Discrete Fourier Transform Research Articles

Analysis on nonlinear characteristic of coupling heave and pitch motions of sandglass-type floating body

For its special shape of floating body with oblique side and external expansion, the heave and pitch motions of the sandglass-type Floating Production Storage and Offloading unit (FPSO) have coupling influence and instability phenomenon under harmonic wave excitation force. In order to study the nonlinear characteristic of the sandglass-type floating body, this paper presents the improved incremental harmonic balance (IHB) method in conjunction with the incremental arc-length method, and adopts the Floquet theory to determine the stability of the periodic solutions. Therein, the discrete Fourier transformation is introduced in the traditional IHB method to solve the problem of no analytical expressions for nonlinear FK and hydrostatic forces of the sandglass-type floating body. Considering the dependence of the heave and pitch hydrodynamic coefficients on wave frequency, the coefficients of the Fourier series in the IHB method are modified to cope with the memory effect. Taking a classic Spar platform as the test case, the accuracy of the method in this paper is validated and can be used to analyze the nonlinear coupling stability of the large-scale floating body. Then, the nonlinear responses corresponding to single-DOF heave and single-DOF pitch respectively are studied, and the nonlinear characteristics of hardening-type stiffness are verified by considering the different effects of damping and wave amplitude. Next, the interactive effects between pitch and heave motions of the sandglass-type model are further discussed, which are mainly reflected in two frequency bands representing the hardening-type nonlinearity of pitch and heave motions. Finally, the influence of different upper inclination angle of the floating body on heave and pitch coupling motions is analyzed. The results show that the smaller the upper angle, the larger the nonlinear motion responses. Consequently, the nonlinear characteristics of the heave and pitch motions should be fully noticed and considered in the shape design of the sandglass-type FPSO.

Novel Battery-Supercapacitor Hybrid Energy Storage System for Wide Ambient Temperature Electric Vehicles Operation

Electric vehicles (EVs) are gaining popularity in recent days to reduce the dependency on fossil fuels. Batteries are the main power source in EVs. However, the capacity of the battery degrades when it operates in low temperatures (< 0∘C). Hence, it is essential to maintain the battery temperature (> 0∘C) to operate at maximum capacity. Additionally, the battery alone is not suitable to supply the high transient power requirements of EVs. Thus, this paper proposes a novel integrated converter topology, which facilitates battery heating along with power transfer from the hybrid energy storage (battery and supercapacitors). The internal ac heating uses a resonant network for uniform heating of the battery cells in heating mode. The same inductor of the resonant network is also used for power transfer from hybrid energy storage during the driving mode. The Discrete Fourier Transform (DFT) based integrated inductor design ensures effective EV power sharing between battery and supercapacitors and reduces battery heating time. Thus, the proposed integrated converter reduces the number of converters stages, control complexity and overall cost. The detailed analysis and design are included along with the simulation and experiment results. The results show the uniform internal heating of the battery and efficient power transfer from/to the battery and supercapacitors. The experimentation is performed in a 1kW system considering the European driving cycle.

Passive Tone Detection for Moving Targets Based on Long-Time Coherent Integration

The detection of sinusoidal signals embedded in noise is an important topic in passive sonar signal processing. The performance of existing tone detection techniques is limited by the Doppler frequency shift, which is caused by the relative motion between moving targets and the receiver. In this study, an algorithm based on long-time coherent integration is proposed to achieve robust tonal signal detection under the influence of a Doppler frequency shift. First, the received narrowband signals radiated by moving targets are split into multiple segments through a window-length constraint. The results obtained by applying a discrete Fourier transform (DFT) to the data segments are modeled as a polynomial phase signal in the frequency domain. Then, the polynomial Radon-polynomial Fourier transform (PRPFT) is applied to simultaneously compensate the time-variant frequency drift and phase difference. To avoid the gain loss due to the discretization of the phase difference compensation in PRPFT, a phase compensation factor searching algorithm is proposed. The simulation results show that the proposed algorithm can provide higher frequency resolution and higher coherent integration gain even in the case of a severe Doppler shift. Furthermore, the results of sea trials demonstrate that the proposed method can perfectly achieve coherent integration for signals with a duration of several hundred seconds under different experimental conditions.

Suboptimal Algorithm for Measuring Pitch Frequency Using Discrete Fourier Transform of a Speech Signal

Suboptimal Algorithm for Measuring Pitch Frequency Using Discrete Fourier Transform of a Speech Signal

Efficient 3D Surface Patch Compression and Reconstruction using Parametric Descriptions and Transform Techniques

This paper proposes and demonstrates novel methods for compressing and reconstructing 3D surface patches typically obtained from scanners that rely on stereo vision, structured light, or time-of-flight techniques. The methods involve applying a polygon reduction to the mesh to get a set of vertices lying in structured planes of a sparse, regular grid. The data in each plane is then described parametrically, and a comparative analysis is conducted using the Discrete Fourier Transform (DFT), Discrete Cosine Transform (DCT), and Discrete Wavelet Transform (DWT). Quality factors are employed to further process the transform coefficients, resulting in substantial reductions in the amount of data saved to disk. The paper also defines file formats with the necessary parameters for a complete reconstruction of the sparse mesh. Finally, elliptic Partial Differential Equations (PDE) are used to represent the reconstructed data, and the Laplace equation is iteratively solved between adjacent planes to recover the vertex density of the original mesh. Experimental results demonstrate the effectiveness of the proposed methods, achieving compression rates of over 98% compared to the OBJ file format and over 91% compared to a list of vertices in ASCII format.

Fast and direct inversion methods for the multivariate nonequispaced fast Fourier transform

The well-known discrete Fourier transform (DFT) can easily be generalized to arbitrary nodes in the spatial domain. The fast procedure for this generalization is referred to as nonequispaced fast Fourier transform (NFFT). Various applications such as MRI and solution of PDEs are interested in the inverse problem, i.e., computing Fourier coefficients from given nonequispaced data. In this article, we survey different kinds of approaches to tackle this problem. In contrast to iterative procedures, where multiple iteration steps are needed for computing a solution, we focus especially on so-called direct inversion methods. We review density compensation techniques and introduce a new scheme that leads to an exact reconstruction for trigonometric polynomials. In addition, we consider a matrix optimization approach using Frobenius norm minimization to obtain an inverse NFFT.

Empirical mode decomposition and local binary pattern based feature extraction for face recognition

ABSTRACT Facial recognition is a challenging pattern recognition problem in computer vision. This paper proposes a face recognition system that uses Empirical Mode Decomposition (EMD) and Local Binary Pattern (LBP) based feature extraction for a robust face recognition system. This scheme initially decomposes the image into 2N number of IMF (Intrinsic Mode Function) images, where N numbers of IMF images are estimated in the X direction and N number of IMF images are estimated in the Y direction. From the 2N number of IMFs, the M number of best matching IMF image pairs is estimated using 2D Discrete Fourier Transform (DFT). The IMF pair is added to extract the IC-LBP (Intensity Compensated-Local Binary Pattern) features. The IC-LBP features are extracted from the IMF images such that the center intensity is adjusted based on an adaptive intensity threshold. The use of EMD and IC-LBP features uses the essential descriptors that best represent a facial image. The same process is repeated in the testing phase where the test image is categorized from the trained images using the Naïve Bayes algorithm. The performance evaluation was done using the Yale, MORPH, and FGNET using metrics such as time complexity and recognition rate on different types of test face images like partial faces, different lightning, and rotation. Results show that the proposed face recognition system outperforms the traditional algorithms. Results show that the proposed face recognition system outperforms the traditional algorithms.

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.

A novel hybrid generative adversarial network for CT and MRI super-resolution reconstruction

Objective. Computed tomography (CT) and magnetic resonance imaging (MRI) are widely used in medical imaging modalities, and provide valuable information for clinical diagnosis and treatment. However, due to hardware limitations and radiation safety concerns, the acquired images are often limited in resolution. Super-resolution reconstruction (SR) techniques have been developed to enhance the resolution of CT and MRI slices, which can potentially improve diagnostic accuracy. To capture more useful feature information and reconstruct higher quality super-resolution images, we proposed a novel hybrid framework SR model based on generative adversarial networks. Approach. The proposed SR model combines frequency domain and perceptual loss functions, which can work in both frequency domain and image domain (spatial domain). The proposed SR model consists of 4 parts: (i) the discrete Fourier transform (DFT) operation transforms the image from the image domain to frequency domain; (ii) a complex residual U-net performs SR in the frequency domain; (iii) the inverse discrete Fourier transform (iDFT) operation based on data fusion transforms the image from the frequency domain to image domain; (iv) an enhanced residual U-net network is used for SR of image domain. Main results. Experimental results on bladder MRI slices, abdomen CT slices, and brain MRI slices show that the proposed SR model outperforms state-of-the-art SR methods in terms of visual quality and objective quality metric such as the structural similarity (SSIM) and the peak signal-to-noise ratio (PSNR), which proves that the proposed model has better generalization and robustness. (Bladder dataset: upscaling factor of 2: SSIM = 0.913, PSNR = 31.203; upscaling factor of 4: SSIM = 0.821, PSNR = 28.604. Abdomen dataset: upscaling factor of 2: SSIM = 0.929, PSNR = 32.594; upscaling factor of 4: SSIM = 0.834, PSNR = 27.050. Brain dataset: SSIM = 0.861, PSNR = 26.945). Significance. Our proposed SR model is capable of SR for CT and MRI slices. The SR results provide a reliable and effective foundation for clinical diagnosis and treatment.

Fourier transform bounded Kolmogorov complexity

The Discrete Fourier Transform (DFT) has been extended to lossless compression for binary images. Binarisation is key for DFT to compress losslessly because there exist lossy reconstructions (within a specific range of loss values) which are error-corrected during the binarisation step, effectively making the image lossless. In an ironic twist, the quantisation effect which usually introduces errors, has been utilised to remove noise from lossy reconstructions.

IRDC-Net: An Inception Network with a Residual Module and Dilated Convolution for Sign Language Recognition Based on Surface Electromyography.

Deaf and hearing-impaired people always face communication barriers. Non-invasive surface electromyography (sEMG) sensor-based sign language recognition (SLR) technology can help them to better integrate into social life. Since the traditional tandem convolutional neural network (CNN) structure used in most CNN-based studies inadequately captures the features of the input data, we propose a novel inception architecture with a residual module and dilated convolution (IRDC-net) to enlarge the receptive fields and enrich the feature maps, applying it to SLR tasks for the first time. This work first transformed the time domain signal into a time-frequency domain using discrete Fourier transformation. Second, an IRDC-net was constructed to recognize ten Chinese sign language signs. Third, the tandem CNN networks VGG-net and ResNet-18 were compared with our proposed parallel structure network, IRDC-net. Finally, the public dataset Ninapro DB1 was utilized to verify the generalization performance of the IRDC-net. The results showed that after transforming the time domain sEMG signal into the time-frequency domain, the classification accuracy (acc) increased from 84.29% to 91.70% when using the IRDC-net on our sign language dataset. Furthermore, for the time-frequency information of the public dataset Ninapro DB1, the classification accuracy reached 89.82%; this value is higher than that achieved in other recent studies. As such, our findings contribute to research into SLR tasks and to improving deaf and hearing-impaired people's daily lives.

Identifying pollution dynamics using discrete Fourier transform: From an urban-rural river, Central Mexico

The quality of life and human survival is dependent on sustainable development and sanitation of water bodies in an environment. The present research focuses on cyclicity data of more than 750,000 records of parameters associated with the water quality from a rural-urban river monitoring stations in real-time from River Atoyac in Central Mexico. The events detected in the instrumental records correlated with 2528 laboratory and instrumental determinations. The 64 polluting compounds were grouped into inorganic compounds (metals and metalloids) and organic compounds (pesticides, herbicides, hydrocarbons). Metal associated compounds were grouped along mechanical, pharmaceutical and textile industries which associates itself with the entry of polluting components. The cyclicity of the events was detected through Discrete Fourier Transformation time series analysis identifying the predominant events in each station. These highlight the events at 23–26 h corresponding to a circadian pattern of the metabolism of the city. Likewise, pollution signals were detected at 3.3, 5.5, and 12–14 h, associated with discharges from economic activities. Multivariate statistical techniques were used to identify the circadian extremes of a regionalized cycle of polluting compounds in each of the stations.The results of this research allow pollution prevention using a mathematical analysis of time series of different quality parameters collected at monitoring stations in real-time as a tool for predicting polluting events. The DFT analysis makes it possible to prevent polluting events in different bodies of water, allowing to support the development of public policies based on the supervision and control of pollution.

CubeLearn: End-to-End Learning for Human Motion Recognition From Raw mmWave Radar Signals

mmWave FMCW radar has attracted huge amount of research interest for human-centered applications in recent years, such as human gesture and activity recognition. Most existing pipelines are built upon conventional Discrete Fourier Transform (DFT) pre-processing and deep neural network classifier hybrid methods, with a majority of previous works focusing on designing the downstream classifier to improve overall accuracy. In this work, we take a step back and look at the pre-processing module. To avoid the drawbacks of conventional DFT pre-processing, we propose a complex-weighted learnable pre-processing module, named CubeLearn, to directly extract features from raw radar signal and build an end-to-end deep neural network for mmWave FMCW radar motion recognition applications. Extensive experiments show that our CubeLearn module consistently improves the classification accuracies of different pipelines, especially benefiting those simpler models, which are more likely to be used on edge devices due to their computational efficiency. We provide ablation studies on initialization methods and structure of the proposed module, as well as an evaluation of the running time on PC and edge devices. This work also serves as a comparison of different approaches towards data cube slicing. Through our task agnostic design, we propose a first step towards a generic end-to-end solution for radar recognition problems.

The diachronic development of Debussy’s musical style: a corpus study with Discrete Fourier Transform

Claude Debussy’s personal style is typically characterised as a departure from earlier diatonic tonality, including a greater variety of pitch-class materials organised in fragmented yet coherent compositions. Exploiting the music-theoretical interpretability of Discrete Fourier Transforms over pitch-class distributions, we performed a corpus study over Debussy’s solo-piano works in order to investigate the diachronic development of such stylistic features across the composer’s lifespan. We propose quantitative heuristics for the prevalence of different pitch-class prototypes, the fragmentation of a piece across different prototypes, as well as some aspect of the overall coherence of a piece. We found strong evidence for a decrease of diatonicity in favour of octatonicity, as well as for an increase of fragmentation accompanied by non-decreasing coherence. These results contribute to the understanding of the historical development of extended-tonal harmony, while representing a fertile testing ground for the interaction of computational corpus-based methods with traditional music analytical approaches.

Performance analysis of wireless transmission of compressed images using DCT‐OFDMA system with different compression schemes

AbstractTransmitting images over an Orthogonal Frequency Division Multiplexing Access (OFDMA) system poses a significant challenge. The process entails sending a substantial amount of data, which consumes a significant amount of bandwidth. Consequently, compressing the transmitted image becomes essential to reduce the required bandwidth. The aim of this paper is to examine and analyse the wireless transmission of a compressed image via Discrete Cosine Transform (DCT‐OFDMA). A comparison is made with Discrete Fourier Transform (DFT‐OFDMA), across various subcarrier mapping schemes (localized and inter‐leaved), and different modulation schemes (16 Quadrature Amplitude Modulation (16QAM) and Quadrature Phase Shift Keying (QPSK)) using vehicular A, Stanford University Interim (SUI3), and uniform channel models. To evaluate the performance of the system, the minimum Signal‐to‐Noise Ratio (SNR) necessary to recover the transmitted compressed image is calculated. This work considers nine standard compression techniques. The results are carried out using the MATLAB simulator. According to the simulation results, the minimum SNR required to recover the transmitted compressed image was found to be 19 dB. This result was achieved when using Discrete Cosine Transform‐Loaclized‐Orthogonal Frequency Division Multiplexing Access (DCT‐LOFDMA) with QPSK modulation and set partitioning in hierarchical trees (SPIHT) compression method over the SUI3 channel model. Moreover, it was observed that the DCT‐LOFDMA and DFT‐IOFDMA systems attained equal SNR while utilizing the SPIHT_3D compression technique and QPSK modulation on the SUI3 channel model. Overall, the results suggest that the performance of DCT‐based localized OFDMA is somewhat superior to DFT‐based localized OFDMA, particularly when utilizing the SUI3 channel model and the QPSK modulation scheme. Therefore, it is feasible to transmit and receive a compressed image effectively over an OFDMA system with DCT.

A Parameter Estimation Algorithm for Damped Real-value Sinusoid in Noise

Abstract To improve the parameter estimation performance of damped real-value sinusoid in noise, a novel algorithm with high accuracy and computational efficiency is proposed that combines the characteristics of good anti-interference, small computation of frequency-domain methods, and high parameter estimation accuracy of time-domain methods. First, the Discrete Fourier Transform (DFT) algorithm and the two-point spectrum interpolation algorithm of the frequency-domain methods are used to improve the noise immunity. Then, the linear prediction property and the enhancement filter of the time-domain methods are used to improve the parameter estimation accuracy. In addition, the parameter estimation performance of the proposed algorithm is verified by computational complexity analysis and test experiments, and the practical application effectiveness of the proposed algorithm is demonstrated on the Coriolis Mass Flowmeter (CMF) experimental platform. The experimental results show that the proposed algorithm effectively improves the real-time performance and the parameter estimation accuracy is better than that of the existing excellent algorithms.

Measurement of Complex-Ratio Between Two RF Signals With Spectrum Analysis

A novel method to measure the amplitude-phase differences between two radio frequency (RF) signals is presented, based on spectrum analysis after periodic modulation. Two input signals are alternatively selected to enter the single-channel RF channel by a single-pole double-throw (SPDT) switch, which generates harmonics related to the channel unbalance. Amplitude-phase differences between two input signals can be obtained by analyzing the spectrum of received signal using discrete Fourier transform (DFT) in digital domain. Compared to conventional multichannel RF receivers, the proposed method has a concise structure and low-computational complexity. Simulation results are provided to verify its effectiveness over dynamic ranges of 60 dB and 360 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^\circ$</tex-math> </inline-formula> . A <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L$</tex-math> </inline-formula> -band RF circuit is fabricated to measure the amplitude-phase differences over 35 dB and 360 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^\circ$</tex-math> </inline-formula> dynamic ranges. The measured results show good agreement to those by the vector network analyzer (VNA), certifying the effectiveness of proposed method.

Wavelet-Based Harmonic Magnitude Measurement in the Presence of Interharmonics

The increasing proliferation of power electronic converters, nonlinear loads, and distributed generation are leading to increased levels of harmonic and interharmonics in power networks. As a consequence, power quality (PQ) has become a critical performance indicator for power utilities and end-users. This study proposes a novel harmonic estimation method based on the real-time stationary discrete wavelet packet transform (RT-SDWPT). The proposed technique decomposes an input signal into frequency bands with harmonic information at cutoff frequencies and uses a compensation strategy to estimate root mean square (RMS) values of harmonics at every sampling period. The performance and effectiveness of the proposed method are assessed using real measurement data from field cases and experimental setup. The real measurements include challenging scenarios with harmonics, subharmonics, interharmonics, frequency deviation, and non-stationary PQ events. The proposed method outperforms the harmonic estimation provided by the discrete Fourier transform (DFT)-based approach and existing wavelet packet-based methods in terms of accuracy and speed.

Performance evaluation of DFT based speckle reduction framework for synthetic aperture radar (SAR) images at different frequencies and image regions

Polarimetric Synthetic Aperture Radar (PolSAR) images are widely used for remote sensing and geoscience applications. However, the coherent processing of radar signals in PolSAR imaging leads to the presence of speckle noise, which can significantly degrade image quality and limit the accuracy of subsequent analyses. To address this issue, speckle reduction frameworks are often applied to PolSAR images to reduce the noise level and enhance image quality. In this paper, the performance of Discrete Fourier Transform (DFT) based speckle reduction framework is evaluated on different bands (L, C, and P band) against various evaluation metrics like CV, SD, SNR, ENL, SSI and SMPI. The proposed framework is evaluated by comparing filtered and unfiltered images across different parameters, such as mean, standard deviation, coefficient of variation, equivalent number of looks (ENL), variance, and signal-to-noise ratio (SNR) on all three bands for the diagonal elements (T11, T22, and T33) of T3 matrix. These metrics provide a comprehensive evaluation of the proposed framework’s ability to (i) smoothen homogeneous regions, (ii) preserve contours, and (iii) retain polarimetric information. The framework’s ability to reduce speckle noise and improve image quality is demonstrated through a significant reduction in standard deviation, coefficient of variation, and improvement in SNR and ENL values. The proposed framework successfully preserved polarimetric information while effectively suppressing speckle noise. These results suggest that the proposed framework could be a valuable tool for improving PolSAR image quality and enhancing subsequent processing of PolSAR data.

Bayesian-Optimized Hybrid Kernel SVM for Rolling Bearing Fault Diagnosis.

We propose a new fault diagnosis model for rolling bearings based on a hybrid kernel support vector machine (SVM) and Bayesian optimization (BO). The model uses discrete Fourier transform (DFT) to extract fifteen features from vibration signals in the time and frequency domains of four bearing failure forms, which addresses the issue of ambiguous fault identification caused by their nonlinearity and nonstationarity. The extracted feature vectors are then divided into training and test sets as SVM inputs for fault diagnosis. To optimize the SVM, we construct a hybrid kernel SVM using a polynomial kernel function and radial basis kernel function. BO is used to optimize the extreme values of the objective function and determine their weight coefficients. We create an objective function for the Gaussian regression process of BO using training and test data as inputs, respectively. The optimized parameters are used to rebuild the SVM, which is then trained for network classification prediction. We tested the proposed diagnostic model using the bearing dataset of the Case Western Reserve University. The verification results show that the fault diagnosis accuracy is improved from 85% to 100% compared with the direct input of vibration signal into the SVM, and the effect is significant. Compared with other diagnostic models, our Bayesian-optimized hybrid kernel SVM model has the highest accuracy. In laboratory verification, we took sixty sets of sample values for each of the four failure forms measured in the experiment, and the verification process was repeated. The experimental results showed that the accuracy of the Bayesian-optimized hybrid kernel SVM reached 100%, and the accuracy of five replicates reached 96.7%. These results demonstrate the feasibility and superiority of our proposed method for fault diagnosis in rolling bearings.