Efficient hard-wired digital fast-Fourier-transform processor

A hard-wired dedicated fast-Fourier transform processor is described, which has high speed, low power consumption, small size and low cost. The technique is applicable to any size of transform, and could readily be adapted to employ improved components or a more efficient control algorithm.     

Means of reducing computing time in the fast-Fourier-transform method

A technique is described by which the computing time required for the fast-Fourier-transform algorithm can be reduced at the expense of frequency resolution, with no reduction in accuracy.     

基于拉普拉斯先验算法的多维度频谱感知

全双工认知无线电LAT（Listen-and-Talk）模型能够在次用户传输数据的同时进行频谱感知,这要求感知用户能在次用户自干扰的影响下检测当前是否存在主用户。利用全局功率谱模型的方法实现了对当前用户的使用频段、发射功率和位置坐标的多维度感知,以此辨别该用户的身份。在求解数学模型时,选取了拉普拉斯近似函数用作未知参数的先验概率密度函数,与现有方法相比,提升了算法收敛速度,并获得了准确性更高的结果。     

Multidimensional polynomial transform algorithm formultidimensional discrete W transform

The multidimensional (MD) polynomial transform is used to convert the MD W transform (MDDWT) into a series of one-dimensional (1-D) W transforms (DWTs). Thus, a new polynomial transform algorithm for the MDDWT is obtained. The algorithm needs no operations on complex data. The number of multiplications for computing an r-dimensional DWT is only 1 times that of the commonly used row-column method. The number of additions is also reduced considerably     

Multidimensional frequency estimation using LU decomposition eigenvector–based algorithm

Many algorithms have been proposed for multidimensional frequency estimation from a single snapshot or multiple snapshots of data mixture. Most of these algorithms fail when one or more identical frequencies are found in certain dimensions. In this paper, a multidimensional frequency estimation technique from a single datum snapshot is proposed. It applies LU decomposition (Gaussian Elimination) on an eigenvector-based algorithm for multidimensional frequency estimation. This proposed technique is simulated using a MATLAB code. The average root mean square error (RMSE) is investigated as a performance measure of the proposed technique. A comparison between original eigenvector-based (traditional) and the proposed techniques is introduced. The simulation results show that the RMSE of the proposed technique is less than the original one, and it has a more efficient solution for an identical frequency case but at the expense of complexity.     

Multidimensional Polynomial Transform Algorithm For Multidimensional Discrete Hartley Transform

In this paper, we present an index permutation-based fast algorithm for the multidimensional discrete Hartley transform (MD-DHT). By reordering the MD-DHT input sequence, we first convert the MD-DHT into a multiple sum that contains a number of one-dimensional discrete W transforms (1D-DWTs). We then use a combination of the 1D-DWTs and the multidimensional polynomial transform to compute the multiple sum. It is shown that the number of multiplications and additions required for the proposed algorithm are approximately 1/m and 2m+1/3m times that of the commonly used row-column DHT method, respectively. The developed algorithm is also simple in structure and easy to realize in programming.     

Multidimensional BIFORE transform

The BIFORE transform is generalised to r dimensions. The corresponding power spectrum consists of ?i = 1r(1+ki) spectral points (Nt = 2ki), which are invariant under cyclic shifts of the r-dimensional input data. A physical interpretation of the BIFORE power spectrum is presented.     

Multidimensional bilinear transformations

The bilinear transformation is extended to transform multi-variable polynomials, using discrete convolution and the Kronecker product. This approach is very simple, easy for computer implementation, and useful in complex curve fitting and stability studies of discrete systems and the design of digital filters etc.     

Multidimensional spectral estimation

Methods of multidimensional power spectral estimation are reviewed. Seven types of estimators are discussed: Fourier, separable, data extension, MLM, MEM, AR, and Pisarenko estimators. Particular emphasis is given to MEM where current research is quite active. Theoretical developments are reviewed and computational algorithms are discussed.     

Multicomponent Multidimensional Signals

In this brief paper, we extend the notion of multicomponent signal into multiple dimensions. A definition for multidimensional instantaneous bandwidth is presented and used to develop criteria for determining the multicomponent nature of a signal. We demonstrate application of the criteria by testing the validity of a multicomponent interpretation for a complicated nonstationary texture image.     

观测站存在位置误差条件下基于MDS的多站时差定位算法

为了降低无源定位中观测站站址误差对定位精度产生的不良影响,论文提出了一种基于多维尺度分析的多站无源时差定位解析算法。算法建立了存在站址误差时关于目标位置的线性方程组,推导了方程误差与时差测量误差和站址误差之间的关系式,将误差的统计特性融入到新的加权矩阵之中,使用加权最小二乘方法对目标位置进行了求解。仿真实验表明,算法对于小测量误差具有无偏性,其定位精度能够达到克拉美罗下界,相对于Ho K C的解析算法具有更好的稳健性。      

多维DFT的多维多项式变换与离散W变换算法

本文首先通过引进一种序列的重排技术将m(m2) 维离散Fourier变换 (m-D DFT)转化为一系列的一维广义离散Fourier变换(GDFT)的多重和.然后引入一维离散W变换(DWT)以及多维多项式变换(MD-PT)计算该多重和以减少冗余的算术运算,从而得到了高效的多维DFT算法,该算法与常用的行-列DFT算法相比,乘法仅约为行-列法的1/2m,而加法仅约为行-列法的(2m+1)/4m.对于2维DFT的计算,本文方法同单纯的多项式变换方法相比,乘法与加法分别减少50%与40%左右.另外,本文算法计算结构简单,易于编程实现,通过数值实验验证了本文算法的高效性.     

Multidimensional spherical coordinates quantization

Several investigators have considered polar coordinates quantization of a circularly symmetric source; in particular, the independent bivariate Gaussian source. Their schemes quantize the polar coordinates independently in an attempt to reduce the mean-square error below that of an analogous rectangular coordinates quantizer yet retain an implementation simpler than that of the optimal bivariate quantizer. The design of a spherical coordinates quantizer inkdimensions withk>2(k=2matches published results) is considered. Examples are presented along with comparisons to the rectangular (one-dimensional) and optimal schemes.     

Multidimensional orthogonal FM transforms

The present a novel class of multidimensional orthogonal FM transforms. The analysis suggests a novel signal-adaptive FM transform possessing interesting energy compaction properties. We show that the proposed signal-adaptive FM transform produces point spectra for multidimensional signals with uniformly distributed samples. This suggests that the proposed transform is suitable for energy compaction and subsequent coding of broadband signals and images that locally exhibit significant level diversity. We illustrate these concepts with simulation experiments.     

Error-Correction of Multidimensional Bursts

We present several methods and constructions to generate binary codes for correction of a multidimensional cluster-error, whose shape can be a box-error, a Lee sphere error, or an error with an arbitrary shape. Our codes have very low redundancy, close to optimal, and a large range of parameters of arrays and clusters. Our main results are summarized as follows. A construction of two-dimensional codes capable to correct a rectangular-error with considerably more flexible parameters from previously known constructions. This construction is easily generalized for $D$ dimensions.      

Photopatterned Multidimensional Fluorescent Images

New methods that yield covert fluorescent images are of significant interest for applications in anti‐counterfeit technology. Printing methods that offer access to spatially controlled fluorescence intensity are needed in order to accurately reproduce unique and complex images. Herein, the use of photoreactive inks containing 9,9′‐bis(anthracene)sulfoxide (AnSO) to create complex images with spatially controlled fluorescence intensity is presented. Under UV irradiation, the SO‐bridge between anthracene units in AnSO is extruded to yield the highly luminescent molecule 9,9′‐bianthryl (BA) in quantitative yields. The irreversible formation of BA is leveraged to create multidimensional fluorescent security features that can be patterned using light and easily interpreted using the CCD camera of a mobile phone.     

Multidimensional Modeling of Nanotransistors

In this paper, we review our recent work using the nonequilibrium Green's function method to model nanotransistors. After presenting a motivation for the need of quantum mechanical modeling, an account of the equations and implementation is given for both 1-D and 2-D modeling. Examples are given to highlight the use of the developed models. Finally, possible future directions in quantum mechanical modeling of transport in nanotransistors are highlighted along with computational challenges.     

Multidimensional maximum-entropy covariance extension

A universal characterization of maximum-entropy covariances for multidimensional signals is presented. It is shown that the maximum-entropy extension of an arbitrary partial covariance of a nonstationary multidimensional signal always has a banded inverse, i.e the inverse is sparse and has the same support as the given partial covariance. A dual formulation of the problem that makes it possible to approximate maximum-entropy extensions with models selected from suitably constrained model sets is introduced. It is proved that the best approximation in terms of multidimensional recursible autoregressive models can be determined by solving a set of linear equations. A simple graph-theoretic criterion is introduced to characterize those partial covariances whose maximum-entropy extension coincides with its autoregressive approximation, as in the conventional (one-dimensional stationary) maximum-entropy problem