透镜组合实现光学分数傅里叶变换

从光学系统脉冲响应函数理论的角度分析了秀镜组合实现光学分数傅里叶变换的结构及标准焦距的物理意义，推导了几种较普遍的实现光学分数傅里叶变换的结构，利用该结构可以方便地改变其标准焦距，这对设计由多级数傅里叶变换级联构成的空间变化滤波系统具有重要的指导意义。     

分数傅里叶变换啁啾滤波

针对常规傅里叶变换所不能解决的啁啾噪声滤除问题，利用Wigner分布函数分析分数傅里叶变换的空域和频域特性，提出在分数傅里叶变换域进行啁啾滤波的方法。并将该方法应用到图像处理中，对分数傅里叶变换滤除一维和二维图像的啁啾噪声进行了计算机仿真，获得了满意的效果，结果表明该方法在图像处理中的有效性。     

基于联合广义分数相关器的相关峰特性分析

分析了联合广义分数傅里叶变换相关器相关峰的特性,得到通过改变广义分数傅里叶变换的系统参量可以提高广义分数相关峰性能的结论.进行了数值模拟和光学实验,并根据两者的结果对四个相关峰的性能指标相关峰强度最大值、峰能比、识别能力、信噪比进行了比较分析,说明只要适当控制系统参量,联合广义分数傅里叶变换相关器比联合分数傅里叶变换相关器具有更好的相关性能,有助于提高光学相关器识别的准确率.     

光学分数傅里叶变换及其应用

介绍了分数傅里叶变换的定义及其性质,给出了分数傅里叶变换的光学实验结构,并对分数傅里叶变换在光学信息处理领域中的应用进行了综述。     

傅里叶变换的局限性及其改进方法

从对傅里叶变换的局限性分析入手 ,揭示了窗口傅里叶变换、小波变换和分数傅里叶变换的出现是傅里叶变换本身发展的必然 ,阐明了其改进方法产生的原因及其优缺点 ,分析了其改进方法与傅里叶变化的关系 ,这些有助于加深对傅里叶变换的认识。     

基于连续统快速傅里叶变换的红外光谱处理技术

为实现红外光谱对遥感地物准确的识别,消除高频噪声是光谱特征分析和提取的重要环节。利用光谱连续统处理方法,结合信号时域分析领域快速傅里叶变换提出了一种新的红外光谱滤波方法。该方法首先对红外光谱进行光谱连续统去除,利用快速傅里叶变换将去连续统后光谱转换到频域,设计低通滤波器滤除高频噪声,然后通过快速傅里叶反变换将频域信号转换到时域,最后对信号进行光谱连续统恢复,得到滤除噪声后的红外光谱信号。对比实验表明,连续统快速傅里叶滤波方法比常规的时域滤波方法有更好、更快的滤波效果,解决了传统快速傅里叶红外光谱滤波的吉布斯现象。该方法操作简便、运行速度快捷、滤波效果好,满足了红外光谱地物识别对光谱高质量的要求。     

求解分数傅里叶变换衍射积分的一种快速算法

在对Lohmann 二型分数傅里叶变换(FRT)和菲涅耳衍射积分进行比较的基础上,给出基于快速傅里叶变换(FFT)求解该分数傅里叶变换和菲涅耳衍射积分的快速算法及算法适用范围.数值模拟实验证明了理论的可靠性和算法的高效性.此快速算法为分数傅里叶变换在工程实际中的进一步广泛应用奠定了基础.     

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...     

用全息透镜记录多重分数傅里叶变换全息图

提出一种全息透镜记录多重分数傅里叶变换全息图的新方法，它能在三维空间不同位置和不同方向上分别再现所记录的多个物体的图象，分析了利用全息透镜记录多重分数傅里叶变换全息图的原理及特点，制作了多重分数傅里叶变换全息图，并获得了满意的再现结果。     

利用分数傅里叶变换相关实现散斑相关测量

提出了一种在匹配滤波相关中利用分数傅里叶变换代替傅里叶变换实现散斑相关测量的方法.利用分数傅里叶变换的指数性质,采用把移变后的散斑图像先进行相位调制,再进行分数傅里叶变换的方法,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,可以得到优于傅里叶变换相关的理想输出.     

Acoustic features based on auditory model and adaptive fractional Fourier transform for speech recognition

It is well known that auditory system of human beings has excellent performance which automatic speech recognition(ASR) systems can’t match,and fractional Fourier transform (FrFT) has unique advantages in non-stationary signal processing.In this paper,the Gammatone filterbank is applied to speech signals for front-end temporal filtering,and then acoustic features of the output subband signals are extracted based on fractional Fourier transform. Considering the critical effect of transform order for FrFT,an order adaptation method based on the instantaneous frequency is proposed,and its performance is compared with the method based on ambiguity function.ASR experiments are conducted on clean and noisy Putonghua digits,and the results show that the proposed features achieve significantly higher recognition rate than the MFCC baseline,and the order adaptation method based on instantaneous frequency has much lower complexity than that based on ambiguity function.Further more,the FrFT-based features achieve the highest recognition rate using the proposed order adaptation method.     

The fractional Fourier transform as a simulation tool for lens‐based X‐ray microscopy

The fractional Fourier transform (FrFT) is introduced as a tool for numerical simulations of X‐ray wavefront propagation. By removing the strict sampling requirements encountered in typical Fourier optics, simulations using the FrFT can be carried out with much decreased detail, allowing, for example, on‐line simulation during experiments. Moreover, the additive index property of the FrFT allows the propagation through multiple optical components to be simulated in a single step, which is particularly useful for compound refractive lenses (CRLs). It is shown that it is possible to model the attenuation from the entire CRL using one or two effective apertures without loss of accuracy, greatly accelerating simulations involving CRLs. To demonstrate the applicability and accuracy of the FrFT, the imaging resolution of a CRL‐based imaging system is estimated, and the FrFT approach is shown to be significantly more precise than comparable approaches using geometrical optics. Secondly, it is shown that extensive FrFT simulations of complex systems involving coherence and/or non‐monochromatic sources can be carried out in minutes. Specifically, the chromatic aberrations as a function of source bandwidth are estimated, and it is found that the geometric optics greatly overestimates the aberration for energy bandwidths of around 1%.     

Short-time fractional Fourier methods for the time-frequency representation of chirp signals

The fractional Fourier transform (FrFT) provides a valuable tool for the analysis of linear chirp signals. This paper develops two short-time FrFT variants which are suited to the analysis of multicomponent and nonlinear chirp signals. Outputs have similar properties to the short-time Fourier transform (STFT) but show improved time-frequency resolution. The FrFT is a parameterized transform with parameter, a, related to chirp rate. The two short-time implementations differ in how the value of a is chosen. In the first, a global optimization procedure selects one value of a with reference to the entire signal. In the second, a values are selected independently for each windowed section. Comparative variance measures based on the Gaussian function are given and are shown to be consistent with the uncertainty principle in fractional domains. For appropriately chosen FrFT orders, the derived fractional domain uncertainty relationship is minimized for Gaussian windowed linear chirp signals. The two short-time FrFT algorithms have complementary strengths demonstrated by time-frequency representations for a multicomponent bat chirp, a highly nonlinear quadratic chirp, and an output pulse from a finite-difference sonar model with dispersive change. These representations illustrate the improvements obtained in using FrFT based algorithms compared to the STFT.     

基于听觉模型与自适应分数阶Fourier变换的声学特征在语音识别中的应用

分数阶Fourier变换在处理非平稳信号尤其是chirp信号方面有着独特的优势,而人耳听觉系统具有自动语音识别系统难以比拟的优良性能。本文采用Gammatone听觉滤波器组对语音信号进行前端时域滤波,然后对输出的各个子带信号用分数阶Fourer变换方法提取声学特征。分数阶Fourier变换的阶数对其性能有着重要影响,本文针对子带时域信号提出了采用瞬时频率曲线拟合求取阶数的方法,并将其与采用模糊函数的方法作了比较。在干净与含噪汉语孤立数字库上的语音识别结果表明,采用新提出的声学特征得到的识别正确率相对MFCC基线系统有了显著提高;根据瞬时频率曲线搜索阶数的算法与模糊函数方法相比,计算量大大减少,并且根据该方法提取的声学特征得到了最高的平均识别正确率。      

Double image encryption based on phase-amplitude hybrid encoding and iterative phase encoding in fractional Fourier transform domains

A new method for double image encryption is proposed that is based on amplitude-phase hybrid encoding and iterative random phase encoding in fractional Fourier transform (FrFT) domains. In the iterative random phase encoding operation, a binary random matrix is defined to encode two original images to a single complex-valued image, which is then converted into a stationary white noise image by the iterative phase encoding with FrFTs. Compared with the previous schemes that uses fully phase encoding, the proposed method reduces the difference between two original images in key space and sensitivity to the FrFT orders. The primitive images can be retrieved exactly by applying correct keys with initial conditions of chaotic system, the pixel scrambling operation and the FrFT orders. Computer simulations demonstrate that the encryption method has impressively high security level and certain robustness against data loss and noise interference.     

水下回波处理中分数阶傅里叶变换的带通采样实现方法

利用球形压电陶瓷自身所具有的耐压能力,采用径向极化空气背衬压电球壳换能器作为声学接收敏感元件,设计并制作了一种球形耐压水听器。首先对其低频开路接收灵敏度和谐振频率等声学特性进行了分析和有限元仿真,然后对其强度和稳定性等耐压性能进行了分析和有限元仿真,最后对其声学性能和耐压能力进行了测试。测试表明,该球形耐压水听器的直径为36 mm,工作频段为50 Hz10 kHz,低频接收灵敏度为􀀀198:4 dB(0 dB=1 V/Pa),等效自噪声谱级为46.5 dB@1 kHz,其耐压深度可达3000 m。该耐压水听器为大深度水听器设计提供了参考,在深水声学领域具有重要的应用价值。     

Application of multi-scale chirplet path pursuit and fractional Fourier transform for gear fault detection in speed up and speed-down processes

Demodulation is very important for gear fault detection. However, the demodulation is substantially complicated by the non-stationary nature of the signal during the speed-up and speed-down processes. As such, we propose a new technique to detect gear faults under such conditions based on the multi-scale chirplet path pursuit (MSCPP) algorithm and the fractional Fourier transform (FrFT) method. With the MSCPP algorithm, the instantaneous frequency of the signal component with the largest energy in the multi-components gear vibration signal can be estimated. Then according to the estimated instantaneous frequency, the vibration signal segment whose instantaneous frequency curve approximated as either an ascending or descending linear segment can be obtained from the original gear vibration signal. In other words, the vibration signal segment that can be regarded as a multi-component linear frequency modulated (LFM) signal is extracted. As the FrFT is suitable for multi-component LFM signal analysis, it is then applied to demodulating this vibration signal segment and hence detecting local gear faults based on the revealed modulation phenomenon. The effectiveness of the proposed method has been demonstrated by both simulation and experimental data.     

Modified computational integral imaging-based double image encryption using fractional Fourier transform

In this paper, we propose an image encryption technique to simultaneously encrypt double or multiple images into one encrypted image using computational integral imaging (CII) and fractional Fourier transform (FrFT). In the encryption, each of the input plane images are located at different positions along a pickup plane, and simultaneously recorded in the form of an elemental image array (EIA) through a lenslet array. The recorded EIA to be encrypted is multiplied by FrFT with two different fractional orders. In order to mitigate the drawbacks of occlusion noise in computational integral imaging reconstruction (CIIR), the plane images can be reconstructed using a modified CIIR technique. To further improve the solution of the reconstructed plane images, a block matching algorithm is also introduced. Numerical simulation results verify the feasibility and effectiveness of the proposed method.     

Novel single-channel color image encryption algorithm based on chaos and fractional Fourier transform

A new color image encryption algorithm based on fractional Fourier transform (FrFT) and chaos is proposed. The colors of the original color image are converted to HSI (hue-saturation-intensity), and the S component is transformed by the random-phase encoding based on FrFT to obtain a new random phase. The I component is transformed by double random-phase encoding based on FrFT using the H component and the new random phase as two phase plates. Then chaos scrambling technology is used to encrypt the image, which makes the resulting image nonlinear and disorder both in spatial domain and frequency domain. Additionally, the ciphertext is not a color image but a combination of a gray image and a phase matrix, so the ciphertext has camouflage property to some extent. The results of numerical simulations demonstrate the effectiveness and the security of this algorithm.     

Multiparty Quantum Secret Sharing Using Quantum Fourier Transform

A （n, n）-threshold scheme of multiparty quantum secret sharing of classical or quantum message is proposed based on the discrete quantum Fourier transform. In our proposed scheme, the secret message, which is encoded by using the forward quantum Fourier transform and decoded by using the reverse, is split and shared in such a way that it can be reconstructed among them only if all the participants work in concert. Fhrthermore, we also discuss how this protocol must be carefully designed for correcting errors and checking eavesdropping or a dishonest participant. Security analysis shows that our scheme is secure. Also, this scheme has an advantage that it is completely compatible with quantum computation and easier to realize in the distributed quantum secure computation.