Discrete Fourier Transform Algorithm Research Articles

Simulation Analysis of Phase Jitter in Differential Sampling of AC Waveforms Based on the Programmable Josephson Voltage Standard

The effect of phase jitter on differential sampling using the programmable Josephson voltage standard (PJVS) system is studied in this paper. A phase jitter model is established for the measured signal, and compensation coefficients for phase jitter removal are derived for three different post-processing methods based on the discrete Fourier transform algorithm (DFT). Based on our analysis, the phase jitter compensation coefficients are determined by the phase jitter angle distribution and harmonic order. Furthermore, after analyzing and simulating various common distributions, the phase jitter compensation coefficients have been verified. The simulation shows that when the standard deviation of the phase jitter angle is 20 ns, and the frequency of the measuring waveform is 3.46 kHz, the influence of the phase jitter is 1 × 10−7. The results of the simulation indicate that, in the differential sampling of AC waveforms using a PJVS system, phase jitter is one of the error terms for an uncertainty budget that cannot be neglected, particularly as the frequency of the measured waveforms increases.

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.

A New Method to Construct Algorithms for Fast Discrete Fourier Transform of Finite Complex and Real Signals Based on Thesecond Type Parametric Discrete Fourier Transforms

A New Method to Construct Algorithms for Fast Discrete Fourier Transform of Finite Complex and Real Signals Based on Thesecond Type Parametric Discrete Fourier Transforms

A semi-analytical solution for inhomogeneous material in the quarter space

A semi-analytical model is first presented that thoroughly examines stress distribution patterns in inhomogeneous materials within a quarter space: a scenario of great significance and complexity observed in components such as rail-wheels, roller bearings, and gears. The model utilizes the Hetényi Image Method and Eshelby’s Equivalent Inclusion Method, effectively handling the impact of inhomogeneities and satisfying the boundary conditions of the quarter space. To ensure efficient and accurate analysis, numerical techniques are incorporated, notably the Conjugate Gradient Method and the Discrete Convolution-Fast Fourier Transform algorithm. The model’s validity and robustness are demonstrated through comparisons with the Finite Element Method results, displaying excellent agreement. Parametric analyses reveal that distance, depth to the free surfaces, and shape of the inhomogeneities significantly influence the results. The introduction of an edge decay coefficient, Keg, serves as a practical tool for rapid estimation of edge effects in inhomogeneous materials, significantly contributing to precise predictions of material fatigue and failure.

Uncertainty Propagation of Missing Data Signals with the Interval Discrete Fourier Transform

The interval discrete Fourier transform (DFT) algorithm can propagate signals carrying interval uncertainty. By addressing the repeated variables problem, the interval DFT algorithm provides exact theoretical bounds on the Fourier amplitude and estimates of the power spectral density (PSD) function while running in polynomial time. Thus, the algorithm can be used to assess the worst-case scenario in terms of maximum or minimum power, and provide insights into the amplitude spectrum bands of the transformed signal. To propagate signals with missing data, an upper and lower value for the missing data present in the signal must be assumed, such that the uncertainty in the spectrum bands can also be interpreted as an indicator of the quality of the reconstructed signal. For missing data reconstruction, there are a number of techniques available that can be used to obtain reliable bounds in the time domain, such as Kriging regressors and interval predictor models. Alternative heuristic strategies based on variable—as opposed to fixed—bounds can also be explored. This work aims to investigate the sensitivity of the algorithm against interval uncertainty in the time signal. The investigation is conducted in different case studies using signals of different lengths generated from the Kanai-Tajimi PSD function, representing earthquakes, and the Joint North Sea Wave Observation Project (JONSWAP) PSD function, representing sea waves as a narrowband PSD model.

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.

Fast interpolated DTFT estimators of frequency and damping factor of real-valued damped sinusoids

This paper deals with the estimation of real-valued damped sinusoid frequency and damping factor. To that aim an Interpolated Discrete Time Fourier Transform (IpDTFT) algorithm is proposed which extends to real-valued signal an algorithm proposed in the literature for complex-valued damped sinusoids. The proposed algorithm provides fast estimates of the unknown parameters of either undistorted or distorted real-valued noisy damped sinusoids with accuracy generally better than the one ensured by state-of-the-art estimators, especially when few sinusoid cycles are analysed. Accuracy improvement is obtained by both weighting the acquired signal using a Maximum Sidelobe Decay (MSD) window and compensating the contribution of the spectral image component on the estimated parameters. Analytical expressions for the estimator variances due to wideband noise are also derived.

A Study on a Novel Inverted Ultra-Short Baseline Positioning System and Phase Difference Estimation

Autonomous underwater vehicles (AUVs) are important tools for exploring and studying the ocean. To improve the stealthiness of AUV positioning, a new type of inverted ultra-short baseline (i-USBL) positioning system is proposed in this paper. The system uses a surface GPS buoy as a positioning base station to transmit positioning signals to the AUV, which receives the signals through the i-USBL and calculates its own coordinates. In this way, the power consumption of the AUV will be lower, improving its endurance. In addition, azimuth observation is one of the key observation quantities in ultra-short baseline positioning systems. Therefore, this paper derives two phase difference estimation algorithms for azimuth measurement, which are the Least Mean Square (LMS) algorithm and the Discrete Fourier Transform (DFT) algorithm. Simulation results show that when the signal-to-noise ratio (SNR) is less than or equal to 0 dB, the DFT algorithm has higher accuracy; when SNR is greater than or equal to 10 dB, LMS has slightly higher accuracy than DFT; however, DFT is more stable than LMS at all SNRs. When SNR is 20 dB, the maximum azimuth measurement error of LMS and DFT is 0.3301° and 0.2204°, respectively, which can meet the positioning accuracy requirements. The average running times of LMS and DFT are 0.085 s and 0.011 s, respectively, and LMS has a faster running speed. In summary, the LMS algorithm can be used for azimuth observation when the SNR is good, and DFT can be applied when the SNR is poor.

A Modified DFT-Based Phasor Estimation Algorithm Using an FIR Notch Filter

Accurate and fast extraction of the fundamental parameters of fault signals is a critical issue in the overall performance of protective relays. The decaying DC terms (DDTs) in the fault current challenge the discrete Fourier transform (DFT), the reference algorithm for phasor estimation. To meet this challenge, a new modification for half and full-cycle DFT algorithms is proposed in this paper. In the first step, a finite impulse response (FIR) notch filter designed for fundamental frequency is applied to the output of the DFT algorithm. After that, the outcome of the FIR notch filter and its complex conjugate make it possible to extract error terms. Finally, the estimated phasors are emptied from DDTs error. The ability of the proposed method for estimating phasor and tolerating disturbances was assessed using practical simulated signals. The results perform that the proposed method is much more robust, accurate, and faster than previous methods and enhances the efficiency of the DFT algorithm faced by multiple DDTs.

Compressed Sensing of Traction Motor Bearing Vibration Signals based on Discrete Fourier Transform and Generalized Orthogonal Matching Pursuit Algorithm

For the bogie traction motor bearings of rail vehicles under road transportation conditions, its vibration signal full-time domain data acquisition data volume, storage pressure, subsequent data analysis difficulties, and other problems. This study proposes a data compression acquisition and data reconstruction method for bearing vibration signals based on compressed sensing (CS), which can achieve compressed sampling, transmission, and storage of the original signal with fewer observations, and restore the original signal by combining reconstruction algorithms to achieve low error reconstruction. We study the effects of different sparse transform methods on signal sparsity, as well as the signal sparse performance based on different sparse transforms and the signal reconstruction effect of different reconstruction algorithms, and propose a sparse representation method based on the discrete Fourier transform (DFT) and the generalized orthogonal matching pursuit (gOMP) algorithm for CS. Through simulation and experimental comparison, it is concluded that the method can restore and reconstruct the original high-dimensional signal with small reconstruction error, and solve the problems of massive data, inconvenient transmission, and difficult data analysis in engineering.

Optimization in the space domain for density compensation with the nonuniform FFT

The non-uniform Discrete Fourier Transform algorithm has shown great utility for reconstructing images from non-uniformly spaced Fourier samples in several imaging modalities. Due to the non-uniform spacing, some correction for the variable density of the samples must be made. Common methods for generating density compensation values are either sub-optimal or only consider a finite set of points in the optimization. This manuscript presents an algorithm for generating density compensation values from a set of Fourier samples that takes into account the point spread function over an entire rectangular region in the image domain. We show that the reconstructed images using the density compensation values of this method are of superior quality when compared to other standard methods. Results are shown with a numerical phantom and with magnetic resonance images of the abdomen and the knee.

An Improved Interpolated DFT-Based Parameter Identification for Sub-/Super-Synchronous Oscillations With Synchrophasors

The sub-synchronous resonance oscillations (SSO) caused by considerable renewable energy generations and power electronic devices seriously affect power system stability. Synchrophasor-based SSO parameter identification can effectively monitor SSOs. Aiming at the fundamental and frequency-coupled sub-/super-synchronous components that appear simultaneously in SSOs, an improved parameter identification algorithm is proposed in this paper based on the original interpolation Discrete Fourier Transform (DFT) and Hann-window. As the complement to the original algorithm, the improvements proposed in this paper additionally focus on the influence between the positive-/negative-frequency parts of the sub-/super-synchronous and fundamental components. Thus, the frequency, amplitude, and phase of the fundamental, sub-synchronous, and super-synchronous components can be accurately obtained by the proposed algorithm. This algorithm is compared to the original interpolated DFT and Prony analysis with both the simulated Phasor Measurement Unit (PMU) data and PMU data recorded during an actual SSO incident to verify its correctness and effectiveness. In the improved algorithm, the additional consideration for the super-synchronous component and the additional identified parameters significantly enhance the practical value of the interpolated DFT algorithm.

Review of Discrete Fourier Transform During Dynamic Phasor Estimation and the Design of Synchrophasor Units

In a large and complex interconnected power system, the measurement of synchronized bus voltage and line current plays a vital role in the monitoring and precise control of various sophisticated electrical equipment for secure and reliable operation. Phasor measurement units (PMUs) are incorporated into a wide area of the power system to extract the different signals of synchronized phasors. In this paper, the capacity of the PMU phasor estimation algorithm is explored based on discrete Fourier transform (DFT) under different sampling frequency rates during various dynamic scenarios in accordance with the IEEE C37.118.1a-2014 standard. Furthermore, the performance of the DFT algorithm varies according to the phase angle and dynamic parameters such as frequency, frequency ramp rates, modulation frequency, harmonic levels, step change, decaying dc, and noise levels. The simulation results reveal that accuracy of the phasor estimation algorithm based on DFT can be achieved at high sampling frequency rates. Furthermore, the results of DFT-based phasor estimation are compared with Shank’s estimation method (SEM) and the least-squares estimation method (LEM). The presented method is best suited to PMU algorithms development based on DFT for better visualization of the smart electric grid.

A novel State of Charge and State of Health estimation technique for Lithium-ion cells using machine learning based Pseudo-Random Binary Sequence method

Lithium-Ion batteries are electrochemical storage devices with State of Charge (SOC) and State of Health (SOH) sensitive operations. The accurate estimation of these two parameters is vital for the battery's optimum usage for different applications. Electrochemical Impedance Spectroscopy (EIS) is a benchmark technique that measures the cell internal impedance for online estimation of these parameters. Recent studies have used EIS with Discrete Fourier Transform, neural networks, and other machine learning algorithms for improving the accuracy and reliability of these parameters. However, such methods also increase system complexity, time interval, and cost of the estimation system. Few researchers have also used Pseudo-Random Binary Sequence (PRBS) techniques to improve the speed of EIS estimations. However, they have lower accuracy due to frequency harmonics, and the continued requirement of simultaneous measurements of physical parameters introduces complexity in designing an online estimator. This paper proposes a novel hybrid method of estimating these parameters using a combination of a PRBS and an online piecewise linear machine learning technique. A hardware prototype is developed to validate the proposed method resulting in a cost-effective and simpler method with an estimation accuracy of 98 % at 5-sec intervals.

Robust encrypted face recognition robot based on bit slicing and Fourier transform for cloud environments

In the field of computer vision, face recognition has become a trending research topic, and is widely used in the area of network security. The transmission of data over a network via a cloud server exposes the information to security risks and privacy attacks, meaning that the use of an encryption algorithm is essential. Face recognition algorithms in robotics applications have become cumbersome in terms of the computation speed needed to recognize the image. Since this is a built-in programming function in the robotics board, it will limit the speed and security of data storage. To overcome this issue, a cloud server is utilized as this can improve the processing speed, throughput, efficiency, and robustness of face recognition. Storing images in the cloud server in a secure way requires that the image be encrypted. To achieve this, we propose a hybrid encryption technique based on bit slicing and a discrete Fourier transform (DFT), and develop a secure robotic face image recognition scheme using a MobileFaceNet-CNN model (BS-DFT-MobileFaceNet). The percentages of improvement in terms of accuracy over LeNet, VGG16Net, Alexnet, GoogLeNet, ResNet, MobileFaceNet including raw input image were 17.5%, 7.36%, 22.41%, 22.62%, 8.65%, and 288.89% for raw input images and encrypted images using Genetic Algorithm (GA), DNA Algorithm, Bit slicing, AES, DFT, and BS-DFT encryption algorithms respectively.

Two modified DFT‐based algorithms for fundamental phasor estimation

The discrete Fourier transform (DFT) is a powerful phasor estimation algorithm conventionally used in digital relaying applications. The DFT-based phasor estimation is usually accompanied by oscillatory error due to the presence of the decaying DC (DDC) components in fault current signals. Accordingly, two modified DFT-based phasor estimation algorithms are proposed in this paper. The proposed algorithms accurately estimate the exact fundamental phasor by extracting the DDC components using successive outputs of the conventional DFT algorithm. The performance of the proposed algorithms is validated by the mathematically generated and PSCAD-simulated signals and is compared with previous algorithms. The results demonstrate that the proposed algorithms in this paper are more robust than other ones. Moreover, they are applicable in the DFT algorithm with different data windows.

On the Derivation of Winograd-Type DFT Algorithms for Input Sequences Whose Length Is a Power of Two

Winograd’s algorithms are an effective tool for calculating the discrete Fourier transform (DFT). These algorithms described in well-known articles are traditionally represented either with the help of sets of recurrent relations or with the help of products of sparse matrices obtained on the basis of various methods of the DFT matrix factorization. Unfortunately, in the mentioned papers, it is not shown how the described relations were obtained or how the presented factorizations were found. In this paper, we use a simple, understandable and fairly unified approach to the derivation of the Winograd-type DFT algorithms for the cases N = 8, N = 16 and N = 32. It is easy to verify that algorithms for other lengths of sequences that are powers of two can be synthesized in a similar way.

FPGA-based DFT system design, optimisation and implementation using high-level synthesis

In this paper, a discrete Fourier transform (DFT) algorithm is designed and optimised for the FPGA implementation using the Xilinx VIVADO High-Level Synthesis (HLS) tool. The DFT algorithm is written by C++ programming and simulated for functional verification in the HLS and MATLAB. For hardware validation, the DFT module is packaged as an IP core and tested in a VIVADO project. A Xilinx SDK application written by C language is developed and used for testing the DFT module on a Zynq FPGA development board, ZedBoard. For visualisation of the DFT magnitude spectrum generated in FPGA, a GUI is developed by C# programming and related commands/data can be communicated between the GUI and ZedBoard over the serial port. Experimental results are presented with discussion. The DFT module design, optimisation and implementation as well as the VIVADO project development methods can be extended to other FPGA applications.

Interpolated DFT Algorithm for Frequency Estimation by Using Maximum Sidelobe Decay Windows

A sinusoidal frequency estimator based on interpolated Discrete Fourier Transform (DFT) algorithm by using Maximum Sidelobe Decay (MSD) windows is proposed in this paper. Firstly, the received sinusoid is weighted by an appropriate MSD window. Then DFT is carried out on the weighted sinusoid and the coarse estimation is acquired by finding the position of the maximum DFT sample. Different from all the existing algorithms, the presented estimator adopts the maximum DFT sample and two Discrete Time Fourier Transform (DTFT) spectral lines which are on the same side of the maximum DFT sample in the fine estimation step. MSE formulas of the presented estimator in additive white noise are derived. Simulation results indicate that the presented estimator outperforms the competing estimators.

FPGA Realization of the Observer-Based Sliding Discrete Fourier Transform

Discrete Fourier transform (DFT) is a widely used method of signal analysis in digital signal processing. The DFT converts a signal from time domain to frequency domain for further processing. For fixed-size sliding window applications of the DFT, the observer-based sliding DFT (oSDFT) algorithm has been shown to be stable, accurate, and theoretically faster, than the well-known block-oriented fast Fourier transforms (FFT). However, no hardware implementation of the oSDFT has been proposed yet. In this paper, a hardware optimized implementation of two variants of the algorithm for FPGA is presented. Such implementation is compared with the Xilinx FFT Intellectual Property in terms of processing speed and hardware requirements. The structure is implemented in Verilog HDL using Vivado IDE, with the aim of maximizing the processing speed and minimizing the required hardware resources. The analysis of the FPGA-based oSDFT and FFT circuits in a sample-by-sample processing scenario, reveals that the latency and energy usage of the oSDFT are smaller relative to the FFT. The latency and energy usage per sample processed of the implemented structures are up to 9 and 10 times lower than those of FFT respectively. The required resources for these methods are also presented and analyzed.