利用冲击声辨识声源材料的特征提取

声源辨识属于环境声识别的范畴,是模式识别的一个重要研究方向。冲击声携带了大量的声源物理信息,因此利用冲击声提取特征进行声源材料辨识是提高声目标识别分类性能的重要途径。对球-板撞击物理模型合成的冲击声连续统,提出使用基函数学习法提取目标特征,同时利用短时傅里叶变换和小波包变换进行特征提取,以此为基础完成被击平板的材料识别。研究结果表明,利用基函数学习法获得的特征,对于冲击声分类的效果明显优于短时傅里叶变换和小波包变换方法,说明利用该方法进行冲击声声源材料辨识的可行性和优势。      

光学小波变换

首先讨论了常规傅里叶变换的缺点,导入短时傅里叶变换及小波变换,分析了小波变换的特点和实现小波变换的光学方案,在空域和频域中详细分析了利用高斯－哈尔小波变换进行边缘探测的特征,介绍了小波变换图形识别的结果。     

小波变换及其应用

傅里叶变换是信号分析的最基本工具和方法之一,但其本身仍然存在较大的缺陷,例如不能提供信号在时域上的特征.短时傅里叶变换虽然可以在一定程度上弥补该缺陷,但是它的频率分辨率和时间分辨率都十分有限,只是一种折衷的解决办法.小波变换是一种快速发展和比较流行的信号分析方法,它精确地揭示了信号在时间和频率方面的分布特点,可以同时分析信号在时域和频域中的特征,并可用多种分辨率来分析信号,实现信号的有损和无损传送.文章简要地回顾了小波变换的发展历史,介绍了小波变换的基本思想、主要概念、计算方法和计算流程.最后以四个典型的实例,展示了小波变换在现代工程中的应用和它独特的优势.     

分数域滤波的分数傅里叶变换光学成像性能分析

将分数域滤波同光学成像相结合,提出了一种基于Lohmann Ⅰ型的带有滤波孔径的两级联分数傅里叶变换光学成像系统.根据分数傅里叶变换和菲涅耳衍射之间的关系以及分数傅里叶变换的分数阶可加性,结合分数域滤波分析了分数傅里叶变换光学成像的基本理论.以点扩散函数和调制传递函数作为评价成像质量的准则,详细分析了不同分数阶光学系统...     

瞬态位移干涉仪信号处理新方法

利用短时傅里叶变换计算速度快的特点,先对瞬态位移干涉仪信号进行预处理,得到速度的轮廓范围.据此估计小波变换中尺度因子的范围,然后用连续小波变换的方法对信号再次进行处理,用此方法分析计算机模拟出的位移干涉信号,恢复的速度相对误差小于2％.对高速爆轰实验中的位移干涉信号分别采用短时傅立叶变换、小波变换和二者相结合的方式进行...     

基于S变换滤波解相法的条纹解相研究

S变换可以看作是介于小波变换与窗口傅里叶变换之间的变换,具有很强的时频分析能力,它将一维信号变换为时间(空间)和频率的函数,称为瞬时S变换谱,在沿窗口移动方向上,S变换谱的叠加可得到全局信号的傅里叶频谱。在S变换用于条纹解调时,局部基频的正确提取是确保获得全局信号基频分量的关键。为此研究了不同的滤波过程对S变换解调条纹相位的影响,利用不同的滤波器,在对局部S频谱进行加权滤波后,叠加局部基频,得到全局基频分布,然后再利用逆傅里叶变换获得条纹的相位分布,从而重建被测物体的面形。讨论了阈值滤波、平顶高斯和平顶汉宁滤波、"脊"线拟合后的平顶高斯和平顶汉宁滤波在S变换轮廓术中的应用,通过计算机模拟和实验,初步对比了滤波效果。     

小波包变换对CO-OFDM系统高峰均比的抑制性能研究

针对相干光正交频分复用系统中出现的高峰值平均功率比问题,提出用小波包变换取代传统快速傅里叶变换的相干光正交频分复用系统.仿真实验证明了具有良好正交性的小波包变换对高峰值平均功率比起到一定程度上的抑制作用,且误码率性能优于传统的快速傅里叶变换.随着小波尺度函数及小波函数对称性的提升,其避免信号处理过程中的相移的能力提高,系统性能有所改善.与传统的快速傅里叶变换系统相比,基于小波包变换的系统中,小波基函数haar小波的互补累计分布函数为0.01时,门限值降低约2dB,且在误码率为10-3的情况下,性能优化1.5dB.在此基础上,将小波提升算法应用到相干光正交频分复用系统中,得到的抑制峰均比及误码率性能与应用Mallat算法时一致,但算法的结构复杂度降低.     

小波相位解调轮廓术

针对傅里叶变换轮廓术因混频难以准确提取基频的问题,可将小波变换用于三维形貌相位直接解调。对其原理进行了研究,通过编程实现了小波相位解调。取Morlet复小波作为小波母函数,对调制栅线图逐行进行连续小波变换,从各位置的沿尺度方向的小波变换系数幅值的极值中可直接求取对应的相位数据。由于小波函数具有空域_频率两域的局部化特性,因此它对变形栅具有很强的自适应能力。为验证新方法,对其进行了仿真分析,同时还对石膏半球模型和化妆品瓶进行了实际测量,并分别用傅里叶变换和小波变换进行了处理。结果表明,新方法有效地克服了混频的问题,改善了相位解调效果,提高了测量精度,特别适合于复杂物体的形貌测量。     

小波分析在遥测信号处理中的应用

综述了小波分析的发展现状,通过对比小波变换与短时傅里叶变换之间的差异,指出小波分析是一种多分辨分析方法,特别适合于非平稳信号的分析与处理,并且应用该方法对遥测速变信号进行处理,取得了较好的效果。     

高阶非线性薛定谔方程的分步小波方法

用小波变换代替傅里叶变换解高阶非线性薛定谔方程,为高阶薛定谔方程的数值解提供了一种工具,提高了运算速度.本文分析了高阶非线性薛定谔方程分步解法的一般形式,选用Db10小波,得到了小波微分算子和色散算子对应的矩阵,得出了分步小波方法的算法公式.推导了色散算子和时域信号在小波域相乘的近似运算公式,说明了分步傅里叶方法比分步小波方法的复数乘法次数更多,同时说明了提高运算速度必须舍弃一定的运算准确度.最后以分步傅里叶方法为准,分析了分步小波方法的误差,结果表明:对于一阶孤子,分步小波方法与分步傅里叶方法间的相对误差在1.2%左右波动.     

Correlation functions and correlation times for models with multiplicative white noise

Correlation functions and correlation times for the Stratonovich and Verhulst model are investigated. By transforming the Fourier transform of the corresponding Fokker-Planck equation into a tridiagonal vector recurrence relation, the Fourier transform of the correlation function and the correlation time are expressed in terms of matrix continued fractions or by similar iterations and are thus obtained numerically. By using the inverse Fourier transform, the correlation function itself is calculated. Furthermore an analytic expression in terms of an integral is obtained for the correlation time, which is evaluated exactly in the Verhulst model and asymptotically for large and weak noise strength in the Stratonovich model. A Padé expansion approximating the correlation time for all noise strength is also given.     

Integrability of linear and nonlinear evolution equations and the associated nonlinear fourier transforms

The inverse spectral method is a nonlinear Fourier transform method for solving certain equations. Here, we emphasize that such transforms should be considered in their own right. We also elucidate further the connection between the Fourier transform and inverse spectral methods by establishing that linear equations can also be solved through the inverse spectral method.     

Atmospheric transfer of radiation above an inhomogeneous non-Lambertian reflective ground—I. Theory

A method for solving the three-dimensional equation of transfer for a vertically inhomogeneous atmosphere bounded by a reflecting surface of non-uniform bidirectional reflectance is presented. The technique incorporates a two-dimensional spatial Fourier transform of the transfer equation and solution of the resulting expressions for each Fourier component of the radiation field using the method of Gauss-Seidel iteration. The intensity field in the spatial domain, which is calculated for a variety of altitudes, zenith angles, and azimuths, is reconstructed using the inverse Fourier transform. An empirical surface bidirectional reflectance function is employed, permitting the consideration of non-Lambertian reflective properties.     

Generalized analytic signal associated with linear canonical transform

Analytic signal is tightly associated with Hilbert transform and Fourier transform. The linear canonical transform is the generalization of many famous linear integral transforms, such as Fourier transform, fractional Fourier transform and Fresnel transform. Based on the parameter (a, b)-Hilbert transform and the linear canonical transform, in this paper, we develop some issues on generalized analytic signal. The generalized analytic signal can suppress the negative frequency components in the linear canonical transform domain. Furthermore, we prove that the kernel function of the inverse linear canonical transform satisfies the generalized analytic condition and get the generalized analytic pairs. We show the generalized Bedrosian theorem is valid in the linear canonical transform domain.     

A simple method for phase wraps elimination or reduction in spatial fringe patterns

In this paper, we propose a simple method for processing a 2D wrapped phase map that contains a spatial carrier signal in order to completely eliminate, or greatly reduce, the number of phase wraps in the image. The 2D Fourier transform of the wrapped phase map is calculated. Then the spectrum is shifted to the origin in frequency space. After that, the inverse 2D Fourier transform is computed. Finally, a four-quadrant arctangent function is used to calculate the angle of the complex array that was produced by the inverse 2D Fourier transform. This produces a phase map with a smaller number of 2π phase jumps than the original phase map. In some cases, all of the phase wraps are eliminated and there is therefore no need to unwrap the resultant phase map. The reduction of the number of 2π phase jumps can reduce the execution time and improve the noise performance of some phase unwrapping algorithms such as the Flynn method. The validation of the proposed algorithm is demonstrated experimentally and also via computer-simulation.     

Prony's method applied to estimate noise source locations and their sound powers

An application of Prony's method for evaluating the acoustic power and location of sound sources from spatially sampled data is described. A sound source considered as a point source has an intensity proportional to the inverse square of the distance between source and observation point. The Fourier transform of this intensity function is an exponential function with a real exponent. The shift property of the Fourier transform results in a spectral change in the phase angle, which is expressed in the transform domain by a multiplicative exponential function of pure imaginary exponent. In this paper the usual time axis of the Fourier pair of time and frequency is treated as a variable denoting the location of the sound source. Accordingly, each spectral component of spatially sampled sound intensity generated by n point sources can be expressed as a linear combination of n complex exponentials. By applying Prony's method to the spectral data, these unknown exponents can be calculated numerically. This paper deals with an estimation procedure to find the location and power of a noise source. The estimation is done by minimizing the sum of the squares of the errors between the model and measured data. The proposed method has general applicability to problems where the so-called inverse square law for intensity can be assumed to be valid.     

基于窗口傅里叶变换剪切干涉法波前检测

提出了一种利用二维窗口傅里叶变换从径向剪切干涉条纹中准确得到波前的重建技术。首先对剪切干涉条纹做二维窗口傅里叶变换,设置阈值和频率积分范围后,进行二维窗口傅里叶逆变换,然后对包裹相位做去载频和相位展开处理得到相位差分布,最后使用波前迭代算法从相位差中复原实际波前。模拟计算表明,使用该方法最大相位复原误差为0.82%,均方根值为0.020 9 rad,实验结果验证了该方法的有效性。同时也对窗口傅里叶变换的关键参数,如窗函数的选择、窗口大小的确定以及阈值的选取等进行了简要讨论。与传统傅里叶变换法(FFT)相比,基于窗口傅里叶变换的剪切干涉波前检测法有更高的精度和稳定性,为波前检测提供一种新的处理方法。     

An inverse spectral analysis of transmission problem in thermo- and photo-acoustic tomography

We study an inverse spectral theory in the thermo- and photo-acoustic tomography in imaging science. Under certain non-trapping hypothesis, we study the zero set of the Fourier transform of the observation data. The zero set corresponds to the spectrum of the interior transmission problem. We reduce the problem into an interior transformation problem of two indices of refractions. The inverse spectral problem is to study the inverse uniqueness of the indices of refraction. The zero distribution theory of entire function plays a role.     

Fast algorithm of discrete gyrator transform based on convolution operation

The expression of gyrator transform (GT) is rewritten by using convolution operation, from which GT can be composed of phase-only filtering, Fourier transform and inverse Fourier transform. Therefore, fast Fourier transform (FFT) algorithm can be introduced into the calculation of convolution format of GT in the discrete case. Some simulations are presented in order to demonstrate the validity of the algorithm.     

柯林斯公式的D-FFT计算

将柯林斯公式及其逆运算表示为卷积形式,导出对应的传递函数,讨论使用快速傅里叶变换(FFT)计算柯林斯公式时满足取样定理的条件,基于研究结果,给出光波通过一光学系统的衍射场计算及根据衍射场重建入射平面光波场的实例。