Recursive sliding discrete Fourier transform with oversampled data

The Discrete Fourier Transform (DFT) has played a fundamental role for signal analysis. A common application is, for example, an FFT to compute a spectral decomposition, in a block by block fashion. However, using a recursive, discrete, Fourier transform technique enables sample-by-sample updating, which, in turn, allows for the computation of a fine time–frequency resolution. An existing spectral output is updated in a sample-by-sample fashion using a combination of the Fourier time shift property and the difference between the most recent input sample and outgoing sample when using a window of finite length. To maintain sampling-to-processing synchronisation, a sampling constraint is enforced on the front–end hardware, as the processing latency per input sample will determine the maximum sampling rate. This work takes the recursive approach one step further, and enables the processing of multiple samples acquired through oversampling, to update the spectral output. This work shows that it is possible to compute a fine-grained spectral decomposition while increasing usable signal bandwidths through higher sampling rates. Results show that processing overhead increases sub-linearly, with signal bandwidth improvement factors of up to 6.7× when processing 8 samples per iteration.     

基于余弦变换和小波变换的数字水印算法

在互联网络技术和多媒体技术普及的今天,数字水印技术已经成为目前信息安全技术领域的一个重要方向。本文提出了一种基于离散余弦变换和离散小波变换的数字水印算法,以一个长度为n服从N(0,1)正态分布的随机数序列作为水印信号嵌入到图像最具感知意义的频率部分。实验结果表明,此算法具有良好的视觉效果和鲁棒性。     

一种基于zigzag扫描的DCT鲁棒数字盲水印算法

针对提高水印算法的鲁棒性进行研究,提出一种基于zigzag扫描的DCT鲁棒数字盲水印算法。算法对分块后DCT域的中、低频系数进行zigzag扫描得到一维数列,利用每个数列数学范数比值和量化索引调制原理实现数字水印的嵌入,然后通过最小距离公式对水印提取。与其他算法相比,实验结果显示算法能够抵抗多种攻击,具有较好的透明性与鲁棒性。水印提取过程不需要原载体图像,实现水印信息盲提取。     

Fast 2D discrete cosine transform on compressed image in restricted quadtree and shading format

Given a compressed image in the restricted quadtree and shading format, this paper presents a fast algorithm for computing 2D discrete cosine transform (DCT) on the compressed grey image directly without the need to decompress the compressed image. The proposed new DCT algorithm takes O(K²logK+N²) time where the decompressed image is of size N×N and K denotes the number of nodes in the restricted quadtree. Since commonly K<N, the proposed algorithm is faster than the indirect method by decompressing the compressed image first, then applying the conventional DCT algorithm on the decompressed image. The indirect method takes O(N²logN) time.     

离散余弦变换域图像数字水印技术

基于变换域的水印技术由于其较好的鲁棒性和安全性成为了目前水印技术领域研究的热点.详细地分析了目前离散余弦变换域的图像数字水印技术,对离散余弦变换域的算法进行分类比较,并对拉伸因子a的取值以及对图像水印嵌入效果的影响进行了讨论,提出了一些有效的水印方案,实验结果表明了其对常见攻击的抵抗性.分析和讨论了DCT变换域图像数字水印技术在嵌入水印方面的实现.     

基于加窗型DCT-Ⅳ的OFDM系统的信道估计算法

在总结传统的基于离散傅里叶变换（DFT）的正交频分复用（OFDM）系统的信道估计算法的基础上,提出了一种新的基于加窗型的第四类离散余弦变换（DCT-Ⅳ）的OFDM系统的信道估计算法。该算法利用DCT变换的对称特性消除边缘效应,并且使用加窗抑制信道冲激响应的频谱泄露,然后用低通滤波器消除信道高斯白噪声的干扰。仿真结果表明：在多径衰落信道下,该算法优于基于DFT的信道估计算法,是一种可行而且有效的信道估计算法。     

基于离散余弦变换彩色图像的数字水印研究

为了在彩色图像中嵌入彩色数字水印,同时保持原始彩色图像的完整性及健壮性,提出基于空间域和频率域间转换,配合RGB色彩系统,利用离散余弦变换将图像的空间域表示转换为频率域,将彩色数字水印频域系数经适当处理后嵌入图像的低频部分,使嵌入的彩色数字水印能抵抗各种图像处理时的破坏.实验结果表明:应用该方法嵌入彩色数字水印,不仅不破坏原始彩色图像品质,而且能抵抗外界的破坏,成功取回所嵌信息.     

基于离散余弦变换基函数迭代的人脸图像识别

使用非线性混沌方法处理与识别图像的研究工作逐渐增多,已有文献给出了一种 将正弦函数作为辅助函数与图像构造动力系统,迭代生成混沌吸引子作为图像特征。为进一步 探究图像吸引子作为图像的特性,改进识别效果,使用离散余弦变换(DCT)基函数矩阵代替正 弦函数,迭代生成近似混沌吸引子,用于人脸识别。首先,研究分析了DCT 基函数矩阵的多样 性与振荡特性;然后利用DCT 基函数矩阵与图像矩阵构造迭代表达式,通过给出的迭代算法使 其产生吸引子,再对吸引子进行快速傅里叶变换,计算相关系数,识别人脸图像。对于Yalefaces 图像库,每幅图像都参加训练,识别率可以达到100%,当使用每组前5 幅图像训练提取特征, 识别率可以超过85%;对于CMU PIE 数据库,每幅图像都参加训练,识别率可以超过99%。 该吸引子方法可以作为一种图像底层特征提取方法,有待于进一步深入研究。     

Feature extraction using discrete cosine transform and discrimination power analysis with a face recognition technology

Discrete cosine transform (DCT) is a powerful transform to extract proper features for face recognition. After applying DCT to the entire face images, some of the coefficients are selected to construct feature vectors. Most of the conventional approaches select coefficients in a zigzag manner or by zonal masking. In some cases, the low-frequency coefficients are discarded in order to compensate illumination variations. Since the discrimination power of all the coefficients is not the same and some of them are discriminant than others, so we can achieve a higher true recognition rate by using discriminant coefficients (DCs) as feature vectors. Discrimination power analysis (DPA) is a statistical analysis based on the DCT coefficients properties and discrimination concept. It searches for the coefficients which have more power to discriminate different classes better than others. The proposed approach, against the conventional approaches, is data-dependent and is able to find DCs on each database. The simulations results of the various coefficient selection (CS) approaches on ORL and Yale databases confirm the success of the proposed approach. The DPA-based approaches achieve the performance of PCA/LDA or better with less complexity. The proposed method can be implemented for any feature selection problem as well as DCT coefficients. Also, a new modification of PCA and LDA is proposed namely, DPA-PCA and DPA-LDA. In these modifications DCs which are selected by DPA are used as the input of these transforms. Simulation results of DPA-PCA and DPA-LDA on the ORL and Yale database verify the improvement of the results by using these new modifications.     

Fast 2-D 8×8 discrete cosine transform algorithm for image coding

A new fast two-dimension 8×8 discrete cosine transform (2D 8×8 DCT) algorithm based on the charac-teristics of the basic images of 2D DCT is presented. The new algorithm computes each DCT coefficient in turn more independently. Hence,the new algorithm is suitable for 2D DCT pruning algorithm of prun-ing away any number of high-frequency components of 2D DCT. The proposed pruning algorithm is more efficient than the existing pruning 2D DCT algorithms in terms of the number of arithmetic opera-tions,especially the number of multiplications required in the computation.     

Moving-window discrete Fourier transform

The moving-window discrete Fourier transform (MWDFT) is a dynamic spectrum analysis in which the next analysis interval differs from the previous one by including the next signal sample and excluding the first one from the previous analysis interval (Dillard in IEEE Trans Inform Theory 13:2–6, 1967, Comput Elect Eng 1:143–152, 1973, USA Patent 4023028, May 10, 1977). Such a spectrum analysis is necessary for time–frequency localization of analyzed signals with given peculiarities (Tolimieri and An in Time–frequency representations. Birkhauser, Basel, 1998). Using the well-known fast Fourier transform (FFT) towards this aim is not effective. Recursive algorithms which use only one complex multiplication for computing one spectrum sample during each analysis interval are more effective. The author improved one algorithm so that it is possible to use only one complex multiplication for computing two, four, and even eight (for complex signals) spectrum samples simultaneously. Problems of realization and application of the MWDFT are also considered in the paper.     

Greedily computing associative aggregations on sliding windows

We present an algorithm for combining the elements of subsequences of a sequence with an associative operator. The subsequences are given by a sliding window of varying size. Our algorithm is greedy and computes the result with the minimal number of operator applications.     

基于DCT域的高压缩图像去块效应算法

块离散余弦变换(B lock D iscrete Cosine Transform)的主要缺点是在低比特率时其恢复图像的块边界上会出现明显可见的方块效应,降低了图像的视觉质量.为了尽量消除块效应并保护图像的边缘信息提出了一种基于DCT域的块效应消除算法.该算法充分利用了人类视觉系统(Hum an V isual System)特性,建立了块效应模型并给出一个简便的检测边缘标准,对于平滑区,对影响块效应的参数进行修正,然后用线性函数块代替阶跃函数块去除块效应,最后再对更新块和纹理区在DCT域中进行后滤波.仿真结果验证了本文算法的有效性.     

适用于分布式视频编码框架的整数离散余弦变换算法

鉴于H.264的整数离散余弦变换(DCT)算法及其量化方法复杂度高,难以直接应用于分布式视频编码(DVC)框架的现状,提出了一种基于大跨度定长(步长为2的正整数次方)量化的整数DCT算法及变换基生成方法。该算法充分地利用整数DCT基的可伸缩特性寻找最迎合硬件工作原理的变换基,在保证“小”变换基的同时将编码器的伸缩量化阶段“转移”到解码器一端以降低编码器复杂度。在“转移”过程中,该算法利用DCT系数饱和放大保证图像质量,利用DCT系数的溢出上限保证算法的可靠性,通过减小基偏差提高压缩性能。实验结果表明,与H.264对应模块相比,该算法的量化方式便于位平面提取,在图像质量达到准无损压缩的前提下将编码器的伸缩量化阶段的运算量缩减至16次整型常量加法运算,图像质量与压缩率的性价比提升了23.9%,适用于分布式编码框架。     

基于离散小波变换和离散余弦变换域的扩频水印盲提取算法

针对扩频水印的盲提取问题,提出了一种在数字音频中扩频水印的盲提取算法。算法将扩频后的水印信息隐藏在音频文件小波分解的低频系数再做离散余弦变换(DCT)后的第5个系数中。提取时在扩频序列及其长度均未知的情况下,采用二次谱和奇异值分解(SVD)的方法对嵌入时使用的扩频参数进行估计,实现了数字音频中扩频水印的盲提取。仿真实验表明,所提算法在未知扩频参数的情况下能提取出归一化系数(NC)为1的水印图像并且水印的鲁棒性也很强,在加噪、低通滤波等攻击下估计出的扩频序列正确率能达到90%以上,恢复出的水印图像清晰可见,归一化系数都在0.98以上。     

A comparison of fast inverse discrete cosine transform algorithms

The discrete cosine transform (DCT) is often applied to image compression to decorrelate picture data before quantization. This decorrelation results in many of the quantized transform coefficients equaling zero, hence the compression gain. At the decoder, very few nonzero quantized transform coefficients are received, so the input to the inverse DCT is sparse, greatly reducing the required computation. This paper describes different styles of implementations of fast inverse DCTs designed especially for sparse data and compares them on workstation processors.This research has been sponsored by ARPA     

基于量化的二维DCT优化算法研究

DCT变换广泛应用于图像压缩算法中,在大多数情况下最有用的信息集中在DCT系数的低频序列中,而对那些经过量化后为零的系数进行计算,不但费时且计算量大幅增加。据此提出了两种新的二维DCT快速截取算法,使得计算一个8×8的二维DCT变换所需的乘法运算次数减少了60％,加法运算次数减少了77％。经过实验验证该算法在峰值信噪比PSNR值损失很少的情况下,显著地降低了算法的复杂度。     

Sketching asynchronous data streams over sliding windows

We study the problem of maintaining a sketch of recent elements of a data stream. Motivated by applications involving network data, we consider streams that are asynchronous, in which the observed order of data is not the same as the time order in which the data was generated. The notion of recent elements of a stream is modeled by the sliding timestamp window, which is the set of elements with timestamps that are close to the current time. We design algorithms for maintaining sketches of all elements within the sliding timestamp window that can give provably accurate estimates of two basic aggregates, the sum and the median, of a stream of numbers. The space taken by the sketches, the time needed for querying the sketch, and the time for inserting new elements into the sketch are all polylogarithmic with respect to the maximum window size. Our sketches can be easily combined in a lossless and compact way, making them useful for distributed computations over data streams. Previous works on sketching recent elements of a data stream have all considered the more restrictive scenario of synchronous streams, where the observed order of data is the same as the time order in which the data was generated. Our notion of recency of elements is more general than that studied in previous work, and thus our sketches are more robust to network delays and asynchrony. The work of the authors was supported in part through NSF grants CNS 0520102 and CNS 0520009. A preliminary version of this paper appeared in Proceedings of the ACM Symposium on Principles of Distributed Computing (PODC) 2006, pages 82–91. Work done while the third author was at Rensselaer Polytechnic Institute. Authors are listed in reverse alphabetical order.     

“离散时间傅里叶变换”教学方法探讨

离散时间傅里叶变换是数字信号处理课程中重要的教学内容之一,本文利用ZT和离散时间傅里叶变换之间的关系来探讨离散时间傅里叶变换的教学方法。几年的教学实践表明,运用该教学方法进行“离散时间傅里叶变换”的教学,可以收到较好的教学效果。     

OFDM系统中基于离散余弦变换的信道估计

提出了两种基于离散余弦变换（DCT）的信道估计方法,适用于多径衰落的正交频分复用（OFDM）系统。利用DCT的能量压缩特性,能有效消除传统基于离散傅立叶变换（DFT）估计算法在信道延时不是采样周期整数倍,或系统子栽波数不等于有用于载波数时产生的频谱泄漏。根据DCT与DFT的等效关系,通过构造不同的对称数据序列,推出两种相应的基于DCT信道估计,其中一种具有更好的性能,另一种更利于实现。仿真和分析结果表明：在多径衰落信道下,两种基于DCT的方法能有效降低频谱泄漏造成的信道估计误差,具有比基于DFT方法更好的性能。