傅里叶变换同轴数字全息记录余弦变换谱系数

余弦变换广泛应用于图像和视频的压缩编码以及模式识别之中。余弦变换为实偶对称的傅里叶变换,把实偶对称物体传送到位于傅里叶变换透镜前焦面的空间光调制器上,采用单色均匀平面激光光波照射,则在后焦面上为光波复振幅分布为实偶对称物体的傅里叶变换,即为物体的余弦变换。由于余弦变换谱系数既有正实数又有负实数,提出了采用傅里叶变换同轴数字全息方法记录余弦变换谱系数,通过把数字全息图减去参考光光强和物光光强而得到余弦变换系数。理论推导和实验结果表明了该方法的可行性,该方法可应用于图像的快速余弦变换。     

Denoising in digital speckle pattern interferometry using fast discrete curvelet transform

In digital speckle pattern interferometry, the denoising of speckle fringe patterns is of vital importance for quantitative extraction of phase distribution. A filtering method of fast discrete curvelet transform based on weighted average thresholding technique is proposed in this paper for noise removal in speckle fringe patterns. Both computer-simulated and experimental digital speckle pattern interferometry fringe patterns are adopted to evaluate the performance of the proposed filtering method. In addition, a widely used and representative filtering method, windowed Fourier filter, is introduced for making a comparison and validation in the image processing effect, and the parameter of peak signal noise ratio is also used for assessment of denoising effect. It is shown from the filtered results that the filtering method of fast discrete curvelet transform is effecitve to remove speckle noises and simultaneously preserve fringe structure information.     

Regularization of the inverse heat conduction problem by the discrete Fourier transform

Two methods of solving the inverse heat conduction problem with employment of the discrete Fournier transform are presented in this article. The first one operates similarly to the SVD algorithm and consists in reducing the number of components of the discrete Fournier transform which are taken into account to determine the solution to the inverse problem. The second method is related to the regularization of the solution to the inverse problem in the discrete Fournier transform domain. Those methods were illustrated by numerical examples. In the first example, an influence of the boundary conditions disturbance by a random error on the solution to the inverse problem (its stability) was examined. In the second example, the temperature distribution on the inner boundary of the multiply connected domain was determined. Results of calculations made in both ways brought very good outcomes and confirm the usefulness of applying the discrete Fournier transform to solving inverse problems.     

GPU Computing based fast discrete wavelet transform for l1-regularized SPIRiT reconstruction

Parallel imaging is a technique to shorten the acquisition time by reducing the data size in phase encoding direction. Compressed Sensing is a technique to improve the performance of parallel imaging based reconstruction methods such as l₁-regularized SPIRiT by adding the regularization term, which leads to frequent calculations of Discrete Wavelet Transform (DWT) with high time cost. However, clinical practice of MRI scan requires fast or real-time reconstruction with high image quality. In this paper, by taking advantage of the properties of parallel imaging and GPU computing, we develop a fast three-dimensional DWT for parallel imaging based reconstruction methods such as l₁-regularized SPIRiT. Computational results show that fast DWT in l₁-regularized SPIRiT MRI reconstruction is approximately three times faster than the conventional DWT. Computational results also show that fast DWT for reconstructing an 80?×?150?×?32?×?80 Cardiac MRI dataset by l₁-regularized SPIRiT is approximately 20 per cent faster than l₁-regularized SPIRiT of the conventional DWT.     

Processing relative humidity data using discrete Fourier transform to control strain in art objects

Sustainable management of cultural heritage collections requires tools that, on the one hand, quantitatively relate risk of damage to environmental impacts and, on the other hand, can be easily used by conservation professionals and decision makers in heritage buildings or buildings housing collections. This paper explains how continual processing of ambient relative humidity (RH) data monitored in museums or historical buildings is used to assess quantitatively the climate‐induced physical damage risk to art objects. The software continually decomposes RH data into a set of elementary sinusoidal RH fluctuations using discrete Fourier transform. The user needs to provide basic characterisation of objects in the collection. Then each elementary sinusoidal RH fluctuation is transformed, using the precalculated database, into an elementary strain fluctuation experienced by the object. The complete strain history is calculated by the superposition of all elementary strain fluctuations. The risk of damage can be assessed by comparing strain against a critical level selected—the damage criterion. Wooden panels have been selected to illustrate the approach, and its reliability was demonstrated by comparison with the strain versus time histories obtained by full finite element modelling. The proposed approach based on the analysis of moisture response of objects is significant progress to current practices of evaluating climate parameters themselves.     

基于离散傅立叶变换扩频的广义多载波系统收发机频域简化实现方法

针对基于离散傅立叶变换扩频的广义多载波(DFT-S-GMC)系统的收发机时域实现方法复杂度较高的问题,提出了一种频域等效收发机实现方法;利用滤波器组各子带频率响应能量比原型滤波器的时域冲击响应能量集中的特性,提出了一种基于该频域实现方法的收发机简化实现方法和结构.仿真和分析表明,在多径信道下,采用频域简化实现结构的收发机与现有基于时域实现结构的收发机的误码率(BER)性能几乎相同,但与现有时域实现方法相比,采用频域简化实现方法,DFT-S-GMC系统发射机的实现复杂度可显著降低.     

散斑分数傅里叶联合变换相关测量研究

提出数字散斑联合变换分数相关测量方法,利用分数相关可以锐化相关峰的作用,在数字散斑联合变换相关运算中用分数傅里叶变换代替傅里叶变换,提高测量精度。通过对散斑图像进行相位调制,有效地解决了分数傅里叶变换的移变性带来的谱移问题。编程模拟和对拉伸试件位移场测量的结果表明,只要选择合适的分数傅里叶变换级次和相位调制函数,可以使相关峰的半宽度从4～5pixel锐化到仅1pixel,得到优于傅里叶变换相关的理想输出。     

3rd-order Spectral Representation Method: Simulation of multi-dimensional random fields and ergodic multi-variate random processes with fast Fourier transform implementation

This paper introduces a generalized 3rd-order Spectral Representation Method for the simulation of multi-dimensional random fields and ergodic multi-variate stochastic processes with asymmetric non-linearities. The formula for the simulation of general $d$-dimensional random fields is presented and the method is applied to simulate 2D and 3D random fields. The differences between samples generated by the proposed methodology and the existing classical Spectral Representation Method are analysed. The formula for the simulation of multi-variate random processes is subsequently developed. An important feature of the methodologies is that they can be implemented efficiently with the Fast Fourier Transform (FFT), details of which are presented. Computational savings are shown to grow exponentially with dimensionality as a testament of the scalability of the simulation methodology. Examples highlighting the salient features of these methodologies are also presented.     

A novel hybrid combination optimization algorithm based on search area segmentation and fast Fourier transform

A novel hybrid optimization algorithm combining search area segmentation technique and the fast Fourier transform (HSAS/FFT) is presented to solve the numerical optimization problems. Firstly, the spectrum of each dimension of the objective function can be acquired by the FFT. The search space is segmented by using the spectrum to ensure that each subspace is unimodal. Secondly, the population of subspaces is produced and the optimal individual can be obtained by gradient descent algorithm. Finally, the local optimal solution in the optimal subspace is generated by the binary search algorithm. Make the optimal individual the new search space and repeat the process until meeting the termination condition. The proposed HSAS/FFT was tested on the CEC2017 benchmark, which evaluates the performance of the proposed algorithm on solving global optimization problems. Results obtained show that HSAS/FFT has an excellent performance and better convergence speed in comparison with some of the state-of-the-art algorithms.     

Parameter diagrams for the fractional fourier transform

Abstract

A simple diagram illustrates the relations between six parameters of the generalized FRT. The diagram is developed to illustrate a variety of equations which have appeared in the literature, particularly in relation to free-space propagation, Gaussian beams, optical filtering experiments, and the ABCD matrix. Analysis of the effect of imperfect collimation and of the production of a Radon-Wigner spectrum using a varifocal lens are given as examples of the technique.     

Representation-theoretical properties of the approximate quantum Fourier transform

Among the transformations used in quantum computing the discrete Fourier transform (DFT) plays a key role. A striking fact is that the computational complexity of the DFT with respect to the quantum gate model is polylogarithmic in the length of the input data. In this paper we consider approximate Fourier transformations which are obtained by pruning the twiddle factors of DFT. A parameter is used which determines the level of pruning. The extreme cases are no pruning, which leads to the DFT, and complete pruning, which leads to the Hadamard transform. Our main result is to give a representation-theoretical interpretation of the transformation obtained for all intermediate levels of pruning. We show that the resulting approximate quantum Fourier transforms are basefield transformations, i. e., they decompose the regular representation of the cyclic group over non-splitting fields. Thomas Beth passed away on August 17, 2005. The results presented here had been obtained in joint work with him and had been included into the first author’s Ph.D. thesis. These results have not been published yet.     

广义特征值问题的快速傅里叶变换法

针对广义特征值问题提出离散傅里叶变换法。该方法把结构的动力响应看作是一种信号,利用快速傅里叶变换进行分析,从而得到结构的振动频率。该方法避免对刚度矩阵求逆,可同时计算出所有的特征值,是一种直接方法。数值算例验证了该方法的正确性。     

茶叶近红外光谱数据的离散余弦变换压缩方法

利用离散余弦变换具有的去相关能力,通过引入阈值和保留能量来定量描述茶叶近红外光谱数据 离散余弦变换后的特性.结果表明,离散余弦变换对近红外光谱具有较强的压缩能力。     

Fast Fourier transform on multipoles (FFTM) algorithm for Laplace equation with direct and indirect boundary element method

In this paper, the fast Fourier transform on multipole (FFTM) algorithm is used to accelerate the matrix-vector product in the boundary element method (BEM) for solving Laplace equation. This is implemented in both the direct and indirect formulations of the BEM. A new formulation for handling the double layer kernel using the direct formulation is presented, and this is shown to be related to the method given by Yoshida (Application of fast multipole method to boundary integral equation method, Kyoto University, Japan, 2001). The FFTM algorithm shows different computational performances in direct and indirect formulations. The direct formulation tends to take more computational time due to the evaluation of an extra integral. The error of FFTM in the direct formulation is smaller than that in the indirect formulation because the direct formulation has the advantage of avoiding the calculations of the free term and the strongly singular integral explicitly. The multipole and local translations introduce approximation errors, but these are not significant compared with the discretization error in the direct or indirect BEM formulation. Several numerical examples are presented to compare the computational efficiency of the FFTM algorithm used with the direct and indirect BEM formulations.     

An overview of LULU operators and discrete pulse transform for image analysis

Abstract

This paper presents an overview of LULU operators and discrete pulse transform (DPT). Data extraction from signals and images is a popular area of research. Different methods are being used for data extraction such as different types of linear and nonlinear operators. LULU operator is one of the most important rank selector nonlinear filters used for data analysis which is widely being used for signal analysis, especially in impulse noise filtering. It is computationally more efficient and the behaviour of the operator is simple to describe. Based on the composition of different orders of LULU operators, DPT on multi-resolution is defined, which describes the sequences into pulses with different magnitudes. DPT allows a multi-resolution measure of roughness of images and sequences. It is a powerful technique for image analysis and can also be used for the estimation of standard deviation of a random distribution.     

基于分数阶Fourier变换的机械变速过程信号分析

研究了旋转机械的变速测量过程，通过引入分数阶傅立叶变换（FRFT），推导证明了分数阶傅立叶变换对扫频信号具有良好的时频聚焦性，因此应用分数阶傅立叶变换来分析旋转机械的变速过程的测量信号，可以有效地解决机械转速不恒定对信号分析的影响，提高信号分析、状态监测以及故障诊断的准确性。     

Improved guaranteed computable bounds on homogenized properties of periodic media by the Fourier–Galerkin method with exact integration

Moulinec and Suquet introduced FFT‐based homogenization in 1994, and 20years later, their approach is still effective for evaluating the homogenized properties arising from the periodic cell problem. This paper builds on the author's (2013) variational reformulation approximated by trigonometric polynomials establishing two numerical schemes: Galerkin approximation (Ga) and a version with numerical integration (GaNi). The latter approach, fully equivalent to the original Moulinec–Suquet algorithm, was used to evaluate guaranteed upper–lower bounds on homogenized coefficients incorporating a closed‐form double‐grid quadrature. Here, these concepts, based on the primal and dual formulations, are employed for the Ga scheme. For the same computational effort, the Ga outperforms the GaNi with more accurate guaranteed bounds and more predictable numerical behaviors. The quadrature technique leading to block‐sparse linear systems is extended here to materials defined via high‐resolution images in a way that allows for effective treatment using the FFT. Memory demands are reduced by a reformulation of the double‐grid scheme to the original grid scheme using FFT shifts. Minimization of the bounds during iterations of conjugate gradients is effective, particularly when incorporating a solution from a coarser grid. The methodology presented here for the scalar linear elliptic problem could be extended to more complex frameworks. Copyright © 2015 John Wiley & Sons, Ltd.     

Interferometric time delay correction for Fourier transform spectroscopy in the extreme ultraviolet

We demonstrate a Fourier transform spectrometer in the extreme ultraviolet (XUV) spectrum using a high-harmonic source, with wavelengths as short as 32 nm. The femtosecond infrared laser source is divided into two separate foci in the same gas jet to create two synchronized XUV sources. An interferometric method to determine the relative delay between the two sources is shown to improve the accuracy of the delay time, with corrections of up to 200 asec required. By correcting the time base before the Fourier transform, the frequency resolution is improved by up to an order of magnitude.