Self-convolution Window Research Articles

Two-dimensional Hanning self-convolution window for enhancing Moiré fringe alignment in lithography

The current image processing techniques heavily rely on classic windows for suppressing spectral leakage. However, the limited capability of these classic windows to suppress spectral leakage restricts their application in the field of high-precision measurement. This paper proposes a novel family of windows capable of suppressing spectral leakage associated with the Moiré fringes pattern, thereby enhancing the accuracy of lithography alignment. Specifically, a novel two-dimensional Hanning self-convolution window is introduced, which is derived from the Hanning window to inherit its advantage of ultra-rapid sidelobe decay. The behaviors of the main lobe and desirable sidelobes of the 1st- to 4th-order are examined. Additionally, a novel fringe phase extraction algorithm is established based on the proposed window, which demonstrates high accuracy and efficiency. Simulation and experimental results validate the feasibility and practicality of the proposed window. In particular, the proposed window outperforms classic windows in suppressing spectral leakage, thereby successfully enhancing the phase extraction accuracy to achieve high-precision misalignment measurement at the sub-2-nm level (1.47 nm @ 3σ criterion). The proposed method can be easily extended to other real engineering applications utilizing fringe to achieve high-precision measurements, such as fringe projection profilometry, damage detection, and visual mechanical vibration monitoring.

Minor Defect Location of Power Cable Based on 2nd-order Chebyshev Self-convolution Window

Power cable is extremely important to the stability of the power grid. It is often difficult to determine the location of cable minor defects. Based on previous studies, this paper improves a detection method based on the reflection coefficient, which can effectively locate the minor defect. First, the distributed parameter model of cable is established, and the reflection coefficient is obtained. The 2nd-order self-convolution Chebyshev window function having good positioning effects is selected as the preprocessing function for the real part of the reflection coefficient. Then Discrete Fourier Transform is used to obtain the defect location image. The simulation results indicate that the proposed measure can locate the weak defect in the cable well and improve the positioning accuracy, which shows great application potential.

An online correction system for electronic voltage transformers

As a vital piece of equipment, electronic voltage transformer is widely used in the power system measurements. The current calibration techniques of this asset class exhibit several issues including complex real time implementation. In contrary with existing calibration techniques, this paper proposes a new correction system for electronic voltage transformers, which can be conducted online without causing any interruption to the electricity grid. The new proposed correction system utilizes an SF6 cylinder capacitor and employs an advanced signal processing technique based on the improved Rife frequency shift algorithm. The improved Rife frequency shift algorithm is a combination of the Hanning self-convolution window and the conventional Rife algorithm, which features simple calculation and high accuracy. Results show that the accuracy of the proposed algorithm is higher than the conventional commonly used interpolation algorithms. Compared with the existing traditional calibration techniques, the proposed system features easy online implementation, simple calculation and high accuracy. The robustness of the proposed system is validated through simulation analysis and practical field measurements.

A Novel Interpolated DFT Synchrophasor Estimation Algorithm With an Optimized Combined Cosine Self-Convolution Window

With the current power system being electronicized nowadays, synchrophasor estimation (SE) plays an increasingly critical role in the monitoring, analysis, and protection of the state of the power grid. One proposal has been brought to enhance the commonly used discrete Fourier transform (DFT) algorithm that has a large error due to the inherent spectral leakage and fence effect in asynchronous sampling by interpolations. This article proposes an SE algorithm based on an optimized combined cosine self-convolution (OCCSC) window. Using the sidelobe characteristics of the window functions as the evaluation index, an optimized combined cosine window is obtained by the accelerated particle swarm optimization (APSO) algorithm. The window function’s self-convolution is used to further expand its excellent characteristics. Based on these characteristics, combined with interpolated DFT, simulations and experimental verifications compared with other algorithms show the effectiveness of the proposed algorithm.

High-Precision Harmonic Analysis Algorithm Based on Five-Term MSD Second-Order Self-Convolution Window Four-Spectrum-Line Interpolation

For the frequency spectrum leakage and fence effect generated in Fast Fourier Transform (FFT) during asynchronous sampling and integral period truncation affect the precision of harmonic detection, a new algorithm for harmonic analysis based on four-spectrum-line interpolation FFT with second-order self-convolution window with five-term Maximum-Sidelobe-Decay (MSD) was proposed and the polynomial fitting method was used to construct the four-spectrum-line interpolation correction formula. The simulation results showed that this algorithm could improve the detection accuracy of amplitude, phase and frequency by 1-2 orders of magnitude compared with other commonly used windowed interpolation algorithms.

Feature Extraction Method of Ball Mill Load Based on Adaptive Variational Mode Decomposition and Improved Power Spectrum Analysis

The real-time working conditions of the ball mill in the grinding process are complicated, which makes it difficult to accurately obtain the internal load status of the ball mill. In this paper, the energy difference between the original cylinder vibration signal and the intrinsic mode function is proposed as the evaluation parameter of the adaptive variational mode decomposition (VMD) layer number, and a new autocorrelation function is constructed. The intrinsic mode function is processed by introducing the energy centrobaric method of the Nuttall self-convolution window. Accordingly, a ball mill load feature extraction method based on adaptive VMD and improved power spectrum estimation is proposed, and the ball mill load identification system based on LabVIEW is developed. The number of layers of intrinsic mode function could be adaptively determined. And the algorithm’s ability to resist mode aliasing and false components of this method is improved, which improves the accuracy of ball mill load detection. The measured results show that internal load features of ball mill during the grinding process are effectively extracted, and the mill load status is accurately identified, which provide an accurate and reliable basis for grinding optimization control and efficiency.

Spatial resolution enhancement of DFT-BOTDR with high-order self-convolution window

Abstract Brillouin optical time-domain reflectometer based on discrete Fourier transform has attracted interest for the simple structure, low cost, and fast data processing. In this paper, a 4th-order Hanning self-convolution window method is demonstrated to enhance the spatial resolution of DFT-BOTDR system. The Brillouin backscattering is profile-weighted by convolving with a 4th-order Hanning self-convolution window. The center frequency of the Brillouin spectrum is determined by the weighted function, where the spectrum power is concentrated in the main lobe, leading to an optimized spatial resolution. Experiments of strain sensing on a 5 km long sensing fiber with pulse width of 300 ns and sampling rate of 625 MS/s are carried out. The theoretical spatial resolution is 41 m with traditional rectangular window. The experimental results show that the spatial resolution is improved by ∼31 m with the proposed 4th-order Hanning self-convolution window. The sensing system is promising in accurate location of distributed sensing.

A Novel Approach to ECG R-Peak Detection

Electrocardiogram (ECG) signal processing and analysis is becoming more and more popular as it is useful in diagnosis and prognosis of human heart and clinically automatic machine estimation is based upon it. R-peak is the most important component in ECG beat and is widely used to investigate normal and abnormal subjects (patients). From the last few decades, R-peak detection in ECG has been the most challenging topic in the biomedical research. As QRS complex has high frequency in ECG as compared to other waves (P, T, U-wave), so majority of algorithms estimate QRS complex by either filtering or suppressing the lower frequency waves, including various artifacts like baseline wander, power line interference, and electromyograph noises. This paper demonstrates a new kind of ECG denoising algorithm based on self-convolution window (SCW) concept. The SCW based on Hamming window, herein referred to as Hamming self-convolution window, is used to design a new kind of filter which possesses negligible ripples in the stop band, as compared to the conventional window-based filters. This algorithm is validated on MIT-BIH arrhythmia database and the results outperform in terms of sensitivity, positive predictivity, and error rate obtained as 99.93%, 99.95%, and 0.117%, respectively, as compared to the other well-established works. The approach has also outperformed the results of well-established window-based filters (Hamming and Kaiser) in terms of reduced false negative, false positive, and error rate.

Fault Location Scheme for Transmission Lines Using Kaiser Self-Convolution Windowed FFT Phase Comparison

In order to improve the fault location accuracy, and eliminate the influence of spectral leakage in power transmission line fault location, we proposed a novel fault location scheme for transmission lines based on multi-measurements and phase comparison with Kaiser self-convolution windows FFT, which can locate the fault between two adjacent towers in the fault-prone segment. It is based Kaiser self-convolution window's excellent performance of leakage suppression, which can effectively solve the phase current fault component is relatively large errors due to spectral leakage problem. Firstly, this paper analyzes the causes of the phase spectrum leakage, then elaborates the sidelobe characteristics of Kaiser self-convolution window, and lists phase comparative fault location using steps, finally, verifies the correctness of the proposed method by simulation. The results show that the proposed method can effectively suppress spectral leakage, has a high location accuracy, a wide applicability and its solving of phase difference is precise.

Frequency Estimation of Distorted and Noisy Signals in Power Systems by FFT-Based Approach

This paper focuses on the accurate frequency estimation of power signals corrupted by a stationary white noise. The noneven item interpolation FFT based on the triangular self-convolution window is described. A simple analytical expression for the variance of noise contribution on the frequency estimation is derived, which shows the variances of frequency estimation are proportional to the energy of the adopted window. Based on the proposed method, the noise level of the measurement channel can be estimated, and optimal parameters (e.g., sampling frequency and window length) of the interpolation FFT algorithm that minimize the variances of frequency estimation can thus be determined. The application in a power quality analyzer verified the usefulness of the proposed method.

An Online Calibration Method for Electronic Voltage Transformers Based on IEC 61850-9-2

Since electronic voltage transformers (EVTs) based on IEC 61850-9-2 are widely used in the substations, especially in the automating substations, their calibration becomes very important. Generally, the calibration of EVTs needs for the power to be interrupted and causes power outage, and also the faults of the running transformers cannot be found in time. For this reason, an online calibration system is proposed in this paper. By employing a specially designed remote-controlled hoisting unit and standard voltage transformer, the proposed system can calibrate EVTs without interrupting the power service and the power outage can be avoided. A two-order Hanning self-convolution window algorithm is adopted to suppress the influence of spectrum leakage caused by frequency fluctuation and harmonic interference. Tests have been performed in the China Electric Power Research Institute. The results show that the proposed system has good performance and it can reach the accuracy class of 0.05 in complicated electromagnetic fields.

Harmonic Analysis Based on Blackman-Harris Self-Convolution Window

This paper presents a method of harmonic analysis -- Blackman-Harris self-convolution window harmonic analysis method. Self-convolution window has lower side lobe and decays faster, analyze its performance and compare it with Blackman Window, Blackman-Harris window and Hanning window, calculation formula of frequency, amplitude and initial angle of the fundamental wave and every harmonic are deduced with the phase difference correction algorithm. Blackman-Harris self-convolution window has an excellent side lobe performance, which can effectively suppress the effect of spectrum leakage, embedded systems is easy to implement with spectrum phase difference correction algorithm. Simulation results show that: for Blackman-Harris self-convolution window function, there is a good effect of suppressing spectral leakage, the accuracy of harmonic parameters analysis is better than the classical window function.

Parameter Estimation of Power System Signals Based on Cosine Self-Convolution Window With Desirable Side-Lobe Behaviors

Parameter estimation is an important topic in power system signal-processing tasks. A new class of windows, the cosine self-convolution window (CSCW), is proposed. The main-lobe and side-lobe behaviors of the first to the third order CSCWs are studied. A CSCW-based improved fast Fourier transform algorithm (FFT) for estimating power system signal parameters, such as frequency, phase, and amplitude, is given. The CSCW has a low peak side-lobe level, a high side-lobe decaying rate, and a simple spectral representation. Leakage errors and harmonic interferences are thus reduced considerably by weighting samples with the CSCW. The CSCW-based improved FFT algorithm can be easily implemented in embedded systems. The effectiveness of the proposed method was analyzed by means of computer simulations and practical experiments for multifrequency signals with the variations of the power system frequency as well as the presence of white noise and interhamonics.

Triangular Self-Convolution Window With Desirable Sidelobe Behaviors for Harmonic Analysis of Power System

Weak harmonic components can easily be obscured by nearby strong harmonics due to the spectral leakage in the power system. To obtain a window suitable for solving the problem, the triangular self-convolution window (TSCW) is constructed, with the triangular window being the parent window to take advantages of its narrow major lobe and simple computation. A TSCW-based phase difference correction algorithm for calculating the power system signal parameters, such as frequency, phase, and amplitude, is presented in this paper. The TSCW has a low peak sidelobe level, a high sidelobe rolloff rate, and a simple spectral representation. Leakage errors and harmonic interferences are thus considerably reduced by weighting samples with the TSCW. The TSCW-based phase difference correction algorithm is free of solving high-order equations, and the overall method can easily be implemented in embedded systems. The effectiveness of the method proposed was analyzed by means of computer simulations and practical experiments for multifrequency signals without noise and with quantization noise.

Frequency estimation of electric signals based on the adaptive short-time Fourier transform

Frequency is an important parameter in the monitoring, control, and protection of power systems and electric equipment. In this article, based on the adaptive short-time Fourier transform, a new digital algorithm is presented to estimate the frequency of electric signals. The novel window, called the Rectangle Self-Convolution Window, is adapted to eliminate the impact of harmonics, and the window length is adjusted according to the variation of signal frequency. The algorithm is easy to implement with high precision and short response time as well as a wide measuring range. It is thus suitable for real-time detection, especially when the frequency changes abruptly and the signal is corrupted by harmonics. Simulation results and practical application show that it is feasible and effective under different conditions.

Hanning self-convolution window and its application to harmonic analysis

The Hanning self-convolution window (HSCW) is proposed in this paper. And the phase difference correction algorithm based on the discrete spectrum and the HSCW is given. The HSCW has a low peak side lobe level, a high side lobe roll-off rate, and a simple spectrum representation. Hence, leakage errors and harmonic interferences can be considerably reduced by weighting samples with the HSCW, the parameter estimation by the HSCW-based phase difference correction algorithm is free of solving high order equations, and the overall method can be easily implemented in embedded systems. Simulation and application results show that the HSCW-based phase difference correction algorithm can suppress the impacts of fundamental frequency fluctuation and white noise on harmonic parameter estimation, and the HSCW is advantageous over existing combined cosine windows in terms of harmonic analysis performance.