关于DFT中的延拓原理及计算结果物理意义的一些讨论

在信号分析领域,DFT（离散傅立叶变换）是一个常见术语。但关于DFT中的延拓原理及计算结果的物理意义作者始终感到有些迷惑。而且,关于DFT及其逆变换IDFT的计算目前存在两套公式,这两套公式并存的原因是什么,它们的物理意义区别在哪里,作者始终未在文献中得到明确和满意的答案。本文在查阅了较多文献的基础上,对这些问题作了深入的研究,分析和澄清了以前对这些问题的一些模糊认识,对DFT中的延拓提出了一种新的见解（零延拓观点）,从而较合理地描述出了DFT两个公式计算结果的明确物理意义。     

基于频域导频时域处理的OFDM系统信道估计算法

针对正交频分复用(OFDM)系统,提出了一种适用于时变信道的信道估计算法。该方法利用频域导频,经离散傅立叶变换(DFT),获得的信道冲击响应等效于利用频域导频对应的时域序列和接收信号进行循环相关获得的信道冲击响应。因此,避免了在时域采用复杂的循环相关运算。同时,通过消除频域导频时域序列的自相关误差,能有效降低由DFT谱泄漏导致的信道估计误差。仿真和分析表明,在时变多径衰落信道下,提出的信道估计方法的性能比传统的基于DFT的算法和频域维纳滤波算法有明显提高。     

一种小波和余弦变换组合域内鲁棒的自适应零水印算法

克服了传统数字水印方案在嵌入水印时要对原始图像数据进行一定修改从而导致嵌入水印图像质量下降的局限性,提出了一个基于离散小波变换和离散余弦变换组合域内鲁棒的自适应零水印算法.算法首先对原始数字图像进行适当层次的离散小波变换,并对得到的小波逼近子图进行离散余弦变换,然后依据待嵌入二值字符水印的大小和相应的系数差值要求自适应...     

基于DCT 的三维网格模型数字水印算法

基于离散余弦变换(DCT)技术和扩频通信技术提出三维模型稳健水印嵌入算法. 算法将原始的一维二值水印序列利用扩频通信技术生成可以直接嵌入的水印信息;利用主成分分析(PCA)方法,将原始模型变换到仿射(旋转、 平移和均匀缩放)不变空间中,选取模型顶点到其中心距离作为水印嵌入单元,基于双极性量化嵌入单元离散余弦变换系数的方法嵌入水印并实现水印的盲提取. 该算法嵌入的水印信息具有不可见性,能够抵抗模型的旋转、平移、均匀缩放等常见攻击. 仿真实验验证了算法的有效性.     

基于二值离散运算的自适应数字图像水印算法

论文提出了一种在小波变换域内基于二值离散运算的自适应数字图像水印算法.算法利用人眼视觉掩盖特性,根据要嵌入的伪随机数水印长度自适应地选择原始图像小波逼近子图中纹理信息丰富的图像子块,通过对这些图像子块系数的二值离散修改实现水印的嵌入,水印检测无需原始图像.由于水印的嵌入与检测是基于二值离散运算,所嵌入的水印具有很理想的鲁棒性,能免疫于常规图像处理方法的有限攻击.同时,嵌入的水印具有理想的隐蔽效果,完全满足水印不可觉察性要求.     

一种低复杂度的DFT-S-OFDM系统迭代检测算法

针对LTE上行的单载波频分多址系统--离散傅立叶变换扩频的正交频分复用(DFT-S-OFDM)系统,提出了一种低复杂度的迭代检测实现方法.由于传统方法根据发射机与信道级联系统的等效传输矩阵,完成最小均方误差(MMSE)的迭代检测,但非对角矩阵求逆复杂度较高,因此,所提出的新方法对发送端DFT扩频后的信号先进行单点的MMSE检测,然后根据逆离散傅立叶变换(IDFT)解扩后的后验均值和方差等效得到输出外信息比特似然比.仿真结果表明,所提出迭代检测接收算法的性能与传统方法相近,而其实现复杂度则有较大降低.     

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。     

基于小波与DCT域易损水印算法研究

易损水印是数字媒体内容完整性保护重要技术手段。文中用离散小波变换(DWT)和离散余弦变换(DCT)相结合算法实现对图像内容完整性保护。通过MATLAB仿真实验表明该算法有较强嵌入检测能力。     

一种新的自适应量化数字音频水印算法

文章中提出了一种新的自适应量化数字音频水印算法，该算法首先将视觉可辨的二值水印图像降维成一维水印序列，并对水印序列进行随机置乱与BCH纠错编码，再将原始数字音频信号划分成音频数据段，最后选择音频段进行快速傅立叶变换(FFT)，并依据人类听觉系统(HAS)模型自适应确定量化步长量化FFT系数嵌入水印信息。该算法提取水印信息时不需要原始数字音频信号。仿真结果表明：该自适应量化数字音频水印算法不仅具有较好的透明性，而且对诸如叠加噪声、有损压缩、低通滤波、重新采样等攻击均具有较好的鲁棒性。     

一种非盲检测的二维工程图数字水印算法

提出了一种基于傅立叶描述子的二维工程图的数字水印方法。该方法通过从工程图中提取特定顶点构造出复值信号量再进行傅立叶变换,通过对变换后的傅立叶变换系数幅值进行调制,嵌入符合N(0,1)分布的伪随机水印序列。通过实验确定水印检测中相关测试的阀值,从而根据相关值检测水印的存在与否。实验结果证明这种方法对平移、旋转、添加及删除部分实体等攻击具有良好的鲁棒性。     

3种频域数字水印算法的分析和比较

阐述了离散傅里叶算法(DFT)、离散余弦算法(DCT)、离散小波变换算法(DWT)这3种常用的频域数字水印算法的原理,并分别采用不同算法对数字图像进行了水印嵌入,检测其峰值信噪比(PSNR)和相关系数(NC)的值,分析并比较了这3种算法的优缺点,证明了离散小波变换在频域算法中能够得到最好的效果。     

Increase in the accuracy of evaluating spectra of discrete signal realization

An improved algorithm for calculating spectra with the use of a rapid Fourier transform and quadrature equations of the trapezium and Simpson’s methods is considered. The relative error of calculation by comparing the relative deviation of a continuous spectrum of final realization of the signal from spectra, found by means of improved algorithms at a discrete set of frequencies, is analyzed. A more precise initial estimation of a spectrum is obtained using the improved calculation algorithms. __________ Translated from Metrologiya, No. 8. pp. 27–31, August, 2007.     

Simple method for simultaneously measuring the magnitude and direction of 2D in-plane displacement in white-light speckle photography

A simple method for simultaneously measuring the magnitude and direction (or argument) of a 2D in-plane displacement vector is presented. The theoretical mechanism for extracting the desired displacement signal from random noises produced by the nonoverlapping area of the recorded specklegrams of the test specimen surface is derived in detail. This procedure is realized by establishing a 1D displacement model in a white-light speckle photographic system using discrete Fourier transform shifting theorem. Results of the computer simulation and experiment show that the present method exhibits advantages such as convenient displacement direction determination, better robustness and wider measurement range than those of the traditional fringe analysis-based method. These characteristics make the proposed method a potential approach in practical applications.     

Discrete Fourier Transform for Short Samples in the Presence of Noise

We consider the dependences of the error of a discrete Fourier transform on the length of the realization of the considered signal. The introduction of a procedure of making a preliminary determination of the period makes it possible to consider signals in short samples and this significantly reduces the computing and apparatus costs.     

Two-Dimensional Interpolation Criterion Using DFT Coefficients

In this paper, we address the frequency estimator for 2-dimensional (2-D) complex sinusoids in the presence of white Gaussian noise. With the use of the sinc function model of the discrete Fourier transform (DFT) coefficients on the input data, a fast and accurate frequency estimator is devised, where only the DFT coefficient with the highest magnitude and its four neighbors are required. Variance analysis is also included to investigate the accuracy of the proposed algorithm. Simulation results are conducted to demonstrate the superiority of the developed scheme, in terms of the estimation performance and computational complexity.     

Discrete chirp Fourier transform based analysis of reconstructed interference fields in digital holographic interferometry

In digital holographic interferometry, the information on the measurand is encoded in the phase of the reconstructed interference fields. This letter introduces a new method for the analysis of the reconstructed interference fields using discrete chirp Fourier transform (DCFT). In the proposed method, the interference phase to be estimated is modelled as a piecewise polynomial signal. Each row of the reconstructed interference field is subsequently divided into several segments, and a parametric estimation of the phase using DCFT is performed in each segment. We show that the phase estimated in this manner is accurate and continuous, thereby enabling us to bypass the commonly followed practices of filtering and 2-D phase unwrapping. Simulation and experimental results substantiate the effectiveness of the proposed method.     

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。     

基于归一化的全息水印技术

提出了一种结合了归一化技术和全息技术的数字水印技术。首先,利用归一化技术对图像作归一化运算,同时利用全息技术将水印二值图处理为全息图;其次,取归一化后图像分块离散余弦变换的中频系数,对中频系数所组成的矩阵作离散小波变换;最后将全息图嵌入到离散小波变换的低频分量中。由于图像归一化技术具有抗仿射变换的性能,同时全息技术具有很强的抗裁切的性能,所以此数字水印技术具有很强的抗仿射变换的性能,可以广泛的用于数字作品的版权保护。     

Method of compact archiving of signals in time delay spectrometry

Using a time delay spectrometry system as an example, we consider ways of compactly archiving discrete signals with distinct spectral peaks in the low-frequency range.Translated from Izmeritelnaya Tekhnika, No. 10, pp. 23–26, October, 2004.     

Flexible multiple-image encryption algorithm based on log-polar transform and double random phase encoding technique

We present a novel multiple-image encryption algorithm by combining log-polar transform with double random phase encoding in the fractional Fourier domain. In this algorithm, the original images are transformed to annular domains by inverse log-polar transform and then the annular domains are merged into one image. The composite image is encrypted by the classical double random phase encoding method. The proposed multiple-image encryption algorithm takes advantage of the data compression characteristic of log-polar transform to obtain high encryption efficiency and avoids cross-talk in the meantime. Optical implementation of the proposed algorithm is demonstrated and numerical simulation results verify the feasibility and the validity of the proposed algorithm.