Watermarking Digital 3-D Volumes in the Discrete Fourier Transform Domain

In this paper, a robust blind watermarking method for 3-D volumes is presented. A bivalued watermark is embedded in the Fourier transform magnitude of the 3-D volume. The Fourier domain has been selected because of its scaling and rotation invariance. Furthermore, in order to decrease the detection time, a special symmetry of the watermark is exploited. The proposed method is proven to be resistant to 3-D lowpass filtering, noise addition, scaling, translation, cropping and rotation. Experimental results prove the robustness of this method against the above-mentioned attacks.     

基于修正离散傅里叶变换的频域卷积混合盲分离

针对频域卷积混合盲分离,依据所导出的卷积混合信号每帧的频域表示模型,提出了一种最小均方误差意义下的最优变换--修正离散傅里叶变换,用于代替频域卷积混合盲分离中常用的离散傅里叶变换.在每个频率片上,卷积混合信号的修正离散傅里叶变换系数在最小均方误差意义下最接近于源信号频谱的瞬时混合.相对于离散傅里叶变换系数,现有瞬时混合盲分离算法能从修正离散傅里叶变抉系数中更精确地估计各频率片上分离矩阵,从而提高现有频域卷积混合盲分离算法的分离性能.仿真结果证明了修正离散傅里叶变换对现有频域卷积混合盲分离算法的有效性.     

基于连续傅里叶变换计算离散傅里叶变换的一种算法

介绍一种利用连续信号的傅里叶变换计算离散序列离散傅里叶变换的算法,给出了这种算法的应用实例,并对此算法的有效性进行了验证.     

离散Fourier变换并行算法综述

本文详细介绍了1－D DFT精确计算的六步框架并行算法和按位并行计算法,以及按位计算法在2－D Mesh和Torus上的模拟实现,同时介绍了近似计算中的基于奇异值分解的算法和基于快速多极方法的算法。对于2－D DFT,本文介绍了并行行列算法和并行多项式变换算法,并分析了其优缺点。     

一种基于FFT计算离散小波变换的方法

将小波变换和快速傅里叶变换（FFT）方法相结合,分析研究了用快速傅里叶变换计算离散小波变换的方法,总结变换结果和滤波器长度之间的移位关系,并提出通过把输入信号信号循环移位,实现完全重构的方法。这种方法计算的时间复杂度和快速傅里叶变换相当。     

Implementation Issues in the Fourier Transform Algorithm

The Fourier transform of Boolean functions has received considerable attention in the last few years in the computational learning theory community, and has come to play an important role in proving many important learnability results. The aim of this work is to demonstrate that the Fourier transform techniques are also a useful and practical algorithm, in addition to having many interesting theoretical properties. In fact, this work was prompted by a genuine problem that was brought to our attention; researchers at a company were trying to come by a method to reverse-engineer a state-free controller. They had the capability of querying the controller on any input, thus setting them in the membership query model, in which the Fourier transform algorithm is set.In order to keep the algorithm run-time reasonable and still produce accurate hypotheses, we had to perform many optimizations. In the paper we discuss the more prominent optimizations, ones that were crucial and without which the performance of the algorithm would severely deteriorate. One of the benefits we present is the confidence level the algorithm produces in addition to the predictions. The confidence level measures the likelihood that the prediction is correct.     

基于离散傅里叶变换的姿态算法研究

捷联惯性导航系统已经在航空航天的各个领域中获得了广泛应用.捷联惯性导航系统根据固定在载体上的陀螺仪输出的角度或者角速率信息实时计算载体相对于惯性参考系的姿态变换矩阵.为确保姿态实时计算精度,根据信号处理中信号重构的相关理论,利用角速率信息求解四元数姿态微分方程的离散傅里叶方法,并以典型圆锥运动作为输入条件对算法进行仿真.仿真结果表明,提出方法在高动态角运动环境下的解算精度要优于四阶龙格库塔算法,由圆锥运动引起的俯仰角算法漂移误差也要小于四阶龙格库塔方法.     

Computing the Discrete Fourier Transform on a Hexagonal Lattice

The computation of the Discrete Fourier Transform for a general lattice in ℝ ^d can be reduced to the computation of the standard 1-dimensional Discrete Fourier Transform. We provide a mathematically rigorous but simple treatment of this procedure and apply it to the DFT on the hexagonal lattice.

基于离散分数傅里叶变换的SVG数字水印技术

提出了一种基于离散分数傅里叶变换(DFRFT)的SVG图形水印算法,用于SVG的版权保护.将水印嵌入到SVG图形控制点坐标构造的复数信号的离散分数傅里叶变换频谱中.经实验结果验证,该算法具有较强的透明性,对于通常的图形几何变换以及局部修改攻击,均有令人满意的鲁棒性.     

A Novel Approach to Fast Discrete Fourier Transform

Discrete Fourier transform (DFT) is an important tool in digital signal processing. In the present paper, we propose a novel approach to performing DFT. We transform DFT into a form expressed in discrete moments via a modular mapping and truncating Taylor series expansion. From this, we extend the use of our systolic array for fast computation of moments without any multiplications to one that computes DFT with only a few multiplications and without any evaluations of exponential functions. The multiplication number used in our method isO(Nlog₂ N/ log₂log₂ N) superior toO(Nlog₂ N) in FFT. The execution time of the systolic array is onlyO(Nlog₂ N/ log₂log₂ N) for 1-D DFT andO(N^k) fork-D DFT (k⩾2). The systolic implementation is a demonstration of the locality of dataflow in the algorithms and hence it implies an easy and potential hardware/VLSI realization. The approach is also applicable to DFT inverses.     

扫频滤波器在分数阶Fourier域的实现

在研究分数阶Fourier城滤波基本理论的基础上,提出了扫频滤波器的工作原理和系统表示.通过对LFM信号和高斯白噪声分离效果仿真,发现分离后信噪比得到了较大提高.仿真实验表明,所提出的分数阶城扫频滤波器在有噪声干扰的情况下能得到较好的干扰分离和滤波效幕.     

System Identification in the Short-Time Fourier Transform Domain With Crossband Filtering

In this paper, we investigate the influence of crossband filters on a system identifier implemented in the short-time Fourier transform (STFT) domain. We derive analytical relations between the number of crossband filters, which are useful for system identification in the STFT domain, and the power and length of the input signal. We show that increasing the number of crossband filters not necessarily implies a lower steady-state mean-square error (mse) in subbands. The number of useful crossband filters depends on the power ratio between the input signal and the additive noise signal. Furthermore, it depends on the effective length of input signal employed for system identification, which is restricted to enable tracking capability of the algorithm during time variations in the system. As the power of input signal increases or as the time variations in the system become slower, a larger number of crossband filters may be utilized. The proposed subband approach is compared to the conventional fullband approach and to the commonly used subband approach that relies on multiplicative transfer function (MTF) approximation. The comparison is carried out in terms of mse performance and computational complexity. Experimental results verify the theoretical derivations and demonstrate the relations between the number of useful crossband filters and the power and length of the input signal     

基于游程检测与快速傅里叶变换的加密比特流识别

为获得链路层中的加密与未加密比特流样本,首先提出了基于游程检测方法的链路层加密比特流识别方案,解决了未知网络环境下的加密与未加密比特流样本获取问题.同时,采用快速傅里叶变换分别对加密与未加密比特流样本进行处理,根据最大差异原则确定了快速傅里叶变换结果的特征点位置,并基于正态分布原理确定了特征点的取值,建立了特征模板.最后,以某无线网络链路层加密比特流为识别对象,对提出的方案的有效性进行了验证.结果表明,该方案对链路层加密与未加密比特流的识别率均可达到95％以上.     

图像小波分解的FPGA实现

小波分析作为信号处理领域中的一种重要方法,在信号处理、模式分析和图像处理等方面得到了广泛的应用。然而小波变换巨大的运算量却使得它在实时处理领域中的应用受到了限制。本文根据离散小波变换的Mallat算法,提出了一种EPGA实现高速小波分解的方法,设计出的小波变换模块结构清晰而且规则,易于级联,可实现多级变换。同时,,运算精度和处理速度均满足实时图像处理的要求。     

基于Hermite特征矢量的二维离散分数维变换

分数维变换（FRFT）是分析时变信号的强有力工具之一,它可实现信号在时频域中任何角度的旋转。由于分数维变换的重要性,实现离散分数维变换（DFRFT）则显得很重要。根据DFRFT具有DFT的Hermite特征矢量这一特性,对二维离散信号进行二维DFRFT分析,此方法即可满足旋转特性,具又可获得与连续FRFT相似的结果。     

基于傅氏和小波变换的图像频域处理研究

信号和系统的分析方法有两种,即时域分析方法和频域分析方法.人们往往习惯于在时域中理解、分析和处理信号,而对信号在频域中的表示,尤其是在时域和频域中均为二维的图像信号处理,则显得有些力不从心,本文研究了基于傅氏变换和小波变换的图像信号频域处理方法,并对实验过程进行了完整的分析.     

提升小波变换的FPGA设计与实现

根据1996年Sweldens等人提出的提升小波变换方法,设计了一种有效的JPEG2000 CDF(2,2)整数小波变换的VL-SI实现结构,并对小波系数的变化范围进行了分析.用VHDL对该结构进行基于FPGA实现的可综合描述,并用EDA软件进行了仿真和综合,硬件仿真结果和软件Matlab实现结果完全一致.     

基于M周期离散分数傅里叶变换的数字水印算法*

由于DFRFT同时包含了频域与时域的信息,在水印的嵌入与提取算法中,根据所取DFRFT的幂次α的不同结果也不一样,增强了水印的保密性。在仿真实验的结果中表明用DFRFT实现的数字水印算法比用傅里叶变换及小波变换实现的数字 算法具有更好的安全性。     

基于改进的离散傅里叶变换图像分割算法研究

研究图像分割特征提取优化问题。由于外界信号噪声等问题而引起图像分割分辨率低,清晰度不高,提取图像的主要特征目标是图像分割中关键的技术,针对传统的图像特征提取分割算法无法完成对图像关键特征信息适度提取,另外图像分割计算复杂,为了有效的对图像进行分割,提出了一种改进的离散傅里叶变换的图像分割算法。采用傅里叶变换算法对图像中感兴趣的区域进行分割出来后,对各个分割区域特点进行描述并组成一定的结构,从而获得最优图像分割结果。仿真结果表明,改进的算法可以有效地提取复杂图像区域中的特征信息,分割效果明显,提高了图像分割的分辨率和清晰度。     

基于离散傅里叶变换的数字高速测频

为了克服传统的过零检测等数字测频方法的缺点,设计了一种基于离散傅里叶变换（DFT）的快速频率测量电路,满足无源定位系统中低信噪比、高脉冲密度环境的实时频率测量的需求。阐述了基于可编程门阵列的DFT算法的实现方法及谱峰的搜索方法,给出了硬件结构形式。该算法电路结构比采用快速傅里叶变换（FFT）的算法硬件结构具有更快的测频速度。