Enhanced Fourier Transform Using Wavelet Packet Decomposition

Many domains, including communication, signal processing, and image processing, use the Fourier Transform as a mathematical tool for signal analysis. Although it can analyze signals with steady and transitory properties, it has limits. The Wavelet Packet Decomposition (WPD) is a novel technique that we suggest in this study as a way to improve the Fourier Transform and get beyond these drawbacks. In this experiment, we specifically considered the utilization of Daubechies level 4 for the wavelet transformation. The choice of Daubechies level 4 was motivated by several reasons. Daubechies wavelets are known for their compact support, orthogonality, and good time-frequency localization. By choosing Daubechies level 4, we aimed to strike a balance between preserving important transient information and avoiding excessive noise or oversmoothing in the transformed signal. Then we compared the outcomes of our suggested approach to the conventional Fourier Transform using a non-stationary signal. The findings demonstrated that the suggested method offered a more accurate representation of non-stationary and transient signals in the frequency domain. Our method precisely showed a 12% reduction in MSE and a 3% rise in PSNR for the standard Fourier transform, as well as a 35% decrease in MSE and an 8% increase in PSNR for voice signals when compared to the traditional wavelet packet decomposition method.

Anti-aliasing nonstationary signals detecion algorithm based on interpolation in the frequency domain using the short time Fourier transform

To eliminate the aliasing that appeared during the measurement of multi-components nonstationary signals, a novel kind of anti-aliasing algorithm based on the short time Fourier transform （STFT） is brought forward. First the physical essence of aliasing that occurs is analyzed; second the interpolation algorithm model is setup based on the Hamming window; then the fast implementation of the algorithm using the Newton iteration method is given. Using the numerical simulation the feasibility of algorithm is validated. Finally, the electrical circuit experiment shows the practicality of the algorithm in the electrical engineering.

NYFR output pulse radar signal TOA analysis using extended Fourier transform and its TOA estimation

Nyquist folding receiver (NYFR) is a typical wideband analog-to-information architecture. Focusing on the non-cooperative receiving, the pulse radar signal intercepted by the NYFR in time domain is analyzed. The NYFR outputs under different input conditions are investigated based on the extended Fourier transform (EFT) and the sampling theorem. Combining with the characteristic of the NYFR output in time domain, a new time of arrival (TOA) estimation method based on the energy envelope and the wavelet transform is proposed. The proposed estimation method can be adapted for the non-cooperative situation. It has no requirement for prior information to determine the threshold and is not necessary to transform the signal into baseband. Simulation results prove the correctness of the NYFR output expressions and show the efficacy of the proposed estimation method. © 2017 Beijing Institute of Aerospace Information.

Adaptive Fourier Decomposition Based Time-Frequency Analysis

The attempt to represent a signal simultaneously in time and frequency domains is full of challenges. The recently proposed adaptive Fourier decomposition （AFD） offers a practical approach to solve this problem. This paper presents the principles of the AFD based time-frequency analysis in three aspects： instantaneous frequency analysis, frequency spectrum analysis, and the spectrogram analysis. An experiment is conducted and compared with the Fourier transform in convergence rate and short-time Fourier transform in time-frequency distribution. The proposed approach performs better than both the Fourier transform and short-time Fourier transform.

Suppression to the cross-channel interference based on the short time Fourier transform

A new cross-channel interference suppression method is proposed to decrease the cross-channel interference in beat signals based on the short time Fourier transform （STY3＂） and the inverse short time Fourier transform （ISTFT） when the dual-orthogonal polarimetric frequency-modulated continu- ous wave （FMCW） radar adopts the opposite-slope linear frequency modulation signal pair in the simultaneous measurement mode. The STFT is applied only on the signals in the cross-interference intervals in the four polarimetric channels to decrease the computation complexity. A mask matrix for suppressing the interference is constructed using the constant false alarm ratio （CFAR） detection on the spectrograms by the STFY. The simulative results show that the cross-channel interference is effi- ciently suppressed by the proposed method. The comparison between the proposed method and the rejection method verifies the improved performance of the proposed method.

Application of short-time Fourier transform to high-rise frame structural-health monitoring based on change of inherent frequency over time

The high-rise frame structure has become more and more widespread, like its damage from the complication of the environment. The traditional method of damage detection, which is only suitable for the stationary signal, does not apply to a high-rise frame structure because its damage signal is non-stationary. Thus, this paper presents an application of the short-time Fourier transform(STFT) to damage detection of high-rise frame structures. Compared with the fast Fourier transform, STFT is found to be able to express the frequency spectrum property of the time interval using the signal within this interval. Application of STFT to analyzing a Matlab model and the shaking table test with a twelve-story frame-structure model reveals that there is a positive correlation between the slope of the frequency versus time and the damage level. If the slope is equal to or greater than zero, the structure is not damaged. If the slope is smaller than zero, the structure is damaged, and the less the slope is, the more serious the damage is. The damage results from calculation based on the Matlab model are consistent with those from the shaking table test, demonstrating that STFT can be a reliable tool for the damage detection of high-rise frame structures.

基于STFT图像和迁移学习的次同步振荡源定位方法

直驱风机与电网交互引发次同步振荡,严重威胁电网的安全稳定运行。为快速定位诱发机组,提出了一种基于短时傅里叶变换(STFT)图像和迁移学习的次同步振荡源定位方法。首先,采用压缩感知技术将出口数据转化为观测信号,再对观测信号进行STFT得到具备振荡特征的映射图,构建映射图与振荡源机组之间的联系;然后,采用对抗式迁移学习架构,结合电力系统,实现对目标域无标签振荡数据的快速泛化;最后,与传统迁移学习方法进行比较,结果表明所提方法在定位准确率和效率方面表现更优,且具备较强的抗噪能力。

基于STFT-ECA-ResNet18网络模型的滚动轴承变负载故障诊断

针对传统方法处理变负载轴承故障诊断时存在的自适应能力弱,模型泛化性差的问题,提出了一种改进的基于深度残差网络的故障诊断方法。首先,将采集到的一维时间序列信号进行短时傅里叶变换得到二维时频数据,再利用二维卷积神经网络从变换后的数据中提取特征。然后,通过高效通道注意力机制获取通道全局信息并对其权值进行调整,以增强改进网络模型的泛化能力,使其在变负载工况下分类效果得到提高。最后,通过仿真对所提方法进行了验证,结果表明相比传统方法诊断效果改进明显。

Wind turbine clutter mitigation using morphological component analysis with group sparsity

To address the problem that dynamic wind turbine clutter(WTC)significantly degrades the performance of weather radar,a WTC mitigation algorithm using morphological component analysis(MCA)with group sparsity is studied in this paper.The ground clutter is suppressed firstly to reduce the morphological compositions of radar echo.After that,the MCA algorithm is applied and the window used in the short-time Fourier transform(STFT)is optimized to lessen the spectrum leakage of WTC.Finally,the group sparsity structure of WTC in the STFT domain can be utilized to decrease the degrees of freedom in the solution,thus contributing to better estimation performance of weather signals.The effectiveness and feasibility of the proposed method are demonstrated by numerical simulations.

空气涡轮起动机异常振动诊断的STFT分析

采用短时傅里叶变换分析方法,对某型空气涡轮起动机在交付前试验流程的起动过程振动响应进行非平稳特征分析,有效识别振动幅值偏大,判定异常振动,避免其交付后出现振动故障。通过对比空气涡轮起动机起动过程的正常状态与振动异常状态的短时傅里叶时频谱分析,获得异常振动的时频谱特征,对导致异常的零部件和装配因素进行了分析。结果表明:将短时傅里叶变换应用于空气涡轮起动机起动过程的振动信号分析能够对振动的非平稳特征进行有效识别。

基于短时傅立叶变换和改进Vision Transformer的滚动轴承故障诊断方法

针对传统故障诊断技术在精确与高效地诊断减速器滚动轴承故障信号方面所面临的挑战,文中提出了一种基于短时傅里叶变换与改进Vision Transformer模型的故障诊断新方法。此方法有效融合了短时傅里叶变换在处理非线性和非平稳信号上的优势以及Vision Transformer在图像分类任务上的卓越性能。通过短时傅里叶变换将一维的振动信号转化为包含时域和频域信息的二维图像数据,进而利用改进的Vision Transformer模型对这些图像数据进行处理,以实现对滚动轴承故障状态的精准诊断。在公开数据集上的实验结果验证了该方法的稳定性与高识别精度,展示了其在滚动轴承故障诊断领域的应用潜力。

基于STFT与改进ConvNeXt配电网故障区段定位方法研究

在目前的配电线路智能故障诊断研究方法中,存在着难以充分提取故障特征、抗噪声干扰能力弱、抗高阻能力差等问题。提出了一种基于短时傅里叶变换(STFT)并引入迁移学习的改进ConvNeXt配电网故障区段定位方法。该方法通过采集配电网各馈线两端的零序电流,计算出各馈线两端的零序电流幅值差,然后将各段的零序电流幅值差拼接成一个组合信号,用STFT处理组合信号,得到时频图,并将得到的时频图分为训练集和测试集。仿真结果表明,基于STFT并改进的ConvNeXt配电网故障区段定位方法在不同的故障距离、不同的接地电阻和不同的初始故障角度下都能有效地实现故障区段的选择,并且该方法具有较强的抗高阻能力以及较强的抗噪声干扰能力,在部分数据丢失的情况下仍能准确进行区段定位。

Quantitative Rectangular Notch Detection of Laser-induced Lamb Waves in Aluminium Plates with Wavenumber Analysis

It is difficult to quantitatively detect defects by using the time domain or frequency domain features of Lamb wave signals due to their dispersion and multimodal characteristics.Therefore,it is important to discover an intrinsical parameter of Lamb waves that could be used as a damage sensitive feature.In this paper,quantitative defect detection in aluminium plates is carried out by means of wavenumber analysis approach.The wavenumber of excited Lamb wave mode is a fixed value,given a frequency,a thickness and material properties of the target plate.When Lamb waves propagate to the structural discontinuity,new wavenumber components are created by abrupt wavefield change.The new wavenumber components can be identified in the frequency-wavenumber domain.To estimate spatially dependent wavenumber values,a short-space two-dimensional Fourier transform(FT)method is presented for processing wavefield data of Lamb waves.The results can be used to determine the location,size and depth of rectangular notch.The analysis techniques are demonstrated using simulation examples of an aluminium plate with a rectangular notch.Then,the wavenumber analysis method is applied to simulation data that are obtained through a range of notch depths and widths.The results are analyzed and rules of the technique with regards to estimating notch depth are determined.Based on simulation results,guidelines for using the technique are developed.Finally,experimental wavefield data are obtained in aluminium plates with rectangular notches by a full noncontact transceiving method,i.e.,laser-laser method.Band-pass filtering combined with continuous wavelet transform is used to extract a certain frequency component from the full laser-induced wavefield with wide band.Shortspace two-dimensional FT method is used for further processing full wavefield data at a certain frequency to estimate spatially dependent wavenumber values.The consistency of simulation and experimental results shows the effectiveness of proposed wavenumber method for quantitative rectangular notch detection.

FM interference suppression for PRC-CW radar based on adaptive STFT and time-varying filtering

The influence of frequency modulation （FM） interfer- ence on correlation detection performance of the pseudo random code continuous wave （PRC-CW） radar is analyzed. It is found that the correlation output deteriorates greatly when the FM inter- ference power exceeds the anti-jamming limit of the radar. Accord- ing to the fact that the PRC-CW radar echo is a wideband pseudo random signal occupying the whole TF plane, while the FM in- terference only concentrates in a small portion, a new method is proposed based on adaptive short-time Fourier transform （STFT） and time-varying filtering for FM interference suppression. This method filters the received signal by using a binary mask to excise only the portion of the TF plane corrupted by the interference. Two types of interference, linear FM （LFM） and sinusoidal FM （SFM）, under different signal-to-jamming ratio （S JR） are studied. It is shown that the proposed method can effectively suppress the FM interference and improve the performance of target detection.

基于STFT-FRFT的声纳脉冲信号实时检测和参数估计

声纳脉冲参数是分辨目标的重要信息来源,在进行目标识别时可以将目标发射的声纳脉冲参数作为一项重要的识别特征,因此正确检测和估计声纳脉冲参数具有重要意义。为解决水下未知声纳脉冲信号实时检测和参数估计的难题,提出了基于短时傅里叶变换(Short Time Fourier Transform,STFT)和分数阶傅里叶变换(Fractional Fourier Transformation,FRFT)相结合的算法(STFT-FRFT)。STFT-FRFT首先对未知信号采用短时傅里叶变换算法和自适应门限设置算法进行脉冲实时预警。脉冲预警后获取未知脉冲的起始位置和截止位置,然后截取本段信号采用分数阶傅里叶变换算法进行脉冲参数估计。理论研究及数据分析表明,此算法不仅可以保证信号检测的实时性,而且能准确估计出声纳脉冲信号的脉宽、中心频率、调频宽度和周期等参数,为后期目标分类识别提供依据。

基于自适应Fourier分解-同步提取变换的机械故障诊断方法

传统的同步提取变换方法(synchronous extraction transform,SET)用于机械故障诊断时,要求多分量信号满足各相邻模态的瞬时频率差大于所选取的SET窗函数频率支撑范围的2倍,否则容易产生频率混叠,实际信号往往无法满足该条件。此外,信号受到噪声的影响,难以获得故障的瞬时频率。针对传统的同步提取变换在机械故障诊断中存在的不足,结合自适应Fourier分解(AFD)和同步提取变换的各自优点,提出了一种基于AFD-SET的机械故障诊断方法。该方法能够有效处理频率接近的非平稳信号,准确地表达信号的瞬时频率,并且具有很快的收敛速度。仿真结果表明,提出的方法能够有效解决传统SET方法中的频率混叠,并具有更高的时频聚集性。将提出的方法应用到滚动轴承故障诊断中,诊断结果表明,该算法正确有效,能够有效提取出故障信号的频率特征。

Rockfall seismic features analysis based on in situ tests:frequency, amplitude, and duration

In the seismic event classification,determining the seismic features of rockfall is significantly important for the automatic classification of seismic events because of the huge amount of raw data recorded by seismic stations in continuous monitoring. At the same time, the rockfall seismic features are still not completely understood.This study concentrates on the rockfall frequency content, amplitude(ground velocity), seismic waveform and duration analysis, of an artificial rockfall test at Torgiovannetto(a former quarry in Central Italy). A total of 90 blocks were released in the test, and their seismic signals and moving trajectories were recorded by four tri-axial seismic stations and four cameras, respectively. In the analysis processing,all the artificial rockfall signal traces were cut separately and the seismic features were extracted individually and automatically. In this study, the relationships between a) frequency content and impacted materials, b) frequency content and the distance between block releasing position and seismic station(source-receiver distance) were discussed. As a result, we found that the frequency content of rockfall focuses on 10-60 Hz and 80-90 Hz within a source-receiver distance of 200 m, and it is well correlated with impacted material and source-receiver distance. To evaluate the difference between earthquake and rockfall, 23 clear earthquake signals recorded in a seven month-long continuous seismic monitoring, carried out with the four seismic stations, were picked out, according to the Italian national earthquakes database(INGV). On these traces we performed the same analysis as in the artificial rockfall traces, and two parameters were defined to separate rockfall events from earthquake noise. The first one, the amplitude ratio, is related to the amplitude variation of rockfall between two stations and is greater than that of earthquakes, because of the higher attenuation occurring for rockfall events, which consists in high frequencies whereas for earthquakes it consists in low frequencies. The other parameter, the shape of waveform of signal trace, showed a significant difference between rockfall and earthquake and that could be a complementary feature to discriminate between both. This analysis of artificial rockfall is a first step helpful to understand the seismic characteristics of rockfall, and useful for rockfall seismic events classification in seismic monitoring of slope.

基于STFT和CNN-Attention的配电终端采集模块故障诊断研究

针对复杂工况运行环境下配电终端采集模块故障类型难以识别的问题,提出一种基于短时傅里叶变换(STFT)、卷积神经网络和注意力机制(CNN-Attention)的配电终端采集模块故障诊断方法。首先,分析配电终端采集模块不同故障类型会产生的对应故障数据,建立故障数据集。然后,基于STFT提取故障数据的故障时频特征以形成时频图,采用CNN-Attention模型对时频图进行故障诊断与匹配。算例分析表明,CNN-Attention的故障检测准确率为97.31%,相较于CNN和极限学习机(ELM)模型,故障诊断准确率分别提升了1.22%和4.4%。Attention机制能够有效解决CNN在特征提取时产生的冗余信息导致模型训练慢、难以收敛的问题。该研究实现了配电终端采集模块具体故障类型的准确识别,能为后续配电终端的运维提供参考。

Short-Term Sinusoidal Modeling of an Oriental Music Signal by Using CQT Transform

In this paper, we propose a method for characterizing a musical signal by extracting a set of harmonic descriptors reflecting the maximum information contained in this signal. We focus our study on a signal of oriental music characterized by its richness in tone that can be extended to 1/4 tone, taking into account the frequency and time characteristics of this type of music. To do so, the original signal is slotted and analyzed on a window of short duration. This signal is viewed as the result of a combined modulation of amplitude and frequency. For this result, we apply short-term the non-stationary sinusoidal modeling technique. In each segment, the signal is represented by a set of sinusoids characterized by their intrinsic parameters: amplitudes, frequencies and phases. The modeling approach adopted is closely related to the slot window;therefore great importance is devoted to the study and the choice of the kind of the window and its width. It must be of variable length in order to get better results in the practical implementation of our method. For this purpose, evaluation tests were carried out by synthesizing the signal from the estimated parameters. Interesting results have been identified concerning the comparison of the synthesized signal with the original signal.

Mathematical theory of signal analysis vs. complex analysis method of harmonic analysis

We present recent work of harmonic and signal analysis based on the complex Hardy space approach.