Discrete Fast Fourier Transform Research Articles

A Multichannel Analysis of Imbalanced Computed Tomography Data for Lung Cancer Classification

Abstract Lung cancer holds the highest fatality rate among cancers, emphasizing the importance of early detection. Computer algorithms have gained prominence across various domains, including lung cancer diagnosis. These algorithms assist specialists, especially in medical imaging, yet current efforts lack comprehensive CT data analysis; especially in handling imbalanced datasets and fully exploiting spatial information. The lack of spatial analysis hinders the ability to identify subtle variations in texture and structure that are crucial for detecting lung cancer early and accurately. Therefore, this study uses a multichannel analysis of computed tomography (CT) images and deep learning-based ensemble learning (MC-ECNN) to find lung cancer even when the data is not balanced. Firstly, the data imbalance issue is tackled through the synthetic minority oversampling technique (SOMTE); afterwards, a multi-channel analysis of the data is performed to explore a distinct set of abstract features. Lastly, a deep ensemble learning method is used to classify the extracted distinct abstract feature set into the appropriate classes. The proposed method uses the discrete Fast Fourier transform (DFFT) and discrete cosine transform (DCT), along with the actual CT scans, for the multi-channel analysis of the data in different domains. The proposed model yielded 99.60% test accuracy on unseen data, which is at least 3% better than the other state-of-the-art studies considered for the comparison. In addition to the classification accuracy, the efficacy of the proposed model has also been justified through precision, recall, F1-score, support value, and misclassification rate.

Numerical modeling of edge inhomogeneity in a macro cantilever beam

This study explores the inhomogeneity problem near the edge of a cantilever beam. Common in gears and turbine blades, inhomogeneities under local edge contact, coupled with macroscale bending effects, result in extreme and complex stress concentration. This model employs the Conjugate Gradient Method to combines the macroscopic beam theory and microscopic elasticity. The Eshelby inclusion method for simulating inhomogeneities. The Hetényi image method is used for address edge contacts in the beam. Enhanced by the Discrete Convolution fast Fourier Transform algorithm, the model’s accuracy and efficiency are validated with the Finite element method. Parametric analysis highlights the influence of distance between indenter and edge, stress components distribution and potential failure in cross-scale challenges.

Inversion of wind load on high-rise buildings under non-stationary and non-Gaussian conditions via DKF and FB-FFT

Wind-induced effects should be especially concerned for the design and maintenance of high-rise buildings, and information of wind load is sometimes prerequisite for related wind-resistant practices. Previous studies have been mainly conducted to deduce wind load on high-rise buildings under stationary and Gaussian conditions. However, due to the inherent randomness, wind load often exhibits non-stationary and non-Gaussian characteristics. This study employs two methods, namely Discrete Kalman Filter (DKF) and Fast Bayesian Fourier Transform (FB-FFT), to estimate wind load on high-rise buildings under non-stationary and/or non-Gaussian conditions. Firstly, a numerical building model is employed to evaluate the inversion performance of the two methods. Subsequently, both methods are applied to determine the wind load on a real building. Results through numerical simulation analysis demonstrate that DKF can invert the base force and modal force accurately under non-stationary conditions. For stationary non-Gaussian cases, the inverted wind load approximates the target force in terms of amplitude, but the inversion result exhibits Gaussian characteristics. FB-FFT can be basically utilized to invert the modal force under varied concerned conditions, yet the estimated wind load for stationary non-Gaussian case is slightly smaller than the target value. In reference to the real high-rise building example, DKF is found to produce similar results to those determined on the basis of wind tunnel test and in-situ measurement. Meanwhile, results of model force obtained via the two methods agree with each other. The above findings suggest that DKF and FB-FFT can be employed, at least partially, to deal with the issues of wind load inversion under non-stationary and non-Gaussian conditions.

High-performance tooth flank collaborative optimization model for spiral bevel and hypoid gears

The tooth flank collaborative optimization considering both geometric and loaded contact performances is an increasingly significant target in design and manufacturing for spiral bevel and hypoid gears. Recently, numerical loaded tooth contact analysis (NLTCA) is always an important access of mapping of the required performance evaluations and design variables. In addition to the conventional solution to NLTCA, an innovative discrete convolution and fast Fourier transformation (DC-FFT) method focusing on the micro-scale tooth flank topography is developed for high-performance spiral bevel and hypoid gears. Then, combining with accuracy and efficiency, a new top-rem tool modification is proposed to establish a new collaborative optimization model. Where, while the target flank can be prescribed by considering the user needs in the actual manufacturing, a small number of tool parameters are selected as the unknown design variables. It can significantly deal with the strong nonlinearity and coupling effect from the traditional modification and improve the optimization efficiency. Moreover, a top-rem tool modification is used as the optimization strategy to get a high optimization accuracy. The spiral bevel gear set from aerospace industrial applications is exercised to demonstrate the impact of the proposed collaborative optimization model on the tooth flank geometric and loaded contact performances.

Very low frequency waves as selective probe for Cysticercus tenuicollis, Hydatid cyst and Coenurus cerebralis bio-analysis using single cell-signal recording

Comparative electric behavior of Cysticercus tenuicollis, Hydatid cyst and Coenurus cerebralis at the Very Low Frequency (VLF) region has been studied in detail. This investigation could be significant, because of the economic and public health importance of these parasitic infections in domestic animals. In this report, a single cell signal recording technique has been adopted for comparison using a stainless steel (type: 316, diameter: ~ 300 µm, height: 2.00 cm) two identical electrode system, implanted on the surface of the tested cysts with inter electrode distance of 0.50 cm at a ~ 6.0 giga ohm (GΩ) sealed condition (based on the situation of the implanted electrode system). This process was achieved based on applying electrical interaction between the cysts and the VLF electrical signal. Relative to the measured time domain signal (Current–time diagram), the frequency domain (Current-frequency diagram) was estimated via applying a “Discrete Fast Fourier Transform” (DFFT) algorithm at a fixed time interval (5.0 min). Factors, having important influence on the sensitivity of the detection system including the type (waveform) of different alternating-current (AC) triggering stimulus signals (such as direct current, square wave, triangular, sin (t), etc.), the amplitude, as well as the frequency were optimized automatically through a written “Visual Basic 6” program by one-factor-at-a-time method. Direct applying this AC triggering VLF voltage to the cysts resulted in tracing an AC electrical current vs. time that considered as the time domain wave. However, this electrical current was decayed rapidly versus time during maximum 30.0 s time scale. Applying the DFFT algorithm to the measured time domain, resulted in accessing to the frequency domain at the selected frequency range between 2 and 5 kHz that was considered as the selected frequency for the selective differentiation of C. tenuicollis, Hydatid cyst and C. cerebralis. The related probable mechanism of this process may be attributed to the correlation between the triggering potential and the cyst’s electrical surface charge (Zeta potential) as the current source under similar conditions. The results of this study may help to introduce a new detection system for in vivo recognition of the cysts in future.

Fusion Based MR Images Denoising Technique Using Frequency Domain and Non-Local Means Filters

The non-invasive and non-ionizing properties of Magnetic Resonance Imaging (MRI) in addition to the associated good image quality as well as high resolution make MRI more attractive than many other medical imaging techniques. However, during the acquisition, transmission, compression and storage processes, the Magnetic Resonance (MR) images are corrupted by various types of noise and artifacts that degrade their visual quality. Most of the existing MR images denoising techniques give good quality images only when the noise density is low with their performances deteriorating as the noise power increases. The few methods that yield high quality images for all noise densities involve multiple complex and time-consuming processes. This paper proposes a computationally simple MR images denoising technique that consistently gives good denoising results for low as well as high noise densities. The proposed procedure fuses an MR image that is denoised by a Modified Discrete Fast Fourier Transform (MDFFT) filter with one that is denoised using a non-local means filter in frequency domain to yield a high quality output image. The main contribution of this proposed method is the employment of a novel image fusion approach that greatly improves the quality of the denoised image. The performance of the proposed technique is compared with those of the Wiener, median, adaptive median and the MDFFT filters. Objective metrics such as the Peak Signal-to-Noise Ratio (PSNR) and the Structural Similarity (SSIM) index were used in the performance assessments. The outcomes of these assessments showed that the proposed algorithm yielded images of higher quality in terms of the PSNR measure than the existing denoising techniques by at least 7.11 dB for a noise density of up to 0.5.

Mechanical Properties of Coupled Bending and Contact to Hollow Cylindrical Roller Contacts

A numerical analysis model of the hollow cylindrical roller is established by coupling the bending of the curved beam and elastic half-space contact theory. Slicing technology is applied to solve the bending deformation of every circle slice. Discrete fast Fourier transform (DC-FFT) and a conjugate gradient method are employed to solve the contact deformation and contact pressure, considering the bending effect in both radial and axial directions. The influence of hollowness on deformation, contact pressure, stiffness, and strain energy for a straight roller contacting a flat plane is studied using the numerical model. The results reveal that with the increase of hollowness, the contact pressure decreases at the end, the edge effect weakens apparently, the contact width and contact deformation increase slightly in the middle part, and the stiffness decreases. The bending deformation and strain energy increase sharply as the hollowness reaches 60%. What's more, the profile of the contact region gradually changes from "outer convex" to "inner concave" at the end, which is also validated by photographing the shapes of the static contact region under various hollowness conditions using an optical interference test.

One-Step Calculation Circuit of FFT and Its Application

Discrete Fourier Transform (DFT) and Fast Fourier Transform (FFT) are core components in the field of signal processing. However, in the existing research, there is no fully analog circuit that can realize the one-step calculation of FFT. Therefore, in this paper, an analog circuit that can calculate FFT and its inverse transform IFFT in one-step is proposed. First, a circuit that can realize complex number operations is designed. On the basis of this structure, a fully analog circuit that can realize fast and efficient computing of FFT and IFFT in one-step is proposed. In addition, different coefficient matching can be obtained to achieve arbitrary points of FFT and IFFT by adjusting the resistance value of the memristor, which has good programmability. Specific examples are given in the paper to evaluate the proposed method. The PSPICE simulation results show that the average accuracy is above 99.98%. More importantly, the calculation speed has been greatly improved compared with MATLAB simulation. Finally, the proposed circuit can be used to quickly solve convolution operation, and the average accuracy can reach 99.95%.

FFT-ASSISTED ALGORITHMS FOR 3D LINE-CONTACT PROBLEMS

The line-contact is a particular type of contact with a contact length much greater than its width. Such contact scenarios can be treated in the frame of a two-dimensional plane-strain problem if the contacting surfaces can be considered nominally smooth. However, surface irregularities inherent to any manufacturing technique lead to a discontinuous contact area that differs from the one derived on the basis of the smooth profile assumption. It is therefore tantalizing to pursue the solution of a line-contact problem using an intrinsically three-dimensional (3D) model, which can only be numerical due to lack of general analytical solutions in contact mechanics. Considering the geometry of the line-contact, a major challenge in its numerical modelling is that the expected contact area is orders of magnitude larger in one direction compared to the other. This may lead to an unreasonably large number of grids in the contact length direction, which translates to a prohibitive computational burden. An alternative approach, employed in this paper, is to treat the line-contact as non-periodic in the contact width direction, but periodic in the contact length direction, with a period equal to the window required to capture and replicate the surface specific texture. This periodicity encourages the contact problem solution by spectral methods based on the fast Fourier transform (FFT) algorithm. Based on this idea, two methods are derived in this paper from the existing Discrete Convolution Fast Fourier Transform (DCFFT) technique, which was previously developed for purely non-periodic contact problems. A first algorithm variant employs a special padding technique for pressure, whereas a second one mimics the contribution of multiple pressure periods by summation of the influence coefficients over a domain a few times larger than the target domain. Both techniques are validated against the existing analytical Hertz solution for the line-contact and a good agreement is found. The advanced methods seem well adapted to the simulation of contact problems that can be approximated as periodic in one direction and non-periodic in the other.

Separation of the Structure Signal by the Maximal Overlap Discrete Wavelet Transform and Fast Fourier Transform

Power spectral density (PSD) is used for evaluating a structure’s vibration process. Moreover, PSD not only shows a discrete form of vibration but also presents various components in a vibration structure. The superposition of multiple vibration patterns on the same spectrum poses difficulty in analyzing the spectral information in the way needed to find the structure’s discrete vibration. This paper proposes a method for separating the synthetic vibration signal into a structure’s discrete vibration and other extraneous vibrations using the maximal overlap discrete wavelet transform (MODWT) method combined with the method of fast Fourier transform (FFT). With the combination of these two algorithms, MODWT and FFT, the signals of the synthesized vibration have been separated into component signals with different frequency ranges. This means that PSD will be formed, which is based on the combination of the single power spectra of the component signals. Thus, the single spectrum of each of these constructed components can be used to evaluate the types of discrete vibrations coexisting in a structure’s vibration process. The survey results in this paper show the sensitivity and suitability of select types of discrete vibrations to be separated out during the assessment of the structural change, so as to achieve the best possible plan for eliminating the unwanted and unexpected noise and vibration components.

Comparison of Machine Learning Algorithms for Induction MotorRotor SingleFault Diagnosis using Stator Current Signal

This quantitive researchwas conducted to compare the efficiency between three groups of machine learning’ classification techniques for detecting broken rotor bar (BRB)fault in induction motor using stator currents signals with two different signal processing method. Thus, the main purpose of the article is to find out the most suitable method of distributing and extracting data for the fault diagnosis problems. Two of the most common used signal processing method –Discrete Wavelet Transform (DWT) and Fast Fourier Transform (FFT)has been implemented to extract the statiscal features of the faults. Then in the next logical steps, also the most important step, fault diagnosis, three classification algorithms: Support Vector Machines (SVM), K-nearest Neighbors (KNN), and Ensembles are chosen to evaluate the performance and the impact of those different classifiers for induction motor fault diagnosis. Hence, the study found there are five classifiers (Fine Gaussian SVM, Fine KNN, Weighted KNN, Bagged Trees and Subspace KNN) are best suited for the proposed problem when providing nearly 100% classification accuracy for all fault that the other 12 classifiers can not perform well.

Iris-based human identity recognition with machine learning methods and discrete fast Fourier transform

One of the most important modules of computer systems is the one that is responsible for user safety. It was proven that simple passwords and logins cannot guarantee high efficiency and are easy to obtain by the hackers. The well-known alternative is identity recognition based on biometrics. In recent years, more interest was observed in iris as a biometrics trait. It was caused due to high efficiency and accuracy guaranteed by this measurable feature. The consequences of such interest are observable in the literature. There are multiple, diversified approaches proposed by different authors. However, neither of them uses discrete fast Fourier transform (DFFT) components to describe iris sample. In this work, the authors present their own approach to iris-based human identity recognition with DFFT components selected with principal component analysis algorithm. For classification, three algorithms were used—k-nearest neighbors, support vector machines and artificial neural networks. Performed tests have shown that satisfactory results can be obtained with the proposed method.

Laminar Flow over a Square Cylinder Undergoing Combined Rotational and Transverse Oscillations

This work numerically investigates the effects of combined rotational and transverse oscillations of a square cylinder on the flow field and force coefficients. The primary non-dimensional parameters that were varied are frequency ratio fR (0.5, 0.8), Re (50-200), phase difference (ϕ) between the motions and rotational amplitude (θ0) with the influence of the last three parameters being discussed in detail. The amplitude of transverse oscillations is fixed at 0.2D, where D is the cylinder width. The study has been validated using the mean drag coefficient for stationary and transversely oscillating square cylinders from literature. Output data was obtained in the form of force coefficient (Cd), vorticity and pressure contours. The governing equations for the 2dimensional model were solved from an inertial frame of reference (overset meshing) using finite volume method. The interplay between the convective field and prescribed motion has been used to explain many of the results obtained. The relative dominance of cylinder motion over the flow stream was determined using Discrete Fast Fourier Transform. The influence of Re on Cd disappears when the motions are completely out of phase (ϕ = π). In general, the Cd for low Re flows exhibited low sensitivity to change in other parameters. Direct correlation has been observed between frontal area, vortex patterns and drag coefficient

Comparison of Discrete Fourier Transform and Fast Fourier Transform with Reduced Number of Multiplication and Addition Operations

Fast Fourier Transform is an advanced algorithm for computing Discrete Fourier Transform efficiently. Although the results available from the operation of Discrete Fourier Transform (DFT) and Fast Fourier Transform (FFT) are same, but exploiting the periodicity and symmetry property of phase factor Fast Fourier Transform computes the Discrete Fourier Transform using reduced number of multiplication and addition operations. The basic structure used in the operations of Fast Fourier Transform is the Butterfly structure. For the implementation of Fast Fourier Transform the two methods are used such as decimation in time (DIT) and decimation in frequency (DIF). Both the methods give same result but for decimation in time of Fast Fourier Transform bit reversed inputs are applied and for decimation in frequency of Fast Fourier Transform normal order inputs are applied, and the result is reversed again. In this paper, operations for DFT and FFT have been discussed and shown with examples. It is found that generalized formula for FFT have been described same in the books, but the expressions in the intermediate computations for the first decimation and second decimation are different in the various books of Digital Signal Processing. The expressions in the intermediate computation of FFT described in different books are broadly compared in this paper

Determination of Riboflavin by Nanocomposite Modified Carbon Paste Electrode in Biological Fluids Using Fast Fourier Transform Square Wave Voltammetry

Herein, fast Fourier transformation square-wave voltammetry (FFT-SWV) as a novel electrochemical determination technique was used to investigate the electrochemical behavior and determination of Riboflavin at the surface of a nanocomposite modified carbon paste electrode. The carbon paste electrode was modified by nanocomposite containing Samarium oxide (Sm2O3)/reduced graphene oxide (RGO) (2:1) to improve detection sensitivity of Riboflavin under optimal experimental conditions. Furthermore, the signal-to-noise ratio was significantly increased by application of discrete fast Fourier transformation analysis, background subtraction and two-dimensional integration of the electrode response over the selected potential range and the time window. Obtained cyclic voltammograms demonstrated a diffusion-controlled reversible electron transfer reaction for Riboflavin in phosphate buffer solution (pH=7.2). The peak potential values were pH-dependent, involving the same numbers of protons and electrons. To obtain the maximum sensitivity, some effective parameters such as scan rate (10 mV/s), accumulation time (0.2 s) and potential (+400 mV), frequency (1420 Hz) and amplitude (20 mV) were optimized. As a result, determination of Riboflavin using FFT-SWV showed a linear range of response from 10 to 400 nM (R2=0.9993), with limit of detection of 0.86 nM. An acceptable recovery percent was also obtained for Riboflavin in human plasma samples as criteria of measurement applicability of the proposed modified electrode.

Three-dimensional rolling/sliding contact on a viscoelastic layered half-space

This paper proposes an efficient contact model for a viscoelastic layered half-space where coating and substrate have different creep functions (i.e. different viscoelastic behaviours). The problem is formulated in three dimensions for an imposed pressure and shear field. The influence coefficients are calculated with the Papkovich-Neuber potentials and computation performed using Discrete Convolution and Fast Fourier Transform (DC-FFT) algorithms. From there, an elastic/viscoelastic correspondence is applied to move the elastic solution to a viscoelastic one. The Generalized Maxwell viscoelastic model is used and presented in the form of Prony series. A validation is performed using not only results within the literature but also by comparison with a finite element analysis. Next, a parametric study is done to analyse the influence of different parameters such as the elastic modulus ratio, the relaxation time ratio, the coating thickness or the rolling velocity. The model allows the analysis of the transient regime for which most of the known models struggle. It allows also to calculate 3D stresses and so to extract the stresses at the interface between the coating and the substrate so one can estimate the risk of failure such as delamination.

An ANOVA-Based Fault Diagnosis Approach for Variable Frequency Drive-Fed Induction Motors

In this article, an analysis of variance (ANOVA)-based fault diagnosis approach using experimental data is proposed for variable frequency drive (VFD)-fed induction motors. Line-to-neutral voltages at the motor terminal and the stator currents, measured from two identical 0.25 HP three-phase squirrel-cage induction motors fed by a voltage source inverter-based low-voltage VFD under healthy and faulty cases, are evaluated. Harmonic spectra of the measured voltage and current are obtained by Discrete Fast Fourier Transform (DFFT). Through the coherence and magnitude consistency analysis, the fundamental and 5th harmonic of the stator current are chosen as “signature frequency components.” ANOVA along with the multiway analysis are then applied to signature frequency components, their mean and standard deviation are identified as “fault signatures”; and the p -value from the inter-group analysis of the mean and standard deviation is used to classify faults. To facilitate fault diagnosis for untested motor operating conditions, formulas to calculate fault signatures are derived by surface fitting using tested data.

Fourier spectral methods for phase field fracture modelling of CMCs

Numerical homogenization of multiphase brittle materials, such as ceramic matrix composites is obviously a computationally intensive task. Common approach involving multiscale finite element models remains quite limited to scientific applications instead of being a reasonable alternative for analytical constitutive models. Despite the exponential growth of computational resources (known as Moore’s law) numerical complexity of the underlying algorithms is simply too high to ensure proper scaling to millions of elements. One of the approaches in-between continuous and discrete mechanics is the use of fast Fourier transform (FFT). The aim of this paper is to extend FFT-based methodology beyond its usual elastic regime, using mathematical formalism developed earlier for FE by means of variational principles. Governing equations are formulated in the frequency domain and solved iteratively on a parallel system. Well-known computational specifics of the discrete FFT algorithm itself provide uncompromised efficiency and a first, promising step towards truly multiscale mechanical analysis of random microstructures.

Discrete convolution and FFT method with summation of influence coefficients (DCS–FFT) for three-dimensional contact of inhomogeneous materials

Certain contact problems must be treated as three-dimensional (3D) axial periodic problems, such as the contact of cylinders with rough surfaces and/or inhomogeneities in the materials, whose structural features in contact are confined in a finite domain in one direction but extended infinitely in the other direction. A novel numerical model for simulating the contact of machined cylindrical components containing inhomogeneities is developed via extending the concept of the 3D line-contact fast Fourier transform (FFT) algorithms. Due to the stochastic similarity of asperity and inhomogeneity distributions in the length direction, the cylinder is divided into N segments in the length direction while taking the roughness and inhomogeneities in one of these segments as representatives. The periodic convolution and FFT is used in the length direction, together with superposing the influence coefficients (ICs) of the N segments, while the discrete (circular) convolution and fast Fourier transformation (DC–FFT) is used in the non-periodic direction; this is named the DCS–FFT algorithm. The accuracy of the DCS–FFT algorithm is examined by the comparison of the numerical results for a degenerated cylindrical contact with the corresponding analytical solution, and its efficiency is evaluated through the comparison of its execution speed with that of two other FFT-based algorithms. The developed method is implemented to study the influence of inhomogeneities on subsurface stress distributions with/without the periodic length direction extension and superposition of inhomogeneity ICs. A criterion is provided to decide whether the DCS procedure is needed for the contact analysis of inhomogeneity-containing cylinders.

Comparison of deep learning models for multivariate prediction of time series wind power generation and temperature

Wind power experienced a substantial growth over the past decade especially because it has been seen as one of the best ways towards meeting climate change and emissions targets by many countries. Since wind power is not fully dispatchable, the accuracy of wind forecasts is a key element for the electric system operators, as it strongly affects the decision-making processes. The planning horizon can be short term (1 -3 months) and long-term (6–12 months) depending on the process.The objective of this paper is to conduct a performance comparison of five deep learning models each combined with three types of data pre-processing and used for short term and long-term multi-variate predictions. The input data are time series of the wind power capacity factor and the temperature. In addition, this paper sets out to demonstrate and review the state-of-the-art deep learning models for prediction with a secondary objective to present the reader a reference point to better understand which model to choose and what factors are significant. The first contribution of this paper is to apply, assess and compare a selection of the novel and cutting-edge deep learning models for multi-variate prediction. Multi-variate predication is achieved through a proposed multiple input and multiple output (MIMO) architecture. Compared to traditional prediction models, machine learning techniques have the advantage of generalization. Among various techniques deep learning is particularly getting more attention due to the applicability to various dataset such as numerical and character. This investigation focuses on five models — Deep Feed Forward (DFF), Deep Convolutional Network (DCN), Recurrent Neural Network (RNN), Attention mechanism (Attention) and Long Short-Term Memory Networks (LSTM). The second contribution is to propose a novel approach to transform the time series dataset to signal for input and reconstruct the model predictions through inverse transformation, by means of the so-called discrete wavelet transformation and fast Fourier transformation. The different models are assessed also by comparing their performance with and without the input dataset manipulation through wavelet and FFT transformation. Beyond that, the model performances are outlined in detail, to give the reader an overview of the models to choose from for short-term or long-term prediction. The results demonstrate that the Attention and DCN perform best with Wavelet or FFT signal, whereas some other models perform better with no data preprocessing.