Fractional Fourier domain hopped communication method based on chirp modulation for underwater acoustic channels

To improve the data rate of underwater acoustic frequency-hopped communications, frequency hopping is applied to different orders of fractional Fourier domain (FrFD), to enable non-intrusive, bandwidth-limited acoustic communications. An FrFD frequency-hopped communication method based on chirp modulation, namely multiple chirp shift keying-FrFD hopping (MCSK-FrFDH), is proposed for underwater acoustic channels. Validated by both simulations and experimental results, this method can reach a bandwidth efficiency twice more than conventional frequency-hopped methods with the same data rate and anti-multipath capability, suggesting that the proposed method achieves a better performance than the traditional frequency hopped communication in underwater acoustic communication channels. Results also show that in practical scenarios, the MCSK-FrFDH system with longer symbol length performs better at the low signal-to-noise ratio (SNR), while the system with larger frequency sweeping range performs better at a high SNR.

Design and simulation of digital channelized receivers in fractional Fourier domain

An approach is proposed to realize a digital channelized receiver in the fractional Fourier domain （FRFD） for signal intercept applications. The presented architecture can be considered as a generalization of that in the traditional Fourier domain. Since the linear frequency modulation （LFM） signal has a good energy concentration in the FRFD, by choosing an appropriate fractional Fourier transform （FRFT） order, the presented architecture can concentrate the broadband LFM signal into only one sub-channel and that will prevent it from crossing several sub-channels. Thus the performance of the signal detection and parameter estimation after the sub-channel output will be improved significantly. The computational complexity is reduced enormously due to the implementation of the polyphase filter bank decomposition, thus the proposed architecture can be realized as efficiently as in the Fourier domain. The related simulation results are presented to verify the validity of the theories and methods involved in this paper.

Analysis of fMRI Single Subject Data in the Fourier Domain Acquired Using a Multiple Input Stimulus Experimental Design

Analysis of functional MRI (fMRI) blood oxygenation level dependent (BOLD) data is typically carried out in the time domain where the data has a high temporal correlation. These analyses usually employ parametric models of the hemodynamic response function (HRF) where either pre-whitening of the data is attempted or autoregressive (AR) models are employed to model the noise. Statistical analysis then proceeds via regression of the convolution of the HRF with the input stimuli. This approach has limitations when considering that the time series collected are embedded in a brain image in which the AR model order may vary and pre-whitening techniques may be insufficient for handling faster sampling times. However fMRI data can be analyzed in the Fourier domain where the assumptions made as to the structure of the noise can be less restrictive and hypothesis tests are straightforward for single subject analysis, especially useful in a clinical setting. This allows for experiments that can have both fast temporal sampling and event-related designs where stimuli can be closely spaced in time. Equally important, statistical analysis in the Fourier domain focuses on hypothesis tests based on nonparametric estimates of the hemodynamic transfer function (HRF in the frequency domain). This is especially important for experimental designs involving multiple states (drug or stimulus induced) that may alter the form of the response function. In this context a univariate general linear model in the Fourier domain has been applied to analyze BOLD data sampled at a rate of 400 ms from an experiment that used a two-way ANOVA design for the deterministic stimulus inputs with inter-stimulus time intervals chosen from Poisson distributions of equal intensity.

Automatic detection and assessment of crack development in ultra-high performance concrete in the spatial and Fourier domains

Automatic detection and assessment of surface cracks are beneficial for understanding the mechanical performance of ultra-high performance concrete(UHPC).This study detects crack evolution using a novel dynamic mode decomposition(DMD)method.In this method,the sparse matrix‘determined’from images is used to reconstruct the foreground that contains cracks,and the global threshold method is adopted to extract the crack patterns.The application of the DMD method to the three-point bending test demonstrates the efficiency in inspecting cracks with high accuracy.Accordingly,the geometric features,including the area and its projection in two major directions,are evaluated over time.The relationship between the geometric properties of cracks and load-displacement curves of UHPC is discussed.Due to the irregular shape of cracks in the spatial domain,the cracks are then transformed into the Fourier domain to assess their development.Results indicate that crack patterns in the Fourier domain exhibit a distinct concentration around a central position.Moreover,the power spectral density of cracks exhibits an increasing trend over time.The investigation into crack evolution in both the spatial and Fourier domains contributes significantly to elucidating the mechanical behavior of UHPC.

Fractional Fourier domain analysis of decimation and interpolation

The sampling rate conversion is always used in order to decrease computational amount and storage load in a system. The fractional Fourier transform （FRFT） is a powerful tool for the analysis of nonstationary signals, especially, chirp-like signal. Thus, it has become an active area in the signal processing community, with many applications of radar, communication, electronic warfare, and information security. Therefore, it is necessary for us to generalize the theorem for Fourier domain analysis of decimation and interpolation. Firstly, this paper defines the digital frequency in the fractional Fourier domain （FRFD） through the sampling theorems with FRFT. Secondly, FRFD analysis of decimation and interpolation is proposed in this paper with digital frequency in FRFD followed by the studies of interpolation filter and decimation filter in FRFD. Using these results, FRFD analysis of the sampling rate conversion by a rational factor is illustrated. The noble identities of decimation and interpolation in FRFD are then deduced using previous results and the fractional convolution theorem. The proposed theorems in this study are the bases for the generalizations of the multirate signal processing in FRFD, which can advance the filter banks theorems in FRFD. Finally, the theorems introduced in this paper are validated by simulations.

Optical vortex copier and regenerator in the Fourier domain

The generation and manipulation of optical vortices are of fundamental importance in a variety of promising applications. Here, we develop a nonlinear optical paradigm to implement self-and cross-convolution of optical vortex arrays, demonstrating the features of a vortex copier and regenerator. We use a phase-only spatial light modulator to prepare the 1064 nm invisible fundamental light to carry special optical vortex arrays and use a potassium titanyl phosphate crystal to perform type Ⅱ second-harmonic generation in the Fourier domain to achieve 532 nm visible structured vortices. Based on pure cross-convolution, we succeed in copying arbitrary-order single vortices as well as their superposition states onto a prearranged array of fundamental Gaussian spots. Also, based on the simultaneous effect of self-and cross-convolutions, we can expand the initial vortex lattices to regenerate more vortices carrying various higher topological charges. Our presented method of realizing an optical vortex copier and regenerator could find direct applications in optical manipulation, optical imaging, optical communication, and quantum information processing with structured vortex arrays.

Comparison of Ziemer FEMTO LDV "Classic" and " Crystal Line" femtosecond laser flap quality by Fourierdomain optical coherence tomography

AIM:To compare the regularity and accuracy of laser in situ keratomileusis(LASIK) flaps created by the Ziemer FEMTO LDV 'Classic'(Ziemer 'Classic') and Ziemer FEMTO LDV Crystal Line femtosecond laser(Ziemer Crystal Line). METHODS:Fourier-domain optical coherence tomography(RTVue OCT) was used to measure the morphology of 200 LASIK flaps of 100 consecutive patients created with the Ziemer Classic(100 flaps) or the Ziemer Crystal Line(100 flaps) at one week postoperatively.Flap thickness was evaluated at 36 specified measurement points on each flap.For all procedures with both lasers,the nominal flap thickness was 110μm.RESULTS:The mean flap thickness of the Ziemer Crystal Line group(102.49±2.68μm) was thinner than that of the Ziemer Classic group(107.65±5.09μm)(P【0.01).Average thickness of all flaps was uniform within 4μm at all measurement points.The flaps in the Ziemer Crystal Line group were more regular than those in the Ziemer Classic group when measured from the center to the periphery.The maximum deviation from the nominal 110μm of 36 measurements was 8μm in the Ziemer Classic group,while in the Ziemer Crystal Line group it was 9μm.Within the 3 600 measurements on the 100 eyes,differences greater than 20μm were observed 0.14% in the Ziemer Classic group,and 0.04% in the Ziemer Crystal Line group. CONCLUSION:The flaps created with the Ziemer FEMTO LDV Crystal Line femtosecond laser are more uniform and thinner than those created by the Ziemer FEMTO LDV Classic femtosecond laser.

Fourier analysis of Schwarz domain decomposition methods for the biharmonic equation

Schwarz methods are an important type of domain decomposition methods. Using the Fourier transform, we derive error propagation matrices and their spectral radii of the classical Schwarz alternating method and the additive Schwarz method for the biharmonic equation in this paper. We prove the convergence of the Schwarz methods from a new point of view, and provide detailed information about the convergence speeds and their dependence on the overlapping size of subdomains. The obtained results are independent of any unknown constant and discretization method, showing that the Schwarz alternating method converges twice as quickly as the additive Schwarz method.

INTERFERENCE MITIGATING BASED ON FRACTIONAL FOURIER TRANSFORM IN TRANSFORM DOMAIN COMMUNICATION SYSTEM

The method of FRactional Fourier Transform (FRFT) is introduced to Transform Domain Communication System (TDCS) for signal transforming in the paper after theoretical analysis. The method yields optimal Basis Function (BF) by FRFT with optimal transform angle. The TDCS using the proposed method has wider usable spectrum, stronger robustness and better ability of anti non-stationary jamming than using usual methods, such as Fourier Transform (FT), Auto Regressive (AR), Wavelet Transform (WT), etc. The main simulation results are as follows. First, the Bit Error Rate (BER) Pb is close to theoretical bound of no jamming no matter in single tone or in linear chirp interference. Second, the interference-to-signal ratio J /E is at least 12dB more than that of Direct Spread Spectrum System (DSSS) under the same BER if the spectrum hopping-to-signal ratio is 1:20 in chirp plus hopping interfering. Third, the Eb /N 0(when estimation difference is 90% between trans- mitter and receiver) is about 3.5dB or about 0.5dB (when estimation difference is 10% between transmitter and receiver) more than that of theoretical result when no estimation difference un-der Pb=10-2.

任意起伏地形下重力异常三维正演及并行计算

为了进一步提高空间-波数域三维重力异常正演算法的适用范围和计算效率,本文采用任意傅里叶变换算法实现了空间-波数域三维重力异常正演,且在NVIDIA CUDA平台上进行CPU-GPU并行加速.任意傅里叶变换算法的基本思想是将二维傅里叶变换转化为两个一维傅里叶变换,一维傅里叶变换积分离散为多个单元积分累加和,离散单元中原函数采用二次插值形函数拟合,求出单元积分的解析表达式.相比现有的傅里叶变换算法,新方法具有采样灵活、积分精度高、计算速度快和傅里叶变换的截断效应小等优势.利用空间-波数域算法的高度并行性,采用CPU并行求解常微分方程,GPU并行计算任意傅里叶变换,实现了CPU-GPU并行加速方案,进一步提升了本文算法效率.利用常密度模型,对比数值解和解析解,结果表明本文算法正确;利用变密度模型对比了任意傅里叶变换算法与高斯快速傅里叶变换算法的计算效率与精度,在相近的数值精度下,本文算法波数选取少,效率高;测试CPU-GPU并行效果,结果表明相比CPU串行算法,CPU-GPU并行算法的计算效率大大提升,千万数量级节点数模型正演仅耗时数秒.最后利用实际地形数据进行三维重力异常场数值模拟,证明了新方法的高效性与实用性,对实现大规模复杂条件下重力异常精细化反演成像与综合解释有重要意义.

基于傅里叶变换的振动切削刀具振幅测量方法

振动切削在当今时代的制造业越来越普遍,而振动切削的关键参数刀具振幅又因能量损失而无法避免,为了能保证良好的切削效果,需要知道实际切削过程中的刀具振幅。目前普遍使用激光测振仪测量振动切削的刀具振幅,但设备较为昂贵。为了实现对振动切削刀具振幅经济有效的测量,提出了一种利用加速度传感器测量振动切削刀具振幅的测量方法。利用加速度传感器获得刀具振动方向的加速度,通过傅里叶变换和频域二次积分以及傅里叶反变换,将加速度信号积分为振幅信号。根据实验结果可知,本测量系统的测量误差低于0.8%。

Laplace-Fourier域多尺度高效全波形反演方法

针对常规Laplace-Fourier域全波形反演计算量大、耗时长的问题,提出一种多尺度高效Laplace-Fourier域全波形反演方法,并针对Marmousi和Overthrust模型进行数值模拟。Laplace-Fourier域多尺度高效全波形反演方法对于不同频率点选择大小不同的网格,并且根据Laplace衰减常数选择不同的模型计算区域深度,既不影响反演精度,又显著提高反演计算效率,同时由于反演网格数减少,反演稳定性也有所提高。Marmousi和Overthrust模型的反演结果验证了算法的有效性,同时在缺失低频信息时,Laplace-Fourier域多尺度高效全波形反演结果仍较好。

分数阶Fourier域谱估计及其应用

本文定义了随机信号的分数阶功率谱和分数阶相关函数,得到了分数阶功率谱和分数阶相关函数的关系.在此基础上,推导出分数阶Fourier域滤波器的输入输出分数阶功率谱的关系.仿真结果表明,分数阶功率谱估计可以用于chirp信号的检测和估计,以及分数阶系统辨识.

离散色散光域傅里叶变换的延时和带宽扩展研究

光域傅里叶变换为射频频谱分析提供了一种新的解决方案。光域傅里叶变换主要受限于大的二阶色散的获得,而离散傅里叶变换只需要控制离散点的相位,理论上可以解决大色散的获得问题。文章利用光纤环作为离散色散器件,用线性调频信号作为待测信号,进行了光域离散傅里叶变换的研究。该系统是一个快速傅里叶变换系统,每次变换用时约2.07ns。用示波器观测线性调频信号变换前与变换后的波形延迟,可以测出该系统的变换延时,约为100ns,其延时大小主要取决于系统中的光纤长度。该系统可以实现对信号的不间断处理。为了扩展系统的瞬时带宽,对片上集成光微环组方案的可实现性进行了分析。

无监督域适应迁移学习在旋转机械故障诊断中的应用

故障诊断在旋转机械领域具有重要的意义,而深度学习和迁移学习的发展为提高故障诊断的准确性和鲁棒性提供了新的途径。针对旋转机械故障诊断问题,提出了一种基于深度对抗神经网络(domain-adversarial neural network, DANN)和多核最大平均差异(multiple kernel maximum mean discrepancy, MK-MMD)的无监督域适应迁移学习方法。首先,收集了源工况和目标工况下的振动信号数据并通过快速傅里叶变换(fast Fourier transform, FFT)转化为频域信号。然后,构建了一个ResNeXt-50特征提取器,并使用DANN和MK-MMD方法进行特征映射和域适应,从而实现源工况到目标工况的迁移学习。试验结果表明,该方法能提高对故障特征的识别精度,且在不同工况下的迁移试验中具有更好的鲁棒性。

离散分数阶Fourier变换的阶数分解算法

分数阶Fourier变换在科学计算和工程中有广泛应用前景,但现有的离散分数阶Fourier变换(DFRFT)缺乏有效的快速算法。本文给出了一种采用阶数分解的DFRFT算法,由特定阶数DFRFT的加权和可得到任意分数阶域的DFRFT,权系数由DFTHermite本征值和附加零构成序列的离散Fourier反变换(IDFT)得到,且在搜索最佳分数阶域的过程中仅需计算一次IDFT,无需重新计算其所有变换核,从而可有效减少运算量,适合于应用在分数阶域的多分量信号检测和滤波处理中,仿真结果表明了该算法的有效性。

基于位移时间序列Fourier分析的滑坡预警研究

滑坡灾害的发生是多种致灾因子共同作用的结果,滑坡位移-时间变化曲线蕴含了造成斜坡滑动位移的各影响因素的内在的趋势性及周期性变化的特征。将Fourier分析理论引入到位移-时间序列分析中,从频率域上来分析位移-时间序列在时间域上突变部分的频域特征,提出了滑坡预警频率域阈值的概念,建立了基于位移-时间序列Fourier分析的滑坡预警分级方法。该研究从频域的角度改进滑坡预警预报方法,从而达到更准确的预测预警效果。

基于FRFT的频域自适应匹配滤波器检测方法

针对浅海混响背景下频域自适应匹配滤波器检测性能下降的问题,提出基于分数阶傅里叶变换(FRFT)的频域自适应匹配滤波器检测方法,该方法利用模板匹配技术,采用滑动窗对接收信号进行最优阶次分数阶傅里叶变换,然后将此过程中得到的FRFT域图与参考信号最优阶次傅里叶变换FRFT域图进行匹配,将离差平方和作为评价相似度的指标,即对离差平方和最小值的位置进行滤波,并对滤波后的信号进行最优阶次分数阶傅里叶逆变换,从而实现混响背景下的目标检测。仿真结果表明,在信混比为-15dB的情况下,该算法可显著提高频域自适应匹配滤波器的检测性能。

基于优化系数的混合域Fourier有限差分叠前深度偏移

为了提高复杂高陡构造区成像精度,提出了基于系数优化的混合域Fourier有限差分叠前深度偏移方法,该方法利用padé近似的有理函数对波场外推算子进行展开,然后利用切比雪夫多项式优化展开式系数,推导得到新的波场外推算子,降低了与波动方程精确波场外推算子的相对误差,提高了对波场外推算子的逼近程度,且在保证计算效率的同时提高了高陡构造区地震偏移成像的精度。对比改进后的混合域Fourier有限差分偏移方法与常规的傅里叶有限差分偏移方法(FFD)对Marmousi模型偏移剖面的成像效果,系数优化后的混合域Fourier有限差分偏移方法具有更高的成像精度。

基于频域控制约束的物理神经网络非线性系统预测方法

针对现有物理信息神经网络利用数值模拟近似物理控制方程带来的高计算代价、边界条件限制等问题,提出一种基于频域控制约束的物理神经网络非线性系统预测方法。首先构建时序特征交替更新的非线性预测网络模型,再在频域建立基于傅里叶谱方法(FSM)的物理控制方程约束,时空数据在网络模型与频域控制约束耦合下实现无标签数据加速训练,完成系统演化学习。最后在Burgers系统上进行湍流预测验证,实验结果表明该方法可在物理规则约束下实现无标签非线性复杂建模,对比主流PINN模型及其变体,具有更快的学习速度与预测准确率。在t≤0.25 s、t≤0.5 s短时预测情况下,经前期20次训练后系统预测均方误差(MSE)相比主流基准模型同期预测,MSE降低了86%与95%,在t≤2 s长时预测情况下,经充分训练后系统预测MSE能降低80%。