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。      

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.     

分数傅里叶变换滤波优化算法及滤波器设计

分数傅里叶变换（FrFT, fractional Fourier transform）是经典傅里叶变换的一种表现形式，可理解为在时 频平面中坐标轴系以原点为轴逆时针旋转一定的角度。通过数学推导，对能否利用分数傅里叶变换进行信号滤波，滤波的优化算法如何，以及滤波器有哪些设计结构等问题进行深入的研究，指出分数傅里叶变换适用于非平稳信号滤波。采用Matlab进行了数值仿真实验。实验结果表明：在信号滤波方面，由于傅里叶变换在处理某些数据时有局限性，因此分数傅里叶变换与傅里叶变换相比具有显著的优势。最后给出FrFT滤波器的设计思想。     

Generalized fractional S-transform and its application to discriminate environmental background acoustic noise signals

We propose a modification of S-transform (ST) by changing the kernel of Fourier transform (FT) with that of fractional Fourier transform (FRFT) and call it generalized fractional ST (GFST). The FRFT is a generalization of FT and it has been shown more useful than the FT for signals with changing frequencies such as chirp signals. The proposed GFST is applied to analyze and classify different environmental background sound mixed with speech signal in the form of additive noise. The simulation results demonstrate that Euclidean distance between the feature vectors computed from generalized fractional ST corresponding to different background noise is increased as compared to ST for the same set of feature vectors and signals.     

Novel optical image encryption scheme based on fractional Mellin transform

A novel nonlinear image encryption scheme is proposed by introducing the fractional Mellin transform (FrMT) into the field of image security. As a nonlinear transform, FrMT is employed to get rid of the potential insecurity of the optical image encryption system caused by the intrinsic object-image relationship between the plaintext and the ciphertext. Different annular domains of the original image are transformed by FrMTs of different orders, and then the outputs are further encrypted by comprehensively using fractional Fourier transform (FrFT), amplitude encoding and phase encoding. The keys of the encryption algorithm include the orders of the FrMTs, the radii of the FrMT domains, the order of the FrFT and the phases generated in the further encryption process, thus the key space is extremely large. An optoelectronic hybrid structure for the proposed scheme is also introduced. Numerical simulations demonstrate that the proposed algorithm is robust with noise immunity, sensitive to the keys, and outperforms the conventional linear encryption methods to counteract some attacks.     

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.     

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.     

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%.     

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.     

On the core of the fractional Fourier transform and its role in composing complex fractional Fourier transformations and Fresnel transformations

By a quantum mechanical analysis of the additive rule F_α[F_β[f]] = F_α+β[f], which the fractional Fourier transformation (FrFT) F_α[f] should satisfy, we reveal that the position-momentum mutualtransformation operator is the core element for constructing the integration kernel of FrFT. Based on this observation and the two mutually conjugate entangled-state representations, we then derive a core operator for enabling a complex fractional Fourier transformation (CFrFT), which also obeys the additive rule. In a similar manner, we also reveal the fractional transformation property for a type of Fresnel operator.     

Fractional Gabor transform

A fractional Gabor transform (FRGT) is proposed. This new transform is a generalization of the conventional Gabor transform (GT) based on the Fourier transform to the windowed fractional Fourier transform (FRFT). The FRGT provides analyses of signals in both the real space and the FRFT frequency domain simultaneously. The space-FRFT frequency pattern can be rotated as the fractional order changes. The FRGT has an additional freedom, compared with the conventional GT, i.e., the transform order. The FRGT may offer a useful tool for guiding optimal filter design in the FRFT domain in signal processing.     

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。     

分数双重非线性相关器特性研究

将分数傅里叶变换引入到双重非线性相关方法中,通过对参考图像和目标图像分数傅里叶变换谱的双重非线性操作实现非线性分数相关.该方法利用非线性参数以及分数阶控制目标的形状和纹理的权重,从而实现目标相关识别的调控.该非线性分数相关系统由一个光电混合装置实现,数值仿真表明,这种光学图像识别系统的优点在于对目标的形状失真和纹理改变...     

基于分数阶傅里叶变换混响抑制的目标回波检测方法

提出了一种声呐发射信号为线性调频信号时,基于分数阶傅里叶变换混响抑制的目标回波信号检测方法。通过计算混响的缓慢时变包络,对混响进行时间域的平稳化处理。对平稳化的混响信号滑动窗截取,对截取信号进行分数阶傅里叶变换,然后在分数阶傅里叶域进行滤波处理,再进行逆分数阶傅里叶变换恢复出时间域信号,最后输出该信号的能量。当滑动窗截取到目标回波信号时,窗内的混响噪声得到抑制,系统输出目标回波的能量,从而实现混响背景下的信号检测。通过计算机仿真和湖试实验结果,表明所提方法可以准确的在混响背景下检测到目标回波信号,并且在混响噪声背景条件下相比于匹配滤波器具有更好的检测性能。      

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.     

A cryptosystem based on deterministic phase masks and fractional Fourier transform deploying singular value decomposition

In this paper, an asymmetric cryptosystem has been proposed to enhance the security of DRPE. The traditional DRPE scheme is thus tweaked by using fractional Fourier transform (FrFT), a class of structured phase masks called as deterministic phase masks (DMKs) and deploying singular value decomposition (SVD). In specific, we propose to organise the encryption procedure by using two DMKs and FrFT, additionally deploying SVD. On the decryption front, the input image is recovered by utilising the inverse singular value decomposition (ISVD) and an angular portion of the deterministic phase masks. The use of FrFT for encryption and decryption would enhance the robustness of DRPE scheme. Deployment of SVD on our asymmetric cryptosystem provides three components for cipher image is yet another added feature that hardens the security of DRPE scheme. DMKs are formed by the deviation from conventional rectangular function and limited range values which delivers key components with reduced size, better performance and lower complexity. The capability study of defined method, includes analysis on SVD, histogram and correlation coefficient. Our system is subject to an occlusion attack and noise attack to evaluate its performance and reliability. Computational analysis outputs and security investigation are offered in aspect to determine the security potential of proposed system. Comparative results are shown for values of mean-square-error and peak-signal-to-noise ratio of DRPE schemes.     

Propagation of Airy beams through a hard-edged aperture

Based on the fact that a hard-edged aperture function can be expanded into a finite sum of complex Gaussian functions, we obtain the analytical formula for the propagation of the Airy beams in free space and through the fractional Fourier transformation (FrFT) system. According to the derived formulas, the propagation properties of the Airy beams in free space and through the FrFT plane with a hard-edged aperture are illustrated numerically.     

Sampling of fractional bandlimited signals associated with fractional Fourier transform

Fractional Fourier transform (FRFT) plays an important role in many fields of optics and signal processing. This paper considers the problem of reconstructing a fractional bandlimited signal with FRFT. We propose a novel reconstruction method for fractional bandlimited signals using the fractional Fourier series (FRFS). The advantage is that the sampling expansion can be deduced directly not based on the Shannon theorem. By utilizing the generalized form of Parseval’s relation for complex FRFS, we obtain the sampling expansion for fractional bandlimited signals with FRFT. We show that the sampling expansion for fractional bandlimited signals with FRFT is a special case of Parseval’s relation for complex FRFS.     

Fractional Fourier transform in information processing, tomography of optical signal, and Green function of harmonic oscillator

A review of the properties of the fractional Fourier transform, which is used in information processing, is presented in connection with the symplectic tomography transform of optical signals. The relationship between the Green function of the quantum harmonic oscillator and the fractional Fourier transform is elucidated. An analysis of electromagnetic signals which uses an invertible map of analytic signal onto the tomographic probability distribution is made. The formal connection of the analysis with the tomography method of measuring quantum states is considered. The relation to other methods of time-frequency quasidistributions (for example, the Ville-Wigner quasidistribution) characterizing a signal is studied. Paper submitted by author in English February 15, 1999.     

Tomographic Representation of Electrocardiogram Signals

We consider signals of an arbitrary nature in the tomographic representation and compare their tomographic representation and the fractional Fourier transform. Also we illustrate how to apply the tomograms and the identical Radon transform for processing medical electrocardiogram (ECG) signals. The first results obtained show that, in contrast to routine Fourier analysis, the Radon transform revealed additional information for patients with early signs of ischemic heart disease (IHD) compared to healthy persons.