Mid-infrared Optical Frequency Comb-based Fourier Transform Spectrometer for Broadband Molecular Spectroscopy

Optical frequency combbased Fourier transform spectroscopy has the features of broad spectral bandwidth,high sensitivity,andmultiplexed trace gas detection,which has valuable application potential in the fields of precision spectroscopy and trace gas detection.Here,we report the development of a mid-infrared Fourier transform spectrometer based on an optical frequency comb combined with a Herriott-type multipass cell.Using this instrument,the broadband absorption spectra of several important molecules,including methane,acetylene,water molecules and nitrous oxide,are measured by near real-time data acquisition in the 2800-3500 cm^(-1)spectral region.The achieved minimum detectable absorption of the instrument is 4.4×10^(-8)cm^(-1)·Hz^(-1/2)per spectral element.Broadband spectra of H_(2)0 are fited using the Voigt profile multispectral fitting technique and the consistency of the concentration inversion is 1%.Our system also enables precise spectroscopic measurements,and it allows the determination of the spectral line positions and upper state constants of N_(2)O in the(0002)-(1000)band,with results in good agreement with those reported by Toth[Appl.Opt.30,5289(1991)].

Eigenvalue spectrum analysis for temporal signals of Kerr optical frequency combs based on nonlinear Fourier transform

Based on the nonlinear Schr?dinger equation(NLSE) with damping, detuning, and driving terms describing the evolution of signals in a Kerr microresonator, we apply periodic nonlinear Fourier transform(NFT) to the study of signals during the generation of the Kerr optical frequency combs(OFCs). We find that the signals in different states, including the Turing pattern, the chaos, the single soliton state, and the multi-solitons state, can be distinguished according to different distributions of the eigenvalue spectrum. Specially, the eigenvalue spectrum of the single soliton pulse is composed of a pair of conjugate symmetric discrete eigenvalues and the quasi-continuous eigenvalue spectrum with eye-like structure.Moreover, we have successfully demonstrated that the number of discrete eigenvalue pairs in the eigenvalue spectrum corresponds to the number of solitons formed in a round-trip time inside the Kerr microresonator. This work shows that some characteristics of the time-domain signal can be well reflected in the nonlinear domain.

Enhanced Wideband Frequency Estimation via FFT: Leveraging Polynomial Interpolation and Array Indexing

Accurate frequency estimation in a wideband digital receiver using the FFT algorithm encounters challenges, such as spectral leakage resulting from the FFT’s assumption of signal periodicity. High-resolution FFTs pose computational demands, and estimating non-integer multiples of frequency resolution proves exceptionally challenging. This paper introduces two novel methods for enhanced frequency precision: polynomial interpolation and array indexing, comparing their results with super-resolution and scalloping loss. Simulation results demonstrate the effectiveness of the proposed methods in contemporary radar systems, with array indexing providing the best frequency estimation despite utilizing maximum hardware resources. The paper demonstrates a trade-off between accurate frequency estimation and hardware resources when comparing polynomial interpolation and array indexing.

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.

Quasi-LFM radar waveform recognition based on fractional Fourier transform and time-frequency analysis

Recent advances in electronics have increased the complexity of radar signal modulation.The quasi-linear frequency modulation(quasi-LFM)radar waveforms(LFM,Frank code,P1−P4 code)have similar time-frequency distributions,and it is difficult to identify such signals using traditional time-frequency analysis methods.To solve this problem,this paper proposes an algorithm for automatic recognition of quasi-LFM radar waveforms based on fractional Fourier transform and time-frequency analysis.First of all,fractional Fourier transform and the Wigner-Ville distribution(WVD)are used to determine the number of main ridgelines and the tilt angle of the target component in WVD.Next,the standard deviation of the target component's width in the signal's WVD is calculated.Finally,an assembled classifier using neural network is built to recognize different waveforms by automatically combining the three features.Simulation results show that the overall recognition rate of the proposed algorithm reaches 94.17%under 0 dB.When the training data set and the test data set are mixed with noise,the recognition rate reaches 89.93%.The best recognition accuracy is achieved when the size of the training set is taken as 400.The algorithm complexity can meet the requirements of real-time recognition.

Comparison of computation time for estimation of dominant frequency of atrial electrograms: Fast fourier transform, blackman tukey, autoregressive and multiple signal classification

Dominant frequency (DF) of electrophysiological data is an effective approach to estimate the activation rate during Atrial Fibrillation (AF) and it is important to understand the pathophysiology of AF and to help select candidate sites for ablation. Frequency analysis is used to find and track DF. It is important to minimize the catheter insertion time in the atria as it contributes to the risk for the patients during this procedure, so DF estimation needs to be obtained as quickly as possible. A comparison of computation tim- es taken for spectrum estimation analysis is presented in this paper. Fast Fourier Transform (FFT), Blackman-Tukey (BT), Autoregressive (AR) and Multiple Signal Classification (MUSIC) methods are used to obtain the frequency spectrum of the signals. The time to produce DF was measured for each method. The method which takes the shortest time for analysis is selected for real time application purpose.

A WEIGHTED GENERAL DISCRETE FOURIER TRANSFORM FOR THE FREQUENCY-DOMAIN BLIND SOURCE SEPARATION OF CONVOLUTIVE MIXTURES

This letter deals with the frequency domain Blind Source Separation of Convolutive Mixtures (CMBSS). From the frequency representation of the "overlap and save", a Weighted General Discrete Fourier Transform (WGDFT) is derived to replace the traditional Discrete Fourier Transform (DFT). The mixing matrix on each frequency bin could be estimated more precisely from WGDFT coefficients than from DFT coefficients, which improves separation performance. Simulation results verify the validity of WGDFT for frequency domain blind source separation of convolutive mixtures.

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.

Frequency spectrum analysis on micro-seismic signal of rock bursts induced by dynamic disturbance

Blasting and breaking of hard roof are main inducing causes of rock bursts in coal mines with danger of rock burst,and it is important to find out the frequency spectrum distribution laws of these dynamic stress waves and rock burst waves for researching the mechanism of rock burst.In this paper,Fourier transform as a micro-seismic signal conversion method of amplitude-time character to amplitude-frequency character is used to analyze the frequency spectrum characters of micro-seismic signal of blasting,hard roof breaking and rock bursts induced by the dynamic disturbance in order to find out the difference and relativity of different signals.The results indicate that blasting and breaking of hard roof are high frequency signals,and the peak values of dominant frequency of the signals are single.However,the results indicate that the rock bursts induced by the dynamic disturbance are low frequency signals,and there are two obvious peak values in the amplitude-frequency curve witch shows that the signals of rock bursts are superposition of low frequency signals and high frequency signals.The research conclusions prove that dynamic disturbance is necessary condition for rock bursts,and the conclusions provide a new way to research the mechanism of rock bursts.

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.

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。

A Contribution to the Analysis of Frequency Response and Impedance Measurements to Evaluation and Diagnosis of Power Transformers

This paper has an objective to show a developed quantitative criterion,based in two mathematical variables that explicit the deviation degree of a normal situation,applying simultaneously data from terminal impedances and frequency response.Based in more than 100-measured equipment,of different applications(step-up transformer,transmission transformer,etc.,),for a period of 10 years,the work presents some examples of practical application of this methodology in Brazilian Electrical System.

Generation of artificial earthquakes for matching target response unsmooth spectrum via wavelet package transform

The seismic records of target response spectrum used in the time-history analysis should be allowed to meet the norms. However, the previous fitting methods of target spectrum are mostly for the situations that the target spectrum is a smooth curve. In many cases, it needs to match unsmooth target spectrum for single determined response spectrum. An adjustment of time history via wavelet packet transform was presented, which is able to fit unsmooth target spectrum. It was found that there is a certain bias between the band center frequency of the component of seismic record after wavelet packet decomposition and the peak frequency of response spectra of wavelet packet components. For this reason, five strategies were presented to select iteration points, and the effects of the five strategies were compared with two calculation examples. It was turned out that the peak frequency of the response spectrum of wavelet packet component can lead to good fitting effect when it is selected as the iteration point. In the iteration process, it shows great promise in fitting non-smooth target spectrum and has a trend of converge.

基于插值fast Fourier transform谐波分析的桥梁状态评估方法

桥梁的环境振动信号包含了各种环境噪声成分,如何从噪声影响中提取桥梁的真实自振频率,并进行桥梁状态评估是亟待解决的问题.本文对环境激励下的大跨桥梁响应信号进行了研究,根据环境激励在低频段近于平白噪声以及线性系统在环境激励下,各输出点测量信号之间相关函数与结构的脉冲响应函数具有相同的数学表达式——均是主频正弦函数的叠加这一特点,建立了插值fast Fourier transform(FFT)频谱校正技术分析各测点相关函数的方法.该方法能在白噪声背景下精确提取桥梁振动频率、幅度和相位等模态参数,简单实用,不仅能在线识别参数,而且对桥梁单点激励和多点同时激励均适用.将校正后的主频与三维有限元计算结果相对比,能对桥梁结构整体状态和工作性能进行评估.最后,一座实桥动力试验和计算结果证明了该方法的能有效用于运营条件下桥梁状态的评估.

Chirp-Rate Resolution of Fractional Fourier Transform in Multi-component LFM Signal

Distinguishing close chirp-rates of different linear frequency modulation （LFM） signals under concentrated and complicated signal environment was studied. Firstly, detection and parameter estimation of multi-component LFM signal were used by discrete fast fractional Fourier transform （FrFT）. Then the expression of chirp-rate resolution in fractional Fourier domain （FrFD） was deduced from discrete normalize time-frequency distribution, when multi-component LFM signal had only one center frequency. Furthermore, the detail influence of the sampling time, sampling frequency and chirp-rate upon the resolution was analyzed by partial differential equation. Simulation results and analysis indicate that increasing the sampling time can enhance the resolution, but the influence of the sampling frequency can he omitted. What＇s more, in multi-component LFM signal, the chirp-rate resolution of FrFT is no less than a minimal value, and it mainly dependent on the biggest value of chirp-rates, with which it has an approximately positive exponential relationship.

Joint timing synchronization and frequency offset acquisition algorithm for MIMO OFDM systems

For multiple-input multiple-output （MIMO） orthogonal frequency division multiplexing （OFDM） systems, a joint timing synchronization and frequency offset acquisition algorithm based on fractional Fourier transform （FRFT） is proposed. The linear frequency modulation signals superimposed on the data signals are used as the training signals. By performing FRFT on the received signals and searching the peak value of the FRFT results, the receiver can realize timing synchronization and frequency offset acquisition simultaneously. Compared with the existing methods, the proposed algorithm can provide better timing synchronization performance and larger frequency offset acquisition range even under multi-path channels with low signal to noise ratio. Theoretical analysis and simulation results prove this point.

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。

Output only modal identification and structural damage detection using time frequency & wavelet techniques

The primary objective of this paper is to develop output only modal identification and structural damage detection. Identification of multi-degree of freedom （MDOF） linear time invariant （LTI） and linear time variant （LTV--due to damage） systems based on Time-frequency （TF） techniques--such as short-time Fourier transform （STFT）, empirical mode decomposition （EMD）, and wavelets--is proposed. STFT, EMD, and wavelet methods developed to date are reviewed in detail. In addition a Hilbert transform （HT） approach to determine frequency and damping is also presented. In this paper, STFT, EMD, HT and wavelet techniques are developed for decomposition of free vibration response of MDOF systems into their modal components. Once the modal components are obtained, each one is processed using Hilbert transform to obtain the modal frequency and damping ratios. In addition, the ratio of modal components at different degrees of freedom facilitate determination of mode shape. In cases with output only modal identification using ambient/random response, the random decrement technique is used to obtain free vibration response. The advantage of TF techniques is that they arc signal based; hence, can be used for output only modal identification. A three degree of freedom 1：10 scale model test structure is used to validate the proposed output only modal identification techniques based on STFT, EMD, HT, wavelets. Both measured free vibration and forced vibration （white noise） response are considered. The secondary objective of this paper is to show the relative ease with which the TF techniques can be used for modal identification and their potential for real world applications where output only identification is essential. Recorded ambient vibration data processed using techniques such as the random decrement technique can be used to obtain the free vibration response, so that further processing using TF based modal identification can be performed.

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.