Separation of overlapping linear frequency modulated (LFM) signals using the fractional fourier transform

Linear frequency modulated (LFM) excitation combined with pulse compression provides an increase in SNR at the receiver. LFM signals are of longer duration than pulsed signals of the same bandwidth; consequently, in many practical situations, maintaining temporal separation between echoes is not possible. Where analysis is performed on individual LFM signals, a separation technique is required. Time windowing is unable to separate signals overlapping in time. Frequency domain filtering is unable to separate signals with overlapping spectra. This paper describes a method to separate time-overlapping LFM signals through the application of the fractional Fourier transform (FrFT), a transform operating in both time and frequency domains. A short introduction to the FrFT and its operation and calculation are presented. The proposed signal separation method is illustrated by application to a simulated ultrasound signal, created by the summation of multiple time-overlapping LFM signals and the component signals recovered with ±0.6% spectral error. The results of an experimental investigation are presented in which the proposed separation method is applied to time-overlapping LFM signals created by the transmission of a LFM signal through a stainless steel plate and water-filled pipe.     

Asymmetric hybrid encryption scheme based on modified equal modulus decomposition in hybrid multi-resolution wavelet domain

In this paper, an asymmetric hybrid encryption scheme, using coherent superposition and modified equal modulus decomposition in a hybrid multi-resolution wavelet, is proposed. The hybrid multi-resolution wavelet is generated using fractional Fourier transform of multiple orders and Walsh transform. The fractional orders of the fractional Fourier transform increase the key space and hence provide additional strength to the cryptosystem. The designed scheme has a large key space to avoid brute-force attack and is non-linear in nature. The scheme is validated on grey-scale images. Computer-based simulations have been performed to verify the validity and performance of the proposed scheme against various attacks. Scheme's robustness to the special attack is also checked. Results show that single equal modulus decomposition with fractional Fourier transform and hybrid transform are vulnerable to the special attack, whereas the proposed scheme endures the special attack.     

基于偶树复小波和改进型阈值函数的降噪方法 及其应用

为更好地保留原有用信号信息,有效恢复强噪声背景下微弱故障信号,提出了一种基于对偶树复小波和改进型阈值函数的降噪方法,将其应用于机械故障诊断,取得了较好效果。运用对偶树复小波变换滤波器设计方法和改进型阈值函数,以实施降噪的具体步骤。该法充分利用了对偶树复小波变换的平移不变的优良特性,同时,改进型阈值函数与传统软、硬阈值降噪算法相比,克服了软阈值信号失真和硬阈值信号不连续、振荡等缺点。实验表明：此法有效去除了噪声,是一种较好的提取微弱故障信号的方法。     

Asymmetric encryption algorithm for colour images based on fractional Hartley transform

This paper presents a new scheme for encryption of single-channel colour images. The scheme uses amplitude- and phase-truncation approach to introduce non-linearity for enhanced security. Further, the colour image encryption is performed in the fractional Hartley domain, which is relatively less investigated. The encryption starts with an affine transform of each channel of the input colour image. Thereafter, one of the channels is considered as the input amplitude image while the other two are used as phase masks, one in the spatial and the other in the frequency domain. A detailed analysis of the scheme’s sensitivity to various encryption parameters has been carried out. In addition, security analysis of the scheme against attacks establishes the scheme’s robustness. The combined use of the affine transform and phase-truncation approach for colour image encryption in the fractional Hartley domain is attempted for the first time in this study. It is shown that the proposed scheme resists the special attack.     

Effective bias removal for fringe projection profilometry using the dual-tree complex wavelet transform

When reconstructing the three-dimensional (3D) object height profile using the fringe projection profilometry (FPP) technique, the light intensity reflected from the object surface can yield abruptly changing bias in the captured fringe image, which leads to severe reconstruction error. The traditional approach tries to remove the bias by suppressing the zero spectrum of the fringe image. It is based on the assumption that the aliasing between the frequency spectrum of the bias, which is around the zero frequency, and the frequency spectrum of the fringe is negligible. This, however, is not the case in practice. In this paper, we propose a novel (to our knowledge) technique to eliminate the bias in the fringe image using the dual-tree complex wavelet transform (DT-CWT). The new approach successfully identifies the features of bias, fringe, and noise in the DT-CWT domain, which allows the bias to be effectively extracted from a noisy fringe image. Experimental results show that the proposed algorithm is superior to the traditional methods and facilitates accurate reconstruction of objects' 3D models.     

Greyscale image encoding and watermarking based on optical asymmetric cryptography and variational image decomposition

In this paper, a novel greyscale image encoding and a watermarking scheme based on optical asymmetric cryptography and variational image decomposition (VID) are proposed. In this proposed scheme, the greyscale watermark is encoded into a noise-like pattern by the phase-truncated Fresnel transform (PT-FrT)-based optical asymmetric cryptography. The greyscale host image is decomposed into its cartoon part and texture part by the VID technique. After that, the encoded watermark is embedded into the host image’s texture part by a discrete wavelet transform (DWT) based fusion approach. The proposed scheme can achieve a better watermark invisibility and a higher robustness by embedding the watermark into the host image’s texture part. Additionally, the proposed scheme can achieve a high security, because the PT-FrT-based optical asymmetric cryptography can resist some common cryptographic attacks. The feasibility, robustness and security of the proposed scheme have been demonstrated by extensive experiments and comparison with other relevant image encoding and watermarking schemes.     

基于双树复小波变换的SiCP/Al复合材料加工表面质量评价

SiC_P/Al复合材料切削加工表面存在大量的凸起、凹坑和沟槽等缺陷,获取表面粗糙度信息时易将缺陷信息计入到粗糙度中,从而影响加工表面质量的合理评价。为提取加工表面粗糙度信息,合理评价SiC_P/Al复合材料加工表面质量,提出一种基于双树复小波变换（DT-CWT）的滤波方法。采用最小二乘法、高斯滤波法和DT-CWT变换的滤波方法对已加工表面进行粗糙度提取,从稳定性及受缺陷影响程度两个方面对三种方法的粗糙度信息提取效果进行对比。结果表明：基于DT-CWT的滤波方法具有较高的稳定性,并能够更有效区分表面粗糙度及缺陷信息,更适于SiC_P/Al复合材料加工表面粗糙度信息提取。应用基于DT-CWT的滤波方法,对不同Al基体的SiC_P/Al复合材料切削加工表面质量评价的结果表明：SiC_P/2024Al复合材料表面质量明显优于SiC_P/6063Al复合材料。     

基于线性调频信号二次相位变换的主动声呐目标速度估计

分数阶傅里叶变换常用于主动声呐线性调频信号的分析,通过搜索变换参数可以估计目标的相对速度.但是由于其参数搜索计算量偏大,在自主式水下航行器等计算力有限的小平台难以实时处理.针对该问题提出了一种基于二次相位变换的线性调频信号速度估计方法,根据多普勒频移后线性调频信号的二次相位变换的解析解,分析了二次相位变换后变换域频谱展...     

基于无迹卡尔曼滤波的动态贝叶斯小波变换在轴承故障诊断中的应用

针对工程实际中滚动轴承发生故障的类型具有典型性和故障信号具有冲击性,且振动信号的频率成分因外界环境的影响而变得极其复杂的特点,提出了一种基于负熵和无迹卡尔曼滤波的动态贝叶斯小波变换方法。该方法将SE(Squared Envelope) Infogram方法应用到无迹卡尔曼滤波方法(Unscented Kalman Filter, UKF)中,利用SE Infogram确定滤波器参数初值,即中心频率与带宽的初值,结合UKF对中心频率与带宽进行优化,以最优中心频率与带宽对振动信号进行滤波分析,对滤波后的信号进行包络解调分析,实现轴承微弱故障特征的提取。利用负熵指标代替以往研究所用的峭度指标,可以有效消除或削弱高峰值干扰的影响。最后,通过对仿真信号和轮对轴承试验信号对提出的方法进行了验证。结果表明,该方法能够有效提取强背景噪声下轴承外圈、内圈故障和滚动体故障,验证了该方法对轴承微弱故障诊断的有效性。     

Dimensional scalable lossless compression of MRI images using haar wavelet lifting scheme with EBCOT

Modern medical imaging requires storage of large quantities of digitized clinical data. To provide high bandwidth and to reduce the storage space, a medical image must be compressed before transmission. One of the best image compression techniques is using the Haar wavelet transform. The method of discrete cosine transform (DCT) is chosen to be the preprocessing scheme to identify the image frequency information and has excellent energy compaction property. The block coding algorithm uses a wavelet transform to generate the sub band samples, which can be quantized and coded. It is more robust to errors than many other wavelet‐based schemes. In this article, simulations are carried out on different medical Images and it demonstrates the performance in terms of peak signal to noise ratio (PSNR) & bits per pixel (BPP). Our proposed method is found to preserve information fidelity while reducing the amount of data. © 2014 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 24, 175–181, 2014     

Optical watermark scheme based on singular value decomposition ghost imaging and particle swarm optimization algorithm

An optical image watermarking algorithm, based on singular value decomposition (SVD) ghost imaging and multiple transforms, is designed. The watermark image is first encrypted by applying an SVD ghost imaging system, then the encrypted watermark is embedded into the cover image with the help of multiple transforms, including lifting wavelet transform (LWT), discrete cosine transform (DCT), discrete fractional angular transform (DFAT) and SVD. Four sub-band images are produced from the host image by LWT and DCT. The improved DFAT, whose scaling factors and parameter are optimized by particle swarm optimization algorithm, is operated in the new matrix. Afterwards, SVD is executed in the two-part image and the encrypted watermark is embedded in the host image by mutual operation of different matrices. Simulation results validate that the proposed watermark scheme is superior in the aspects of security, robustness and imperceptibility.     

基于无参数经验小波变换的风电齿轮箱故障特征提取

风电机组通常以集群规模化运行,机组结构复杂、振动测点多,所产生的振动数据量大,仅靠人工进行故障诊断具有较大挑战。提出基于无参数经验小波变换的风电齿轮箱故障特征提取方法,运用尺度空间方法和经验法则对振动信号的傅里叶谱进行自动分割,获得不同的滤波频带,据此设计一系列经验小波滤波器对信号进行分解和重构,获得不同频带下的经验模式,进一步采用裕度因子对分解后的经验模式进行排序,选取裕度因子最大的经验模式作为故障敏感模式;该方法能在无需预设任何参数的情况下对振动信号进行分解与故障特征提取,具有自适应性。风电试验台和实测风电齿轮箱故障案例验证了方法的有效性。     

抗打印扫描彩色图像水印算法

目的设计一种适用于彩色打印扫描图像的鲁棒性盲水印算法。方法结合四元数傅里叶变换及离散小波变换的优点,提出了一种双变换域全息水印算法。利用四元数傅里叶变换及离散小波变换,将全息水印信息分散嵌入到彩色宿主图像3个色彩分量的低频小波系数区域,而不引起大的图像失真,同时,算法实现了盲提取。结果算法满足不可见性要求,同时打印扫描实验证明,该算法具有抵抗打印扫描攻击的能力。结论结合四元数傅里叶变换及离散小波变换的双变换域水印算法,保留了2种变换域在处理彩色图像中的优点,在应用于打印扫描彩色图像时,效果比现有算法更好。     

Method to eliminate the zero spectra in Fourier transform profilometry based on a cost function

To increase the accuracy, speed, and robustness of 3D measurements in Fourier transform profilometry (FTP), this paper introduces a cost function according to the intrinsic features of the amplitude and frequency modulated (AF/M) signal and proposes two new algorithms to eliminate the background components of the fringe pattern based on the proposed cost function. Finally, the standard Fourier transform (FT) is used to calculate the phase of the pattern, which no longer contains background components. The two proposed methods are both data-driven and require no parameter adjustments in advance. Theoretical analysis and 80 experimental results show that the proposed cost function is valid. The results of more than 80 experiments with different types of fringe patterns, different carrier frequencies, and different noise variances with frequency overlap and sudden phase variation show that the proposed two methods are more accurate and robust than the 2D Gabor wavelet transform, the 2D Fan wavelet transform, and the 1D complex Morlet wavelet transform profilometry, and they are approximately 70 times faster than the 1D complex Morlet wavelet transform profilometry.     

基于倍福PLC的779型条盒包装机烟包制动系统的改造

目的 为解决FOCKE-FX 779型条盒包装机因故障引起的设备快速停机,复位启动后因烟包制动系统不稳定而造成的烟包擦碰、夹烟问题,设计一套基于倍福PLC的烟包挡块机构,辅助原机制动系统完成烟包的准确定位.方法 通过设计电气控制逻辑,在倍福PLC中完成控制程序编写,将原机制动气囊正压空气接通信号和烟包堆垛到位信号关联到挡块机构的控制电磁阀,实现烟包挡块机构与烟包制动系统的控制一致性,同时保证挡块机构按照设定控制次数7次,配合原制动气囊对烟包进行制动,增强制动系统的稳定性.结果 改造后的烟包制动系统稳定性得到明显提升,消除了因烟包定位不准出现擦碰而带来的产品质量隐患,779型条盒包装机的总停机率由5.08％降低到2.27％,设备"产质耗"指标得到明显改善.结论 烟包挡块机构工作稳定,功能可靠,后期免维护性强,满足了生产设备稳定性需求,能为同类型问题的处理提供参考和借鉴.     

Transceiver scheme for single-carrier frequency division multiple access implementing the wavelet transform and peak-to-average-power ratio reduction methods

Single-carrier frequency division multiple access (SC-FDMA) has been adopted as a possible air interface for future wireless networks. It combines most of the advantages of orthogonal frequency division multiple access (OFDMA) and the low peak-to-average-power ratio (PAPR) of single-carrier transmission. This study proposes a new transceiver scheme for SC-FDMA systems implementing the wavelet transform to decompose the transmitted signal into approximation and detail components. The approximation component can be clipped or companded whereas the detail component is left unchanged because of its sensitivity to noise. Wavelet filter banks at the transmitter and the receiver demonstrate the ability to reduce the distortion in the reconstructed signal while retaining all the significant features present in the signal. The performance of the proposed scheme is investigated with different PAPR reduction methods. Simulation results show that the proposed scheme with the hybrid clipping and companding method provides a significant performance enhancement when compared with the conventional SC-FDMA system, while the complexity of the system is slightly increased.     

Diagnostic ultrasound tooth imaging using fractional Fourier transform

An ultrasound contact imaging method is proposed to measure the enamel thickness in the human tooth. A delay-line transducer with a working frequency of 15 MHz is chosen to achieve a minimum resolvable distance of 400 μm in human enamel. To confirm the contact between the tooth and the transducer, a verification technique based on the phase shift upon reflection is used. Because of the high attenuation in human teeth, linear frequency-modulated chirp excitation and pulse compression are exploited to increase the penetration depth and improve the SNR. Preliminary measurements show that the enamel-dentin boundary creates numerous internal reflections, which cause the applied chirp signals to interfere arbitrarily. In this work, the fractional Fourier transform (FrFT) is employed for the first time in dental imaging to separate chirp signals overlapping in both time and frequency domains. The overlapped chirps are compressed using the FrFT and matched filter techniques. Micro-computed tomography is used for validation of the ultrasound measurements for both techniques. For a human molar, the thickness of the enamel layer is measured with an average error of 5.5% after compressing with the FrFT and 13.4% after compressing with the matched filter based on the average speed of sound in human teeth.     

基于Radon变换与Schur分解的彩色图像水印算法

目的 针对彩色图像盲水印算法较为复杂且抗旋转能力差等问题,结合矩阵Schur分解和Radon变换提出一种抗旋转攻击的彩色图像盲水印算法。方法 该算法首先提取彩色宿主图像的U通道图像,其次对U通道图像经NSCT变换后的低频分量进行分块处理,将每个像素块分解为对称矩阵和反对称矩阵,最后对每块对称矩阵进行Schur分解,将二值水印嵌入至分解后上三角矩阵的最大特征值中。提取水印信息时,利用Randon变换对含水印图像进行几何校正后再进行水印提取操作。结果 文中算法提取水印相似度较高,其NC值达到0.9414;结构相似性较高,其SSIM值达到0.9183。结论 该水印算法在常规信号处理攻击、抗旋转攻击下均具有极强的鲁棒性。     

解析小波及在振动分析中的应用

本文在希尔伯特变换和小波定义的基础上,提出解析小波及解析小波变换,分析了它的一个重要性质即对信号可实现正交滤波、提取包络。最后给出了小波在轴承振动共振解调应用的实例。     

基于脊波变换的扩频水印算法

针对脊波变换域比小波变换域更适合表示图像线状边缘的奇异性的特征,本文设计出一种新的图像水印算法,即将图像分块脊波变换,在脊波变化域上的高频系数中加性地嵌入经零均值互不相关伪随机序列扩频调制后的水印。实验结果表明,本文算法不仅可以抵抗如压缩、加噪、滤波和剪切等各种常见攻击,还能抵抗图像灰度增强和减弱攻击,与小波域水印算法的比较也说明了本文算法的优势。