Chebyshev Window Research Articles

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.

Influence of electrode apodization weighted structure on the performance of SAW temperature sensors

In order to improve the comprehensive performance of the surface acoustic wave (SAW) temperature sensors and reduce clutter interference, the optimized Chebyshev window function, Blackman window function and Hamming window function are used to carry out the apodization weighting design for interdigital transducer (IDT) and reflective grating respectively. The influence of electrode apodization weighted structure on the performance of SAW temperature sensors is systematically studied through experiments. The results show that the apodization weighted design of IDT and reflective gate can effectively improve the resonance peak intensity and reduce the side lobe interference; the IDT and the reflection grating are designed with apodization weighting at the same time, compared with the single reflection grating weighting, the volatility of the side lobe of the Chebyshev window function and the Hamming window function increases, the volatility of the side lobe of the Blackman window function decreases; after electrode apodization optimization, the resonance frequency, Q value of the SAW sensor and the sensitivity to temperature increases; using a hamming window optimized electrode structure, the peak value of S11 is −36.73 dB and the Q value is 15 030. In order to ensure the signal processing ability and comprehensive performance of the sensor, an optimized Hamming window should be used for the electrode design of the SAW sensors.

Research on nondestructive identification and location algorithm of cables with discontinuous conductor diameters based on broadband impedance spectrum

The number of cables in the distribution system is extremely huge, but there are some cables with thinner conductors in the middle section, which may threaten the safety of the system. At present, there is no effective detection method for such problems. Based on the broadband impedance spectrum, this paper proposes an algorithm to identify and locate the cables with discontinuous conductor diameters in the middle using the integral transformation with Chebyshev window. The simulation and experimental results show that the algorithm proposed in this paper can realize the identification and location of the conductor thinning cable in the middle section, and the location error is less than 0.76%.

Principle and Verification of an Improved Algorithm for Cable Fault Location Based on Complex Reflection Coefficient Spectrum

Diagnostic methods for fault location in cable insulation have become increasingly vital with the development of long-distance cables. This article presents an improved method for fault location based on the complex reflection coefficient spectrum (CRCS). First, a mathematical model for a long high-voltage cable line with consideration of a distribution-parameter circuit of cable joints is established in the frequency domain, and the CRCS of the cable with joints is analyzed. Next, based on the principle of frequency domain reflectometry (FDR), an algorithm in time-frequency conversion which uses the CRCS as the analysis spectrum is proposed. And the positioning sensitivity of the method is improved by implementing a data process adopting a Chebyshev window function which is controllable and reduces the sidelobe effect effectively. Furthermore, the improved method is evaluated by performing the simulations and two field verification tests. In a field test for a 5.1-km-long 110 kV cable, the multiple cable joints could be located effectively, and the relative error is between 0.14% and 1.49%. Then, the method was conducted for the positioning of a high-resistance fault and multiple joints on a 2.7-km-long 110 kV cable and the relative error is 0.37%. It is worth noting that the cross-bonding links of both cable tests were artificially replaced with temporary links straight across each joint. For the cross-bonded cable system, the test result shows that an obvious reflection is found at the cross-bonding point, which can reduce the reliability and accuracy of the present method.

Nonlinear Frequency Offset Beam Design for FDA-MIMO Radar.

The beam pattern of frequency diversity array (FDA) radar has a range-angle two-dimensional degree of freedom, which makes it possible to distinguish different targets from the same angle and brings a new approach to anti-jamming of radars. However, the beam pattern of conventional linearly frequency-biased FDA radar is range-angle-coupled and time-varying. The method of adding nonlinear frequency bias among the array elements of the FDA array has been shown to eliminate this coupling property while still allowing for better beam performance of the emitted beam. In this paper, we obtain a decoupled and time-invariant beam direction map using the FDA-multi-input-multi-output (FDA-MIMO) radar scheme and then obtain a sharp pencil-shaped main sphere beam pattern with range-angle dependence using a linear frequency offset scheme weighted by a Chebyshev window. Finally, the anti-interference performance of the proposed method is verified in an anti-interference experiment.

Sensitivity Improvement in Cable Faults Location by Using Broadband Impedance Spectroscopy With Dolph-Chebyshev Window

Cable fault location is generally much more difficult if cable defect has not reached the level of serious breakdown. Traditional methods such as time domain reflectometry (TDR) and partial discharge detection cannot solve this problem well due to their low sensitivity. This paper proposes a new non-destructive detection method based on the impedance spectroscopy (IS), which can effectively locate soft faults in the cable. In this paper, a numerical model for cable with distributed parameters is established firstly. Based on this model, cable faults are extracted from the imaginary part of impedance spectrum with Discrete Fourier Transform (DFT). The Chebyshev window is introduced to suppress interference and enhance signal-to-noise ratio, which improves the sensitivity and accuracy of fault location significantly. Experiments and simulations show that this method can well locate multi-segment defects in cables with good accuracy. The window function successfully amplifies the normalized amplitude of faults and improves the positioning accuracy. Compared with other method, this method reduces distortion points effectively. The fault location error is within 0.53%, which has great potential for field application.

Depth-dependent apodization window based on Chebyshev polynomial for ultrasound imaging.

To improve the image resolution of a portable real-time ultrasound imaging device, this paper proposes a beamformer with composite apodization windows based on Chebyshev polynomial. By introducing the Chebyshev window, the level of sidelobe can be flexibly controlled. The value of weighting changes according to the detection depth and ultrasound attenuation such that it can attain better image resolution than traditional beamformers. The simulations and experiments indicate that the proposed method can flexibly narrow the mainlobe width while keeping the performance of the suppressing artifacts. The full width at half-maximum of this method is 14.1%-27.8% and 4.2%-25.0% narrower than those of traditional apodization methods in the field II simulations and Geabr_0 experiment, respectively.

A method for locating and diagnosing cable abrasion based on broadband impedance spectroscopy

Modern power systems contain different types of cables and that makes it important to diagnose defects before they result in faults. Existing cable inspection methods, such as dielectric loss measurement and partial discharge, still fail to detect and locate weak cable defects. This paper presents a novel non-destructive method for detecting wear and aging defects based on broadband impedance spectroscopy (BIS) is proposed. A digital model of the cable distribution parameters is developed in this paper. The effects of different angular wear defects on the impedance spectroscopy were compared, and the degree of defects was successfully distinguished by discrete Fourier transform (DFT). The severity of the defect can be determined from the difference in peak height at the defect location after normalization. By using DFT and the Chebyshev Window it was also possible to identify two defects in the cable within 0.47% deviation of the defect position.

Research on fault diagnosis of planetary gearbox based on variable multi-scale morphological filtering and improved symbol dynamic entropy

Under complex working conditions with noise interference, the fault feature of planetary gearbox is difficult to be extracted and the fault mode is difficult to be identified. To tackle this problem, the technologies of variable multi-scale morphological filtering (VMSMF) and average multi-scale double symbolic dynamic entropy (AMDSDE) are proposed in this paper. VMSMF selects Chebyshev Window as the structural element and automatically selects the optimal-scale parameters according to the signal characteristics of the planetary gearbox, which improves the filtering accuracy and calculation efficiency. AMDSDE fully considers the correlation between various state modes. Once combined with relevant knowledge of Mathematical statistics, the algorithm can effectively reduce misjudgment. Firstly, the turn domain resampling (TDR) is used to transform the time domain signal of variable speed into the angle domain signal that is not affected by speed change. Secondly, the proposed VMSMF is used to de-noise the vibration signal, and the fault signal with a high signal-to-noise ratio is obtained. Finally, AMDSDE is used to extract the entropy value of the fault signal and judge the fault type. The proposed technology is verified by four kinds of signals collected from the sun gear of the planetary gearbox under non-stationary working conditions.

Crack propagation monitoring of rotor blades using synchroextracting transform

Blade fatigue fracture is a serious aero-engine fault that may lead to an aircraft crash. It is essential for ensuring the safety of the aero-engine operation to monitor the blade crack propagation. Generally, the crack propagation of rotor blades can be detected by the natural frequency shift. The time-frequency analysis method with high time-frequency resolution can detect the natural frequency shift during crack propagation. In this paper, the synchroextracting transform with the advantage of high time-frequency resolution is proposed to extract the time-frequency feature of the vibration signal of the cracked blade. In simulation, the crack length is defined to increase exponentially. The blade finite element model is used to generate the simulated signals. Compared with short-time Fourier transform, synchroextracting transform with the advantage of high time-frequency resolution can detect the natural frequency shift of the cracked blade earlier. Furthermore, Chebyshev window is used to solve the problem of spectral leakage caused by an interval sampling strategy. In a spin testing, two blades without artificial cracks suddenly broke. Strain signals are used to verify the effect of time-frequency resolution on crack propagation monitoring. Short-time Fourier transform is difficult to monitor the crack propagation in the spin testing because of the interval sampling strategy. However, synchroextracting transform with the advantage of high time-frequency resolution can detect the crack through the natural frequency shift of the cracked blade. Finally, in order to reveal the damage of the cracked blade, the crack length is estimated qualitatively by combining the natural frequency and the rotational speed measured in experiment with the results of finite element analysis. The feasibility of the crack estimation method is verified by the experiment in a non-rotating case.

The digital beam forming technique in AgileDARN high-frequency radar

An all-digital agile dual auroral radar network (AgileDARN) was developed by the National Space Science Center, Chinese Academic of Sciences (NSSC, CAS). AgileDARN can achieve higher performance and greater flexibility based on highly digitized hardware and its distributed digital signal processing system. Multiple receiving beams can be created within the transmitting beam pattern better to determine the direction of arrival (DOA). In each beam, seven real-time azimuthal sub-beams are synthesized simultaneously with 16 main digital receiver channels. Each sub-beam detects the echo around the transmitting boresight with an angular separation of 0.46°. Comparing the echoes from different sub-beams, the azimuthal geolocation of the irregularities can be improved when their volume is smaller than the beamwidth. Furthermore, the Chebyshev window enables the control of the sidelobes and antenna pattern, effectively suppressing interference. To implement multi-beam forming, extra processing resources of the field-programmable gate array (FGPA) are required. This paper introduces the signal processing procedure and analyzes the requirements on the FPGA resources，and the technique is validated with meteor echoes received by the AgileDARN radar. The azimuthal geolocation of echoes increases by seven times compared with the single beamforming SuperDARN radar.

A Novel NLFM Waveform With Low Sidelobes Based on Modified Chebyshev Window

It is well known that the nonlinear frequency modulation (NLFM) chirp waveform can shape advantageously the power spectrum density (PSD) such that the autocorrelation function exhibits reduced sidelobes as the window function. However, differences between the PSD and window function due to the Gibbs effects caused by the Fresnel integral would lead to deteriorative performance of the NLFM chirp waveform. In particular, the correlation function of NLFM waveform with Chebyshev PSD is seriously inconsistent with the lowest sidelobe level of the Chebyshev window function possesses. To overcome the inconsistency, therefore, in this letter, a novel NLFM waveform with modified Chebyshev window PSD is proposed, which combines the Chebyshev with edge distortion compensation, allowing, in theory, low sidelobe level as Chebyshev window. Using theoretical analysis also confirmed by simulation, this letter shows that the novel NLFM waveform possesses low sidelobes without high computational complexity in design.

New scheme of UHVDC transmission line protection based on Chebyshev window filter

Based on the analysis of the fault current characteristics in ultra-high-voltage DC (UHVDC) transmission lines, a new method to identify the fault by using the polarity of the current mutation is proposed here. Firstly, the protection scheme here is set up as the distributed parameter model to eliminate the influence of distributed capacitance current and data synchronisation on protection. Furthermore, not only the characteristic harmonics of the DC side but also the electromagnetic coupling of the bipolar DC lines and the interference of the high-frequency pulse are considered; the Chebyshev filter is used to select the low-frequency component. Finally, the results of PSCAD/EMTDC simulation show that the proposed scheme not only has the advantages of reliable and low sampling rate, but also has the ability to withstand the transition resistance and the lightning resistance. In a word, the scheme has important reference value for the actual UHVDC projects.

Optimization of frequency characteristics for SAW device using apodization weighting method

In this paper, the positive influence of apodization weighting method on frequency characteristics of surface acoustic wave (SAW) temperature sensor is investigated. Simulation and experiment results show that side lobe suppression abilities of the sensor can be improved by using apodization weighting which is based on Chebyshev window. Meanwhile, we find that the side lobe of the sensor can be further restrained, when the dummy electrodes are removed. Frequency-temperature characteristics of the devices are independent of the inclusion of dummy electrodes. The apodization weighted SAW temperature sensor shows great application potential in occasions with strong electromagnetic interference.

Adaptive Dolph–Chebyshev window‐based S transform in time‐frequency analysis

The S transform is widely used in time-frequency analysis (TFA). However, the standard S transform suffers from the poor energy concentration in time-frequency distribution (TFD). In this study, an adaptive Dolph–Chebyshev window instead of the Gaussian window-based S transform and its fast realisation strategy are introduced for non-stationary signal TFA. By controlling the shape of the Dolph–Chebyshev window adaptively to signal, the new TFA method is able to achieve a high energy concentration in TFD. In addition, the new method is superior to other classical methods for instantaneous frequency estimation. Several examples are presented to illustrate its behaviour on different signals and demonstrate its validity.

Time-selective windowing technique in free-field microphone reciprocity calibration

Time-selective windowing techniques, which effectively remove multi-path noise, have been widely utilized for reciprocity calibration of microphone there are still limitations imposed by overlapping signals, particularly at low frequencies and for high Q microphones. Based on a fast Fourier transform analysis, the leakage due to a limited frequency range makes the overlap problem worse, not be perfectly separated. Instead of using conventional low-pass filters that are designed to have a flat response in the frequency range of interest, in this study, a filter with a Dolph-Chebyshev window shape was proposed because it has low sidelobe levels. After removing multi-path noise with a time-selective window, an inverse filter should be applied to compensate for distortion created by the applied filter. The method suggested in this paper extends the possible frequency range of free-field reciprocity calibration to frequencies below 2 kHz.

Compact Range Performance Evaluation Using Aperture Near-Field Angular Spectrums

For a compact range (CR), the near-field angular spectrum can be obtained by making an inverse Fourier transform of its aperture spatial near field. The characteristics of the aperture design have been carried by the aperture near-field angular spectrum. The direct wave and edge-diffracted waves from the aperture can be separated and distinguished clearly in the angular domain. Therefore, the CR performance can be evaluated and improved accordingly. In this paper, based on the aperture field convolution method and plane wave spectrum (PWS) theory, near-field angular spectrums for different apertures have been computed. The general criteria for the CR aperture design have been discussed. The selections of the whole aperture shape, the serration height, the serration base length, the serration number, and the serration shape (including isosceles and right-angled triangles) have been compared. At last, the near fields of an optimized serrated-edge aperture and an original circular aperture in different transverse planes have been computed and compared. The width and height of the apertures are all 30 wavelengths in free space. In order to suppress the sidelobes, a Chebyshev window with ${- 50} $ dB sidelobes has been adopted in the spatial-angular transform.

Design of Linear-Phase Notch Filters Based on the OMP Scheme and the Chebyshev Window

A novel suboptimal paradigm is developed to compute the power-efficient linear-phase nonequiripple notch filters based on the orthogonal matching pursuit (OMP) scheme and the Chebyshev window. The design procedure proceeds as follows: At each iteration, the OMP scheme is employed to compute an FIR notch filter, which is then refined with a predevised Chebyshev window to improve its performance. The iteration procedure stops when the refined filter meets the predevised design specifications. The simulation results show that the proposed OMP scheme could be used to compute power-efficient linear-phase notch FIR filters.

Pulse compression technique for simultaneous HIFU surgery and ultrasonic imaging: A preliminary study

In an ultrasound image-guided High Intensity Focused Ultrasound (HIFU) surgery, reflected HIFU waves received by an imaging transducer should be suppressed for real-time simultaneous imaging and therapy. In this paper, we investigate the feasibility of pulse compression scheme combined with notch filtering in order to minimize these HIFU interference signals. A chirp signal modulated by the Dolph–Chebyshev window with 3–9MHz frequency sweep range is used for B-mode imaging and 4MHz continuous wave is used for HIFU. The second order infinite impulse response notch filters are employed to suppress reflected HIFU waves whose center frequencies are 4MHz and 8MHz. The prototype integrated HIFU/imaging transducer that composed of three rectangular elements with a spherically con-focused aperture was fabricated. The center element has the ability to transmit and receive 6MHz imaging signals and two outer elements are only used for transmitting 4MHz continuous HIFU wave. When the chirp signal and 4MHz HIFU wave are simultaneously transmitted to the target, the reflected chirp signals mixed with 4MHz and 8MHz HIFU waves are detected by the imaging transducer. After the application of notch filtering with pulse compression process, HIFU interference waves in this mixed signal are significantly reduced while maintaining original imaging signal. In the single scanline test using a strong reflector, the amplitude of the reflected HIFU wave is reduced to −45dB. In vitro test, with a sliced porcine muscle shows that the speckle pattern of the restored B-mode image is close to that of the original image. These preliminary results demonstrate the potential for the pulse compression scheme with notch filtering to achieve real-time ultrasound image-guided HIFU surgery.

A new efficient approach to the design of parametric windows with arbitrary sidelobe profiles

Based on a simple variable transformation in the spectral domain, a new method to parametrize any window in the same way as Kaiser–Bessel or Dolph–Chebyshev windows is presented, allowing a very flexible trade-off between the width of the main lobe and the height of the sidelobes. The derivation of the method is a generalization of the procedure used for the design of Kaiser–Bessel window and van der Maas function, which is related to the Dolph–Chebyshev window. The properties of this spectral transformation are studied. New bases of functions are presented, which can be used to easily design families of windows having a specific asymptotic decrease rate of the sidelobes. Links are made between this work and windows found in the literature.