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.

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.

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.

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.

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.

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.

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.

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.

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.

基于DFT的频率敏感双分支Transformer多变量长时间序列预测方法

在进行多变量长时间序列预测时,仅利用时域分析通常无法充分捕捉长时间序列依赖,而这会导致信息利用率不足、预测精度不够高。因此,结合频域时域分析,提出一种基于离散傅里叶变换(DFT)的频率敏感双分支多变量长时间序列预测(FSDformer)方法。首先,通过DFT实现时间和频率的相互转换,从而将复杂的时间序列数据分解为结构简单的低频趋势项、中频季节项和高频余项3个分量;其次,采用双分支结构,针对中高频分量预测,应用Encoder-Decoder结构,设计了周期性增强注意力机制;针对低频趋势分量预测,采用多层感知机(MLP)结构;最后将中高频分量与低频分量预测结果相加,得到多变量长时间序列的最终预测结果。在2个数据集上把FSDformer与其他5个经典算法进行了对比分析,在Electricity数据集上,当历史序列长度为96,预测序列长度为336时,相较于Autoformer等对比算法,FSDformer的平均绝对误差(MAE)下降了11.5%~29.1%,均方误差(MSE)下降了20.9%~43.7%,达到了最优预测精度。实验结果表明,FSDformer能有效捕捉长时间序列的相关依赖,在提升预测精度和计算效率的同时,增强了模型预测的稳定性。

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。

基于高斯短时分数阶Fourier变换的海面微动目标检测方法

海上目标随海面颠簸导致姿态变化,引起回波功率调制效应,导致回波多普勒体现时变和非平稳特性.为此,本文将微多普勒理论应用于海杂波中弱目标检测,提出一种基于高斯短时分数阶Fourier变换(GSTFRFT)的海面微动目标检测方法.首先,建立海面目标的平动和三维转动回波模型;然后,基于海尖峰判别方法对回波信号进行数据筛选,改善信杂比,并采用GSTFRFT对微动信号进行增强处理,利用海面目标与海杂波的微动特征差异设计恒虚警检测方法;最后,通过GSTFRFT域滤波,提取信号的微动特征并得到瞬时频率.实测雷达数据仿真结果验证了算法的有效性,具有在强海杂波中检测微弱目标的能力.

基于自适应短时Chirp-Fourier变换的瞬时转速估计及应用

回转设备的瞬时转速是实现故障诊断的重要参数之一,也是提取表征设备运行状态其他关键参数的基本前提。针对传统短时傅里叶变换方法存在瞬时转速估计精度不足的问题,提出一种基于自适应短时Chirp-Fourier变换的瞬时转速估计方法。该方法建立调频参数的自适应选取策略,可根据信号的时频分布特性对信号进行自适应匹配分解,不但提高了计算效率,而且避免了谱图模糊问题,实现瞬时转速的精确估计。在此基础上结合信号解调技术,形成无键相幅值相位解调方法,并成功应用于变工况下的齿轮箱故障诊断。

基于分数阶Fourier变换的模糊函数及其在二次调频信号参数估计应用中的研究

作为处理非平稳信号的一种重要工具,模糊函数(ambiguity function,AF)已经被广泛应用于雷达信号处理、声纳技术等领域,并对线性调频信号信号的参数估计具有极好的处理能力。但对应用于众多领域的二次调频信号,模糊函数就显得无能为力了。作为Fourier变换的更广义形式,分数阶Fourier变换(Fractional Fourier trans-form)近年来受到了广泛关注。为解决二次调频信号的估计问题,本文研究了基于分数阶Fourier变换的模糊函数,给出了这种变换的一些新的重要性质,如共轭对称性、Moyal公式、时移性等,推导出了它与经典模糊函数、基于分数阶Fourier变换的Wigner分布、短时Fourier变换、小波变换等其他时频变换的关系。作为应用,最后本文用这种分数阶模糊函数来估计二次调频信号,应用实例的仿真结果表明了分数阶模糊函数在估计二次调频信号参数方面的可行性和有效性。

分数阶Fourier变换与时频滤波

针对LFM信号非平稳性,分析了在分数阶Fourier域对LFM信号作时频滤波的含义,给出了扫频滤波器在分数阶Fourier域的实现方法,并在此基础上推广得到分数阶Fourier域的一般乘法滤波器。通过对实测混响数据和LFM信号的分离效果仿真,发现分离前后信混比得到了较大提高,并且初始信混比越低,则提高效果越明显。

基于分数阶Fourier变换的反辐射导弹检测技术

针对反辐射导弹的检测问题,主要是消除载机信号的干扰。本文研究了单频信号和线性调频信号的分数阶Fourier变换模函数的时移特性。研究表明,单频信号和线性调频信号的FRFT模函数具有不同的时移特性。分数阶Fourier变换是线性变换,不存在交叉项,采用分数阶Fourier变换搜索匹配动目标信号,使其能量汇聚。根据以上特点本文提出了一种基于观测信号以及其时延信号的分数阶Fourier变换模之差的反辐射导弹检测方法。此方法可以有效的消除载机信号的干扰,并且对背景噪声幅度有一定的抑制作用。仿真结果表明,在低信噪比下能有效的检测出反辐射导弹。

应用短时Fourier变换对尾流光学信号分析

为弥补声探测尾流的不足,利用激光的独特优势,采用激光探测舰船尾流的方法.根据光信号的随机特性,确定了信号的分析方法短时Fourier变换.在信号的时频分布图中,表征了信号频率随时间的变化关系.通过对气泡幕光学信号时频图的分析,推测舰艇尾流的强弱.把这种探测手段应用于鱼雷自导,可提高鱼雷的作用距离、减小鱼雷半径,增强战斗力.

分数阶Fourier变换与新型时频滤波器设计

为了无失真地恢复复杂噪声环境中的非平稳信号,提出一种新型分数阶Fourier变换时频滤波器设计方法.该方法先利用Gabor变换得到信号在时频域的分布状况,然后用支撑向量机(SVM)分类算法结合图像分割得到分离时频图像上信号和噪声区域所需的最优分类线,最后用此最优分类线方程确定时频滤波器的阶数和传递函数.在信号和噪声时频域线性不可分的情况下,对SVM分类曲线进行了全局最小二乘分段线性拟合,然后根据拟合生成的方程构造并行多阶滤波器组.为满足实际应用中实时性的要求,对算法的计算复杂度进行了优化.计算机仿真结果验证了该方法的有效性.