DWT变换的另一种快速DHT算法

通过建立各类N阶离散W变换（DWT）到N阶离散Hartley（DHT）的转换,得到了另一种利用DHT统一计算各类DWT的更为简明的快速算法。该算法结构简单,无需事先判断数据长度N的奇偶性,同时可充分利用输入输出数据的对称与反对称性,使运算量进一步减少。     

An Efficient Algorithm for the Computation of the Multidimensional Discrete Fourier Transform

In this paper, we propose a new approach for computing multidimensional Cooley-Tukey FFT's that is suitable for implementation on a variety of multiprocessor architectures. Our algorithm is derived in this paper from a Cooley decimation-in-time algorithm by using an appropriate indexing process and the tensor product properties. It is proved that the number of multiplications necessary to compute our proposed algorithm is significantly reduced while the number of additions remains almost identical to that of conventional Multidimensional FFT's (MFFT). Comparison results show the powerful performance of the proposed MFFT algorithm against the row-column FFT transform when data dimension M is large. Furthermore, this algorithm, presented in a simple matrix form, will be much easier to implement in practice. Connections of the proposed approach with well-known DFT algorithms are included in this paper and many variations of the proposed algorithm are also pointed out.     

Odd-Factor Algorithms for Multidimensional Discrete W Transform

New fast algorithms are proposed for the multidimensional type-II, -III, and -IV discrete W transforms. Detailed procedures of decomposition are given for the twoand three-dimensionalWtransform based on the use of odd factors in the transforms sizes. The proposed algorithms have a regular computational structure, support various transform lengths, and can be easily extended to higher-dimensional computations.     

Hartley变换离散多音调制在可见光通信中的应用

针对传统调制方式难以满足人们对高速通信的要求,结合Hartley变换与离散多音调制(DMT)提出一种用于可见光通信的多载波调制方式.为了实现DMT,采用Harltey变换来代替傅里叶变换,然后对调制信号进行非对称式限幅来降低LED的发射功率.仿真结果表明,相比于直流偏置调制模式,非对称限幅调制模式更为节能.     

基于正交多项式变换的图像融合算法

将1维的OPT推广为2维OPT,在此基础上提出了一种基于正交多项式变换的图像融合算法.正交多项式变换将图像的主要特征映射到时域特征空间,而将图像的细节特征映射为白噪声.融合处理在特征空间中进行.实验结果表明,在降噪方面该算法优于离散小波变换方法、拉普拉斯金字塔方法和Morphological金字塔方法.     

Low-Cost Fast VLSI Algorithm for Discrete Fourier Transform

A primeN-length discrete Fourier transform (DFT) can be reformulated into a (N-1)-length complex cyclic convolution and then implemented by systolic array or distributed arithmetic. In this paper, a recently proposed hardware efficient fast cyclic convolution algorithm is combined with the symmetry properties of DFT to get a new hardware efficient fast algorithm for small-length DFT, and then WFTA is used to control the increase of the hardware cost when the transform length Nis large. Compared with previously proposed low-cost DFT and FFT algorithms with computation complexity of O(logN), the new algorithm can save 30% to 50% multipliers on average and improve the average processing speed by a factor of 2, when DFT length Nvaries from 20 to 2040. Compared with previous prime-length DFT design, the proposed design can save large amount of hardware cost with the same processing speed when the transform length is long. Furthermore, the proposed design has much more choices for different applicable DFT transform lengths and the processing speed can be flexible and balanced with the hardware cost     

补零离散傅立叶变换的插值算法

插值离散傅立叶变换能提高正弦信号参数估计精度,但传统的比值插值算法只适用于数据长度等于离散傅立叶变换长度的场合。本文研究了补零离散傅立叶变换的插值问题,提出一种基于窗函数频谱一阶泰勒级数展开的插值算法,它与原比值法具有类似的形式和相同的计算量,是原比值法在数据长度小于或等于离散傅立叶变换长度时的扩展。性能分析和仿真试验还表明,补零离散傅立叶变换插值算法对频率偏差的敏感度降低,稳定性更好。     

基于DWT的图像数字水印算法研究

该文提出了一种基于DWT多分辨率分解的数字水印技术。利用多分辨率分解技术，分别将原始图像与水印图像进行三层离散小波变换，将相同分辨率层次水印嵌入到对应的相同分辨率层次的原始静态图像之中，使水印对原始图像具有自适应性。实验结果表明，该文提出的水印算法经某些图像处理操作和JPEG压缩后仍是鲁棒的。     

A Fast Computational Algorithm for the Discrete Cosine Transform

A Fast Discrete Cosine Transform algorithm has been developed which provides a factor of six improvement in computational complexity when compared to conventional Discrete Cosine Transform algorithms using the Fast Fourier Transform. The algorithm is derived in the form of matrices and illustrated by a signal-flow graph, which may be readily translated to hardware or software implementations.     

A Fast Computational Algorithm for the Discrete Sine Transform

A sparse-matrix factorization is developed for the discrete sine transform (DST). This factorization has a recursive structure and leads directly to an efficient algorithm for implementing the DST, a feature most desirable and very similar ot that of the DCT. This algorithm requires fewer arithmetic operations compared to that for the discrete cosine transform (DCT).     

Discrete Hartley transform in error control coding

A new class of real-valued linear code obtained by using the discrete Hartley transform (DHT) is defined. The authors have derived the limitation on the choice of parity frequencies so as to define DHT codes with the cyclic-shift property. Then, by introducing the well-established encoding/decoding algorithm for cyclic codes in error control coding, they have constructed the encoder/decoder for the DHT cyclic codes     

逆向工程中对离散点云的特征识别算法探究

基于逆向设计中点云处理的表面识别问题,本文提出了一种基于小波变换的离散点云数据的特征识别算法。首先将离散点云表示成小波变换可以处理计算的形式,然后在此基础上提出了具体的二维和三维离散点云的小波分解算法,最后引入实例,对二维离散点云的小波分解算法进行验证分析。实验结果表明本文提出的算法达到了对点云数据的特征分解的目的。将离散点云数据按特征分解从而提取出不同的特征成分,可以根据后期点云预处理的不同要求,将小波变换后的数据进行进一步的处理。     

Improved Speech Denoising Algorithm Based on Discrete Fractional Fourier Transform

The speech signal and noise signal are the typical non-stationary signals,however the speech signa is short-stationary synchronously.Presently,the denoising methods are always executed in frequency domain due to the short-time stationarity of the speech signal.In this article,an improved speech denoising algorithm based on discrete fractional Fourier transform（DFRFT）is pre sented.This algorithm contains linear optimal filtering and median filtering.The simulation shows that it can easily eliminate the noise compared to Wiener filtering improve the signal to noise ratio（SNR）,and enhance the original speech signal.     

基于小波变换的混沌图像置乱加密算法

给出一种在二维小波变换基础上进行混沌映射,将图像加密的方法。该方法应用二维小波分解算法分解图像信息,再对其实行正弦混沌映射,从而完成图像的加密。解密时,首先对系数进行正弦映射的逆映射,再进行二维小波重构,实现对原始图像的解密。仿真结果证明了该方法的有效性。     

逆向工程中对离散点云的特征识别算法探究

基于逆向设计中点云处理的表面识别问题,本文提出了一种基于小波变换的离散点云数据的特征识别算法。首先将离散点云表示成小波变换可以处理计算的形式,然后在此基础上提出了具体的二维和三维离散点云的小波分解算法,最后引入实例,对二维离散点云的小波分解算法进行验证分析。实验结果表明本文提出的算法达到了对点云数据的特征分解的目的。将离散点云数据按特征分解从而提取出不同的特征成分,可以根据后期点云预处理的不同要求,将小波变换后的数据进行进一步的处理。     

Radix-3$,times,$3 Algorithm for The 2-D Discrete Hartley Transform

In this correspondence, we propose a vector-radix algorithm for the fast computation of a 2-D discrete Hartley transform (DHT). For data sequences whose length is a power of three, a radix-3 times 3 decimation in frequency algorithm is developed. It decomposes a length-N times N DHT into nine length-(N/3) times N (N/3) DHTs. Comparison of the computational complexity with known algorithms shows that the proposed algorithm, in some cases, reduces significantly the number of arithmetic operations.     

基于System Generator的二维离散小波变换的算法实现

结合传统的Mallat算法,利用System Generator平台,提出了一种高速二维小波变换的方法。通过实例图像(64×64)在该平台中开发相关的模块,并进行仿真和逻辑综合,最后充分体现了在System Generator中实现小波变换的优越性。     

New Systolic Algorithm and Array Architecture for Prime-Length Discrete Sine Transform

Using a simple input-regeneration approach and index-transformation techniques, a new formulation is presented in this paper for computing an N-point prime-length discrete sine transform (DST) through two pairs of [(N-1)/4]-point cyclic convolutions, where [(N-1)/4] is an odd number. The cyclic convolution-based algorithm is used further to obtain a simple regular and locally connected linear systolic array for concurrent pipelined implementation of the DST. It is shown that the proposed systolic structure involves significantly less area-time complexity compared with that of the existing structures     

一种分块自适应压缩感知图像重构算法

CS理论中,在离散余弦变换下使用OMP算法重构图像时需要较高的测量值可以获得较好的重构效果,但是存在重构图像模糊的问题.为此,提出了基于离散余弦变换的图像分块自适应正交匹配追踪(BAD-OMP)算法.基于分块压缩感知技术,对图像进行均匀分块处理,根据图像块稀疏性进行自适应采样,再用均值滤波算法平滑处理,从而减少重构所需的测量值,降低块效应.仿真结果表明,采样率取0.1 ～0.35 时,BAD-OMP算法重构图像的PSNR值较OMP算法的PSNR值高9～1 1 dB,实现了在低采样率下获得较高的重构质量.