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.

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.

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(STFT)and the inverse short time Fourier transform(ISTFT)when the dual-orthogonal polarimetric frequency-modulated continuous 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 STFT.The simulative results show that the cross-channel interference is efficiently suppressed by the proposed method.The comparison between the proposed method and the rejection method verifies the improved performance of the proposed method.

Comparing the Time-Deformation Method with the Fractional Fourier Transform in Filtering Non-Stationary Processes

The classical linear filter is able to extract components from multi-component stochastic processes where the frequencies of components do not overlap over time, but fail for those processes where the frequencies overlap over time. In this paper, we discuss two filtering methods for non-stationary processes: the G-filtering method and the Fractional Fourier transform (FrFT) method. The FrFT method is mainly designed for linear chirp signals where the frequency is linearly changing with time. The G-filter can be used to filter signals with wide range of frequency behaviors such as linear chirps, quadratic chirps and other type of chirp signals with strong time-varying frequency behavior. If frequencies of the components can be approximated or separated by a straight line or a polynomial curve, the G-filter can successfully extract components from the original series. We show that the G-filter is applicable to a wider variety of filtering applications than methods such as the FrFT which require data of a specified frequency behavior.

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.

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。

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.

Detecting Periodicity Associated with the Alpha-Helix Structure Using Fourier Transform

Alpha helix is a common type of secondary structure in the protein structure that consists of repeating helical turns. Patterns in the protein sequences that cause this repetitive pattern in the structure have long been sought. We used the discrete Fourier transform (DFT) to detect the periodicity signals correlated to the helical structure. We studied the distribution of multiple properties along the protein sequence, and found a property that showed strong periodicity correlated with the helical structure. Using a short-time Fourier transform (STFT) method, we investigated the amplitude of the periodical signals at each amino acid position. The results show that residues in the helix structure tend to display higher amplitudes than residues outside of the helices. This tendency is dramatically strengthen when sequence profiles obtained from multiple alignment were used to detect the periodicity. A simple method that predicted helices based on the amplitude yielded overall true positive rate (TPR) of 63%, 49% sensitivity, 72% specificity, and 0.22 Matthews Correlation Coefficient (MCC). The performance seemed to depend on the length of helices that the proteins had.

Novel uncertainty relations associated with fractional Fourier transform

In this paper the relations between two spreads, between two group delays, and between one spread and one group delay in fractional Fourier transform （FRFT） domains, are presented and three theorems on the uncertainty principle in FRFT domains are also developed. Theorem 1 gives the bounds of two spreads in two FRFT domains. Theorem 2 shows the uncertainty relation between two group delays in two FRFT domains. Theorem 3 presents the crossed uncertainty relation between one group delay and one spread in two FRFT domains. The novelty of their results lies in connecting the products of different physical measures and giving their physical interpretations. The existing uncertainty principle in the FRFT domain is only a special ease of theorem 1, and the conventional uncertainty principle in time-frequency domains is a special case of their results. Therefore, three theorems develop the relations of two spreads in time-frequency domains into the relations between two spreads, between two group delays, and between one spread and one group delay in FRFT domains.

An HHT-based method to eliminate short-time strong disturbance from measured signals of bridge

According to the characteristic that Hilbert-Huang transform (HHT) can detect abnormity in signals, an HHT-based method to eliminate short-time strong disturbance was proposed. The signal with short-time strong disturbance was decomposed into a series of intrinsic mode functions (IMFs) and a residue by the empirical mode decomposition (EMD). The instantaneous amplitudes and frequencies of each IMF were calculated. And at abnormal section, instantaneous amplitudes and frequencies were fitted according to the data at normal section, replacing the fitted data for the original ones. A new set of IMFs was reconstructed by using the processed instantaneous amplitudes and frequencies. For the residue, abnormal fluctuations could be directly eliminated. And a new signal with the short-time strong disturbance eliminated was reconstructed by superposing all the new IMFs and the residue. The numerical simulation shows that there is a good correlation between the reconstructed signal and the undisturbed signal. The correlation coefficient is equal to 0.999 1. The processing results of the measured strain signal of a bridge with short-time strong disturbance verify the practicability of the method.

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.

The numerical method of Fourier eigen transform and its application in seismicity analysis

This paper′s aim is to study the numerical method of Fourier eigen transform. The characteristics of eigen bases, the Hermite function are analyzed. And a valuable result of eigen coefficients a n by means of Gauss Hermite integral is gotten. Through talking about amplitude frequency peculiarities of basic signals, we prove that the method applied in this paper possesses higher precision and smaller computation quantity. Finally, we conducted quasi real time FET analysis in seismicity, tentatively probed into the feasibility of FET in seismic prediction, obtained something of practical value.

基于Kaiser窗的分数阶Fourier变换与时频分析

分数阶Fourier变换作为传统Fourier变换的推广,与传统Fourier变换分析平稳信号类似,在实现对非平稳信号的时频分析过程中往往出现同样的频谱泄漏问题。为了提高分数阶Fourier变换与时频分析的精度,依据Kaiser窗可自由选择主瓣和旁瓣宽度的特性,提出一种基于Kaiser窗的分数阶Fourier变换算法,论述了Kaiser窗在分数阶Fourier变换中的作用原理,从理论上推导出一般信号基于Kaiser窗的分数阶Fourier变换解析时频表达式以及特性,最终得到非平稳信号的时频分布与时变结构参数识别算法。通过任意线性调频信号的仿真算例以及非平稳激励三层框架结构振动台试验,对结构进行瞬时频率识别和算法的验证。结果表明,瞬时频率识别值与理论值和试验结果吻合良好,Kaiser窗可以提高分数阶Fourier变换算法时频分析的精度,体现出该方法有一定的鲁棒性。

Minimal Generalized Time-Bandwidth Product Method for Estimating the Optimum Fractional Fourier Order

A minimal generalized time-bandwidth product-based coarse-to-fine strategy is proposed with one novel ideas highlighted: adopting a coarse-to-fine strategy to speed up the searching process. The simulation results on synthetic and real signals show the validity of the proposed method.

基于短时傅里叶变换和深度网络的模块化多电平换流器子模块IGBT开路故障诊断

针对现有模块化多电平换流器(MMC)子模块故障诊断过程中所需传感器较多、测量干扰较大等问题,提出一种基于深度学习的MMC子模块IGBT开路故障诊断方法。在对MMC子模块开路故障特征进行分析的基础上,利用短时傅里叶变换(STFT)提取桥臂电压信号的谐波分量信息作为故障诊断所需的特征参数。将所得到的特征参数进行处理后构建故障诊断样本,在通过深度置信网络实现故障类型快速检测的基础上,依据不同故障类型,构建多个基于卷积神经网络的故障定位网络,进而实现开路故障的检测与定位。通过129电平的MMC系统仿真模型和降功率的MMC实验系统搭建,对该文所提方法进行了验证。仿真和实验结果表明,所提故障诊断方法可以在减少传感器数量的基础上实现子模块开路故障的诊断,提高系统的可靠性。

融合CNN和ViT的声信号轴承故障诊断方法

针对轴承故障诊断任务数据量少、故障信号非平稳等特点,提出一种短时傅里叶变换、卷积神经网络和视觉转换器相结合的轴承故障诊断方法。首先,利用短时傅里叶变换将原始声信号转换为包含时序信息和频率信息的时频图像。其次,将时频图像作为卷积神经网络的输入,用于隐式提取图像的深层特征,其输出作为视觉转换器的输入。视觉转换器用于提取信号的时间序列信息。并在输出层利用Softmax函数实现故障模式的识别。试验结果表明,该方法对于轴承故障诊断准确率较高。为了更好解释和优化提出的轴承故障诊断方法,利用t-分布领域嵌入算法对分类特征进行了可视化展示。

基于卷积和长短期记忆网络的地浸开采铀浓度预测研究

文章通过集成经验模态分解(Empirical Mode Decomposition,EMD)、卷积神经网络(Convolutional Neural Networks,CNN)、长短期记忆网络(Long Short-Term Memory,LSTM)、傅里叶变换,提出了一种新型地浸单元浸出液铀浓度预测方法。该方法将浸出液铀浓度监测值时间序列使用EMD进行分解,分解为趋势项、周期项和随机项。通过构建CNN+LSTM网络,并结合傅里叶变换和多项式拟合对铀浓度趋势项、周期项和随机项进行预测,3者预测之和作为铀浓度预测结果。实证结果表明:EMD能够有效分解铀浓度时间序列,模型拟合度比未进行EMD分解的模型提升超50%;基于EMD、CNN+LSTM和傅里叶变换的集成方法预测精度良好,预测的平均绝对百分比误差(Mean Absolute Percentage Error,MAPE)为0.348,与LSTM、反向传播(Back Propagation,BP)和门控循环网络(Gate Recurrent Unit,GRU)等模型相比最高提升超80%。文章提出的集成方法能够准确预测浸采单元铀浓度变化,解决了原有方法和模型无法对非线性、非平稳铀浓度序列进行准确预测的问题,从而为地浸矿山生产规划提供技术支持,并有助于提升中国铀矿山的数字化、信息化程度。

高速铁路0.01~1 m波段高低轨道不平顺特性分析

随着我国高速铁路发展规模的不断扩大及运营速度的不断提升,轨道短波不平顺引起的振动与噪声问题日益严重。深入研究高速铁路短波不平顺的时域、频域与时频域特征,对精准掌握高速铁路轨道短波平顺状态及其引起的车-轨系统振动、伤损等一系列问题具有重要的参考价值。以某高速铁路实测0.01~1 m波段轨面高低不平顺数据为研究对象,经过数据预处理剔除异常值并消除趋势项后,对实测不平顺数据进行时域分析,得到该高铁线路短波不平顺数据的统计与分布特性。采用平均周期图法计算该高铁线路轨道短波不平顺功率谱密度,应用非线性最小二乘拟合优化算法进行拟合,提出高速铁路轨道短波不平顺谱。从时频域角度对该段数据进行经验模态分解与希尔伯特变换,分析该高铁线路短波不平顺的希尔伯特谱与边际谱。研究结果表明:该高铁线路轨道短波不平顺数据各统计量幅值都较小,且近似服从正态分布;该高铁线路轨道短波不平顺功率谱密度存在与钢轨波磨有关的多个周期性成分,提出的高速铁路短波不平顺谱函数能够很好地对实测功率谱密度进行拟合,且拟合效果优于经典的SATO建议的短波谱与50 kg/m钢轨的短波谱;对该高铁线路轨道可能存在的短波病害进行识别与定位,时频域分析的方法可以较好地应用于高速铁路轨道平顺性的分析与日常的管理维护。