experiments, it is concluded that there is an improvement by a factor of 2.8 in the range resolution estimation by the use of Root-MUSIC algorithm over DFT-based analysis in CTFM. In practical experiments, the improvement factor obtained in the range resolution estimation is 2.35.

DWT Feature based Blind Image Steganalysis using Neural Network Classifier

Abstract- The objective of forensic steganalysis is to identify the existence of embedded message and to ultimately retrieve the secret message. In this paper, we have extracted Histogram, Markov and Co-occurrence features from wavelet domain and compared with existing farid 72 DWT features. The performance metrics are MSE (Mean square error) and classification accuracy for blind image steganalysis using two steganography algorithms outguess and nsF5. Neural network back propagation classifier has been used to classify images into stego images and clean images. Experimental results show that the proposed features considerably outperform existing farid 72 DWT features. Keywords — Discrete wavelet transformation, Neural network, Outguess, Steganography, Steganalysis, nsF5. I. INTRODUCTION Steganography[1] is a process in which the message is embedded in a cover medium to create a stego medium with the help of steganography tool that results in changes in the statistical properties of cover medium where medium could be video, text, image, audio etc. Now a day’s wide variety of steganographic tools are freely and widely available on the internet such as StegHide [2], Outguess [3] etc. Statistical un-detectability [4] is the necessity of steganography process, which means that it is difficult or impossible for attacker to judge whether an image is the stego or cover based on the statistics. Steganography hides data in [5] Spatial domain and Transform domain or Frequency domain. Transform Domain is further divided into three categories (a) DCT (Discrete Cosine Transformation technique), (b) DWT (Discrete Wavelet transformation technique), (c) DFT (Discrete Fourier transformation technique).In transform domain, images are initially transformed and then the message is embedded while in spatial domain message is embedded directly inside the pixel.

Fast Time-Domain Finite Element Analysis of 3-D Nonlinear Time-Periodic Eddy Current Problems With ${\rm T},\Phi-\Phi$ Formulation

A method is presented for obtaining the steady-state solution of three-dimensional eddy current problems with nonlinear material properties and periodic excitations using the T, Φ-Φ formulation. The problem is formulated in the time-domain and the application of a fixed-point approach combined with a discrete Fourier-transformation technique ensures that, during one nonlinear iteration step, there is no coupling between the time-steps within one period. The steady-state result is hence obtained by solving half as many time steps as their number in one period. Since the time steps are decoupled, their computation can be readily parallelized resulting in a fast method. Comparison with results obtained by a transient time-stepping technique is presented.

Application of Enhanced Phase-Locked Loop System to the Computation of Synchrophasors

This paper introduces the application of an enhanced phase-locked loop (EPLL) system to the estimation of synchrophasors in a phasor measurement unit (PMU). The major concern is accurate estimation within off-nominal frequency operation of the system. The well-known technique based on discrete Fourier transform (DFT) can provide accurate estimation of the phasors in a three-phase balanced system. However, the negative-sequence component causes errors to the DFT estimates. The DFT cannot accomplish this task in a single-phase system. The EPLL is shown to be a solution for those shortcomings of the DFT technique, both in single-phase and in unbalanced three-phase systems, at the expense of some more complicated structure. Extensive steady-state and dynamic tests are performed and the results are presented and discussed.

Reference Current Computation for Active Power Filters by Running DFT Techniques

This paper analyzes the feasibility and convenience of applying the efficient discrete Fourier transform (DFT) techniques for the computation of reference currents in active power filters. Existing methods designed for this purpose rely on a high-pass filter in order to obtain the harmonic components of the load current to be filtered. Among these methods, the stationary reference frame (SRF) method reveals itself as the most accurate one because of its inherent immunity to distorted voltage conditions. In this paper, two different implementations of the running DFT, including their recursive and nonrecursive versions, are compared to the SRF approach in terms of steady-state performance, adequacy of transient response, and computational effort. In addition to simulation results, an experimental setup is designed to prove the advantages of resorting to the DFT. Conceptual similarities between both schemes are also stressed in this paper.

Uniaxial tensile behavior of a bicrystal copper nanowire: Structural characterization with a Fourier transformation method

Abstract Molecular dynamics simulations have been used to investigate the uniaxial tensile behavior of the [1 1 0]‖[1 0 0] bicrystal copper nanowire. Due to the effect of grain boundary, the bicrystal nanowire breaks at the interface with strain increasing, showing a unique brittle feature. In order to well understand the crystallographic characters, we have developed a discrete Fourier transformation technique to analyze the periodic crystal structure. In particular, the atomic density distribution along the long axis of the nanowire is transformed into a frequency–amplitude relationship or into a normalized atomic density distribution. These two treatments enable us to further study the crystal grain orientation and the crystal structure in the stretching process. The frequency–amplitude analysis provides information about the large-scale crystallographic features while the local characteristics are mainly determined by the normalized atomic density distribution. From analyses of the simulation data, we have found that [1 1 0]‖[1 0 0] keeps good crystalline structure until breaking.

Breaking Behavior of a Bicrystal Copper Nanowire Studied Using a Fourier Transformation Method

Ultra-large scale molecular dynamics simulations were used to investigate the breaking behavior of a [111]︱︱[110] bicrystal copper nanowire. From the periodicity of the copper crystal structure, we developed a discrete Fourier transformation technique to analyze the periodic structure of the crystal system. In particular, the atomic density distribution along the long axis of the nanowire was transformed into a amplitude-frequency relation or into a normalized atomic density distribution. These two treatments enable us to further study the crystal grain orientation and the crystal structure at different stretching moments of the nanowire. The amplitude-frequency analysis provided information about the large-scale crystallographic features while local characteristics were determined by the normalized atomic density distribution. From analyses of the simulation data, we found that the [111]︱︱[110] bicrystal copper nanowire showed an amalgamation of the grain boundary and a rotation of the crystal grains during stretching and this led to a rupture in the [111] crystal grain. After breaking, the nanowire underwent a new recrystallization process as determined by amplitude-frequency analysis and normalized atomic density distribution. The Fourier transformation technique proposed in this work provides a powerful tool for theoretical investigations of nanomaterials.

A Novel Technique for Image Authentication in Frequency Domain Using Discrete Fourier Transformation Technique (IAFDDFTT)

In this paper a novel technique for Image Authentication in Frequency Domain using Discrete Fourier Transformation Technique (IAFDDFTT) has been proposed to authenticate a gray level PGM, TIFF image by embedding a message/image where 2 x 2 submatrix is taken as source matrix from the image matrix and transform into the frequency domain. Two bits of authenticating message/image are fabricated within the real part of each pixel, excluding the first pixel of each submatrix where the position is chosen using a hash function. The process is repeated for each submatrix on row major order to insert authenticating message/image content and 128 bits Message Digest (MD-5), generated from authenticating message/image. Inverse DFT is performed to transform the embedded image from frequency to spatial domain as final step of encoding. The decoding is done through the reverse procedure. The experimental results against statistical and visual attack has been discussed and compared with the existing steganography algorithm like S-Tools. Histogram analysis, noise analysis, and standard deviation computation of source image with embedded image shows the better results in comparison with existing S-Tools.

소형망원경을 이용한 산개성단 NGC 129 영역의 변광성 탐사

소형망원경을 이용하여 산개성단 내 단주기 미세 변광성을 체계적으로 탐사하기 위한 보현산 천문대 측광 모니터링 프로그램 Short Period Variability Survey(SPVS)의 일환으로, 젊은 산개성단 NGC 129의 <TEX>$90'{\times}60'$</TEX> 영역에 대한 V필터 시계열 측광 관측을 수행하였다. 성단의 관측은 보현산 천문대 155mm 소형 굴절 망원경과 <TEX>$3K{\times}2K$</TEX> CCD 카메라를 이용하여 2004년 10월 12일부터 2005년 11월 3일까지 총 11일간 수행되었으며, 그 결과 전체 2400장의 V 필터시계열 CCD 영상자료 및 성단의 색-등급도를 얻었다. 시계열 자료의 기기등급을 표준등급으로 변환하기 위하여 앙상블정규화 기법(ensemble normalization technique)을 사용하였다. 측광 후 총 9537개별의 시간에 따른 광도변화를 조사한결과 총 66개의 새로운 변광성을 발견 하였다. 새롭게 찾아낸 변광성들은 DFT(Discrete Fourier Transform) 분석과 위상 맞추기 방법(phase-matching technique)을 이용하여 변광 주기를 결정하였다. 결정된 변광성의 주기 및 진폭 변화, 색-등급도 상에서의 변광성의 위치 등을 고려하여 변광 유형을 조사한 결과 9개의 SPB형 변광성과 9개의 <TEX>${\delta}$</TEX> Scuti형 변광성, 29개의 식변광성, 17개의 장주기 변광성과 기타 2개의 변광성으로 분류할 수 있었다. 본 연구를 통해, 산개성단에서의 변광성 탐사 연구에 소형망원경이 유용하게 활용될 수 있음을 확인하였다. As part of the SPVS (Short-Period Variability Survey) which is a wide-field <TEX>$(90'{\times}60')$</TEX> photometric monitering program at Bohyunsan Optical Astronomy (BOAO), we performed V band time-series CCD photometric observations ofthe young open cluster NGC 129 for 11 nights between October 12, 2004 and November 3, 2005 using the 155mm refractor equipped with <TEX>$3K{\times}2K$</TEX> CCD camera. From the observation we obtained 2400 V band CCD frames and color-magnitude diagram of the cluster. To transform instrumental magnitude to standard magnitude, we applied ensemble normalization technique to all observed time-series data. After the photometric reduction process, we examined variations of 9537 stars. As a result, sixty six of the new variable stars were discovered. To determine the periods of the sevariables, we used DFT(Discrete Fourier Transform) and phase-matching technique. According to light curve shape, period, amplitude and the position on a C-M diagram, we classified these variables as 9 SPB type, 9 <TEX>${\delta}$</TEX> Scuti type, 29 eclipsing, 17 long term variables. However, two of them were not classified. From this study, we learned that small telescopes could be a very useful tool to observe variable stars in the open cluster in survey program.