Performance of dual tone multi-frequency signal decoding algorithm using the sub-band non-uniform discrete Fourier transform on the ADSP-2192 processor

Efficient decoding of Dual Tone Multi-Frequency (DTMF) signals can be achieved using the sub-band non-uniform discrete Fourier transform (SB-NDFT). In this paper, the details of its implementation on the ADSP-2192 processor are put forward. The decoder performance in terms of its computational complexity and computational speed of this algorithm, implemented on the ADSP-2192 processor, are compared for different implementations of the SB-NDFT algorithm, with and without optimization for the chosen DSP, ADSP-2912. The algorithm is tested for various types of input signals on the DSP and these are compared with the results from Matlab^®. Problems on using other DTMF decoding algorithms that use the conventional discrete Fourier transform (DFT) and the non-uniform discrete Fourier transform (NDFT) are also addressed.     

基于最佳补偿比例因子的整数小波变换

为了提高提升格式下整数小波变换的有损压缩性能,提出了基于最佳补偿比例因子的优化算法。根据变换后小波系数和滤波器的特性,分别采用子带近似线性逼近和量化补偿噪声取代取整运算的方法,求得小波分解后各个子带的最佳补偿比例因子。利用这个比例因子补偿整数小波变换的非线性带来的近似误差以达到优化目的。实验结果表明,在不增加运算复杂度的情况下,所得压缩图像的峰值信噪比(PSNR)与基于浮点运算的传统离散小波变换几乎一样。     

Parallel computation of multidimensional discrete orthogonal transforms reducible to a discrete Fourier transform

Algorithms of parallel computation of multidimensional discrete orthogonal transforms that rely on a previously developed approach to paralleling discrete Fourier transforms and methods of reducing different discrete orthogonal transforms (discrete Hartley transform, discrete cosine transform, etc.) to discrete Fourier transforms of a special form are considered.     

基于算术傅里叶变换的离散Hartley变换的快速算法

离散Hartley变换是一种有用的实值正交变换。文中对其快速算法进行研究,首先介绍利用算术傅里叶变换（AFT）计算离散傅里叶变换（DFT）可使其乘法计算量仅为O（N）,然后文章根据这一特点,分析离散Hartley变换（DHT）的结构特征,通过DFT将AFT和DHT建立了直接联系,提出了一种新的快速DHT算法。算法的计算复杂度能够达到线性O（N）,且算法结构简单,公式统一且易于实现,并与其他快速算法进行了比较,分析可知在数据长度不是2的幂次方时,文中提出的算法的计算时间明显比其他算法的计算时间要小。实验结果也验证了文中算法的有效性,从而为DHT的快速计算开辟了新的思路和途径。     

Unified Parallel Lattice Structures for Block Time-Recursive Real-Valued Discrete Gabor Transforms

In this paper, the 1-D real-valued discrete Gabor transform (RDGT) proposed in the previous work and its relationship with the complex-valued discrete Gabor transform (CDGT) are briefly reviewed. Block time-recursive RDGT algorithms for the efficient and fast computation of the 1-D RDGT coefficients and for the fast reconstruction of the original signal from the coefficients are developed in both critical sampling and oversampling cases. Unified parallel lattice structures for the implementation of the algorithms axe studied. And the computational complexity analysis and comparison show that the proposed algorithms provide a more efficient and faster approach to the computation of the discrete Gabor transforms.     

Fast parallel algorithms for discrete Gabor expansion and transform based on multirate filtering

The Gabor transform has long been recognized as a very useful tool for the joint time and frequency analysis in signal processing.Its real time applications,however,were limited due to the high computational complexity of the Gabor transform algorithms.In this paper,some novel and fast parallel algorithms for the finite discrete Gabor expansion and transform are presented based on multirate filtering.An analysis filter bank is designed for the finite discrete Gabor transform(DGT)and a synthesis filter bank is designed for the finite discrete Gabor expansion(DGE).Each of the parallel channels in the two filter banks has a unified structure and can apply the FFT and the IFFT to reduce its computational load.The computational complexity of each parallel channel does not change as the oversampling rate increases.In fact,it is very low and depends only on the length of the input discrete signal and the number of the Gabor frequency sampling points.The computational complexity of the proposed parallel algorithms is analyzed and compared with that of the major existing parallel algorithms for the finite DGT and DGE.The results indicate that the proposed parallel algorithms for the finite DGT and DGE based on multirate filtering are very attractive for real time signal processing.     

基于辅助双正交的实值离散多Gabor变换

为了改善传统离散Gabor变换的时频分辨率,降低离散Gabor变换计算的复杂性,提出了一种基于多高斯窗的实值离散Gabor变换分析窗的快速求解算法。对多高斯窗下离散Gabor变换双正交关系式进行了简化,给出了分析窗组的代数方程表达式。该算法相对于多高斯Gabor展开的计算复杂度明显降低,仿真实验的结果也证明了该算法的有效性。     

一种多级离散余弦变换和奇异值分解的零水印算法

传统的基于离散余弦变换的数字水印方法在嵌入水印时都要对原始图像数据进行一定的修改导致嵌入水印图像的保真度下降。文章提出了一种基于多级离散余弦变换和奇异值分解的零水印算法,该算法首先对要嵌入的原始图像进行多级离散余弦变换（MDCT）,提取低频子图并对其进行奇异值分解（SVD）;其次对嵌入的水印图像进行置乱,将置乱后的图像进行奇异值分解;最后将原始图像和水印图像两次SVD后的结果进行运算产生密钥图像。由于本文选取的水印为灰度图像而不是伪随机序列或二值图像,因此在水印检测时具有很好的区分度和检测精度。仿真实验表明该算法的鲁棒性优于现有算法,而且在抗各种常见攻击方面性能良好。     

利用循环卷积实现的素长度ＤＣＴ快速算法

提出了一种利用循环卷积（Ｃycli convolution)和扭循环卷积（Ｓkew cyclic eonvolution)实现计算机素长离散余弦变换（ＤＣＴ）的快速新算法,算法将ＤＣＴ系数分成三部分,ＤＣ分量,偶下标分量和奇下标分量,根据数论理论,本文定义了一种新的标变换算子,利用该算子进行下标变换,将偶下标ＤＣＴ系数的计算转化为一个循环卷积,根据不同长度,奇下标ＤＣＴ系数的计算被转化为循环卷 积或扭循环卷积,利用循环卷积和扭循环卷积的高效率和规则的算法,构造具有简单,规则的结构和较低的运算复杂性和奇素长度ＤＣＴ快速算法。     

基于DCT的实值离散Gabor变换最优窗宽选择

文中针对Gabor变换中最优窗函数宽度选择的问题,提出了以提高Gabor表示的聚集性和时频分辨率为目的的基于DCT核的实值离散Gabor变换最优窗函数宽度选择算法。对香农熵的取值范围进行了研究,使其更适合度量时频分布的聚集性,进而根据熵度量实现了与信号非平稳性相适应的最优窗函数宽度的选择。实验结果表明,该算法对单分量及多分量信号都能有效地选择最优窗函数宽度,同时能够获得聚集性好、时频分辨率高的Gabor表示,并且具有很好的抗噪能力。     

一类正交函数系的离散表示及快速变换

V系统是L₂[0,1]上一类新的完备正交函数系,它由分段多项式组成,具有多分辨分析特性和全局/局部性,在几何模型的正交表达方面具有明显的优势,但其快速算法难以得到。利用Haar函数和Legendre多项式构造了一类由分段k次多项式组成的函数系（文中称为W系）,在该函数系上作函数逼近的效果等同于在V系统上的效果,并进一步讨论了一次离散W变换的快速算法,从而部分克服了直接对V系统设计快速算法的困难。     

A new digital implementation of ridgelet transform for images of dyadic length

Ridgelet transform is a new directional multi-resolution transform and it is more suitable for describing the signals with high dimensional singularities. Finite ridgelet transform is a discrete version of ridgelet transform, which is as numerical precision as the continuous ridgelet transform and has low computational complexity. However, finite ridgelet transform is only suitable for images of prime-pixels length, which is a limitation of its applications in image processing. In this paper, a new digital implementation of ridgelet transform that is suitable for images of dyadic length is proposed. This method not only expands the applications of finite ridgelet transform, but also simplifies the algorithm. First, we introduce the concept of ridgelet transform in the continuous domain. Then, we illustrate finite ridgelet transform and the new method. Finally, we compare the new method with finite ridgelet transform by applying both digital ridgelet transforms to the denoising of images embedded in additive white Gaussian noise and the new method gets a better performance in image denoising. The new algorithm can also be used as the important building block in curvelet transform and get surprising visual performances in denoising for natural image.     

Image Data Compression using Zonal Sampling and Piecewise-Linear Transforms

In this paper, image data compression methods based on sample selection in the piecewise-linear transform domain will be presented. The image is subjected to a 2-dimensional piecewise-linear transformation and some coefficients will be selected using threshold method and a proposed zonal sampling method. In the proposed zonal sampling method all samples outside the selected zone will be discarded completely (no zeros are replaced). The inverse transformation in this case will have a dimension equal to that of the selected zone. Thus the number of computations needed for the inverse transformation is reduced. The Peak Signal-to-Noise Ratio (PSNR) is used as a measure of quality of the reconstructed images. Comparisons of the compression ability using piecewise-linear transforms and some selected orthogonal transforms such as Walsh and cosine transforms are given. The results obtained by using the proposed zonal sampling method show that the piecewise-linear transforms have a better performance than the orthogonal transforms.     

基于Finite Ridgelet变换的图像线性特征提取

线性特征是图像的一种重要局部特征,它常常决定图像中目标的形状。线性特征的提取在图像匹配、目标描述与识别以及运动估计、目标跟踪等领域具有十分重要的意义。常用的线性特征检测方法有Radon变换和Hough变换,但检测曲线复杂度会很高。本文提出一种多尺度几何分析的线性特征检测方法,该方法以finite ridgelet理论为基础,结合正交小波变换对线性特征进行提取。Finite ridgelet变换对于含有直线奇异的多变量函数具有良好的逼近特性,能够获得连续空间函数的稀疏表达,同时具有区域平滑性、很好的可逆性和去冗余性。实验结果表明,本方法即使在背景复杂的环境下也具有良好的检测效果。     

扩频通信抗干扰中的局部离散余弦变换技术

提出一种新的基于局部离散余弦变换(Local discrete cosine transform，LDCT)的时频域干扰抑制方法。与传统的块变换(Discrete cosine transform，DCT)不同，LDCT基函数具有良好的时域能量集中特性，可迅速捕获信号中的时变成分，有效跟踪信号时频结构的变化，实现时频平面的任意时间分割。仿真结果表明，基于LDCT的时频域信号处理方法可有效地抑制各种脉冲型时变干扰，明显改善系统性能。     

Two-dimensional discrete cosine transform on sliding windows

The discrete cosine transform (DCT) has been successfully used for a wide range of applications in digital signal processing. While there are efficient algorithms for implementing the DCT, its use becomes difficult in the sliding transform scenario where the transform window is shifted one sample at a time and the transform process is repeated. In this paper, a new two-dimensional sliding DCT (2-D SDCT) algorithm is proposed for fast implementation of the DCT on 2-D sliding windows. In the proposed algorithm, the DCT coefficients of the shifted window are computed by exploiting the recursive relationship between 2-D DCT outputs of three successive windows. The theoretical analysis shows that the computational requirement of the proposed 2-D SDCT algorithm is the lowest among existing 2-D DCT algorithms. Moreover, the proposed algorithm enables independent updating of each DCT coefficient.     

适应度平均选择的离散差分演化算法

如何将差分演化算法用于离散领域是该领域的一个重要问题.提出一种适应度平均选择的离散差分演化算法,提出的算法中每个个体有均等的机会被选择用于引导算法的进化,这种选择方式有助于克服贪婪选择操作导致的种群多样性下降过快而使算法易陷入局部最优的问题.最后在多维背包问题上的实验结果表明提出的算法具有良好性能.     

基于混沌和Walsh变换的二值图像加密算法

提出一种基于混沌映射和Walsh变换的二值图像加密算法。首先对二值图像进行混沌加密,再对混沌加密后的图像用Walsh变换进行置乱,实现图像信息的高强度加密。运用Walsh变换可以在很大程度上节约计算时间。仿真实验结果表明,混沌序列与Walsh变换相结合的方法加密强度高,计算时间短。     

滑动DCT-LMS自适应算法研究与FPGA实现

研究一种改进的低复杂度复数滑动离散余弦变换(DCT)最小均方(LMS)自适应算法,并设计该算法的FPGA实现结构。在常规LMS算法的输入端前添加改进的滑动DCT,降低输入信号之间的关联性,提高自适应算法收敛速度。改进的滑动DCT算法针对硬件实现进行了优化,提高其在硬件实现中稳定性和精度。给出算法在FPGA实现框图、结果和Matlab仿真结果的对比,以及算法在FPGA中的资源使用。算法已经在实际工程中应用,效果远优于常规LMS自适应算法。     

Applications of the naturalness preserving transform to image watermarking and data hiding

The paper presents an image watermarking technique using the naturalness preserving transform (NPT). The goal is to produce an invisible and robust watermark that resists signal processing and geometric distortion attacks. Unlike traditional techniques, the proposed algorithm inserts and extracts the watermark via a special orthogonal transform class in between the spatial and frequency representations of the host image data. Two modified forms of the NPT employing the Hartley and discrete cosine transforms, respectively, are presented in order to improve the quality of the transformed image. Enhancements for the quality of the transformed images are achieved via reduction to the artifacts that occur to images transformed via the classical Hadamard-based NPT. The proposed watermark has demonstrated robustness against a variety of image attacks including, JPEG compression, low pass filtering, image cropping, and noise. The marked image must be severely degraded in order to prevent the reconstruction of the watermark.