长度为pm的离散哈脱莱变换分离基算法

Soo-Chang Pei,Ja-Ling wu(1986)和茅一民(1987)提出了长度为2^m的分离基2/4哈脱莱变换算法。本文将分离基算法推广到长度为p^m的哈脱莱变换,并证明基p²算法实乘次数比基p算法少,而基p/p²算法实乘次数比前两者都少。作为例子,给出了长度为N=3^m的基3/9哈脱莱变换快速算法和流图。     

使用数论变换的超快速傅里叶变换

本文证明用数论变换(NTT)能非常有效地计算离散傅里叶变换(DFT)值,而乘法次数可进一步减少。这是因为考虑数论变换和离散傅里叶变换的某些简单特性,把一个长度为P的离散傅里叶变换实乘总数减少到(P-1)。这样,每点所需实乘法次数还不到一次。适当选择变换长度和数论变换,每点     

文摘

因傅里叶变换全息图在目标像以外,能再现点对称的图像,故损失掉一半光。因此,本文提出了只再现目标像的哈脱莱变换全息图的方法。当考虑2值相位型全息照相时,因博里叶变换全息图投影相位为0或π,故相位产生误差。而哈脱莱变换则是实数变换,故只用0或π.用2值相位调制器件无误差地显现全息图。哈脱莱变换全息图需要有周期结构,但从哈脱莱变换和傅里叶交换之间的关系看,可以用简单的光学系统实现图像再现。在P_1处配置哈脱莱变换     

二维离散傅里叶变换DFT（2^n;2）计算复杂性与张量乘积

本文从(?)单代数中的直和、张量乘积与离散傅里叶变换之间的关系出发,提出用直和、张量乘积表示的二维离散傅里叶变换DFT(2(?))各种算法的矩阵表示式。这种矩阵张量乘积表示式不仅揭示了各种DFT((?)2)算法之间内在联系和便于比较它们的计算复杂性,而且给出获得最小乘法次数的DFT(2(?)2)算法的途径,从而从理论上论证计算DFT(2(?)2)所需的最小实数乘法次数为2(?)-3n2(?)+3.2(?)+8。     

一种新的三维离散Hartley变换的分裂基快速算法

 离散Hartley变换(Discrete Hartley Transform,DHT)作为实值离散傅立叶变换的一种替代,在信号和图像处理领域已有广泛应用,针对现有三维DHT快速算法均仅能计算长度为2的整数次幂的DHT,本文提出一种适用于更多不同长度三维DHT的分裂基-2/4快速算法,较之将已有最优算法补零计算的方法,该算法有效的降低了计算复杂度.     

DFT(2~m)通用递归分解算法

本文从DFT的变换矩阵分解成矩阵Kronecker积形式出发,提出一种通用递归分解算法(GRFA)。采用不同的分解基,可导出常规FFT、MD-FFT、SR-FFT和RCFA等各种递归分解算法的矩阵Kronecker积表示式。从GRFA出发,论证了DFT(2~m)递归分解算法的最小实数乘法次数是(m-3)2~m+4。SR-FFT或RCFA算法是OFT(2~m)递归分解算法实数乘法次数最少的最佳算法。     

快速计算实序列DFT的新算法

本文提出一种实傅里叶变换(RFT)的新定义,用这种定义推导出计算实序列离散傅里叶变换(DFT)的一种快速算法(FRFT);它是当前同类算法中乘法次数、总运算次数、存储量均属最低水平的结构性最强的一种同址算法。     

基于幅度谱编码的基函数生成算法性能分析

通过对变换域通信系统的基函数生成算法的研究,在传统的使用一维伪随机( PN )序列对相位进行随机化方法的基础上,提出了一种新的基于随机幅度谱编码的算法用于基函数生成：用另一个一维PN序列与基函数的幅度谱向量进行点乘,对其随机化处理,该方法生成的基函数较传统的一维PN序列方法产生的基函数的随机性提高N( N为基函数长度)倍,大大增强了系统的抗截获能力和多址容量;最后对系统的误码率进行了仿真,验证了该方法可以提高多址通信时的系统性能。     

分离矢量基2D FFT新算法

近来,分离基FFT算法已推广到二维矢量基FFT。本文提出一种分离矢量基2DFFT新算法。它将(N×N)点2DDFT分解为一个(N/2)×(N/2)点基22DDFT和十二个(N/4)×(N/4)点基42DDFT外加一些乘法和加法,从而使运算复杂性进一步减少。     

具有三层复合结构的P型硅外延片制备工艺研究

对10.16 cm(4英寸)三层复合结构P型硅外延片的制备工艺进行了研究。利用PE-2061S型桶式外延炉,在重掺硼的硅衬底上采用化学气相沉积的方法成功制备P~-/P~+/P/P~+型硅外延层。通过FT-IR(傅里叶变换红外线光谱分析)、C-V(电容-电压测试)、SRP(扩展电阻技术)等测试方法对各层外延的电学参数以及过渡区形貌进行了测试,最终得到结晶质量良好、厚度不均匀性<3%、电阻率不均匀性<3%、各界面过渡区形貌陡峭的P型硅外延片,可以满足器件使用的要求。     

Split-radix algorithms for length-p m DHT

The split-radix 2/4 algorithm for discrete hartley transform (DHT) of length-2 ^m is now very popular. In this paper, the split-radix approach is generalized to length-p ^m DHT. It is shown that the radix-p/p ² algorithm, is superior to both the radix-p and the radix-p ² algorithms in the number of multiplications. As an example, a radix-3/9 fast algorithm for length-3 ^m DHT is developed. And its diagram of butterfly operation is given.     

SPLIT-RADIX ALGORITHMS FOR LENGTH-p~m DHT

The split-radix 2/4 algorithm for discrete Hartley transform(DHT)of length-2~m isnow very popular.In this paper,the split-radix approach is generalized to length-p~m DHT.It isshown that the radix-p/p~2 algorithm is superior to both the radix-p and the radix-p~2 algorithmsin the number of multiplications.As an example,a radix-3/9 fast algorithm for length-3~m DHTis developed.And its diagram of butterfly operation is given.     

任意长度离散Hartley变换的快速算法

本文把长为plq(p为奇数,q为任意自然数)的DHT转化为Pl个长为q的DHT的计算及其附加运算,附加运算只涉及P点cos-DFT和sin-DFT的计算;对长度(P1l,1,Psls 2l (p1, , ps为奇素数)的DHT,用同样的递归技术得到其快速算法,因而可计算任意长度的DHT;文中还论证了计算长为N的DHT所需的乘法和加法运算量不超过O(Nlog2N)。当长度为N=pl时,本文算法的乘法量比其他已知算法更少。     

各类离散W变换的快速Hartley变换算法

本文通过建立各类N阶离散W变换(DWTs)到N阶离散Hartley变换(DHT)的转换,得到了一种利用DHT 统一计算各类DWTs的非常简单的快速算法.该算法结构简单,且每一种转换过程总的运算量均低于5N.     

A fast algorithm for discrete hartley transform of arbitrary length

DHT of length p~lq(p is odd and q is arbitrary) is turned into p~l DHTs of length qand some additional operations, while the additional operations only involves the computation ofcos-DFT and sin-DFT with length p. If the length of a DHT is p_1~(l_1)…P_N~(l_N)2~l(P_1…,P_N are oddprimes), a fast algorithm is obtained by the similar recursive technique. Therefore, the algorithmcan compute DHT of arbitrary length. The paper also Proves that operations for computingDHT of length N by the algorithm are no more than O(Nlog_2N), when the length is N=p~l,operations of the algorithm are fewer than that of other known algorithms.     

神经网络实现的任意长度DCT快速算法

介绍一种新的DCT计算方法,它以DHT为基础,利用Hopfield神经网络的并行特征来提高DCT的计算性能。该方法与现有方法比较,复杂度降低,乘法运算量为(2N-1),加法运算量为3N-2,并且适合任意长度的DCT计算,因而在图像处理中具有较好的应用前景。     

A Low‐Complexity 128‐Point Mixed‐Radix FFT Processor for MB‐OFDM UWB Systems

In this paper, we present a fast Fourier transform (FFT) processor with four parallel data paths for multiband orthogonal frequency‐division multiplexing ultra‐wideband systems. The proposed 128‐point FFT processor employs both a modified radix‐2⁴ algorithm and a radix‐2³ algorithm to significantly reduce the numbers of complex constant multipliers and complex booth multipliers. It also employs substructure‐sharing multiplication units instead of constant multipliers to efficiently conduct multiplication operations with only addition and shift operations. The proposed FFT processor is implemented and tested using 0.18 µm CMOS technology with a supply voltage of 1.8 V. The hardware‐ efficient 128‐point FFT processor with four data streams can support a data processing rate of up to 1 Gsample/s while consuming 112 mW. The implementation results show that the proposed 128‐point mixed‐radix FFT architecture significantly reduces the hardware cost and power consumption in comparison to existing 128‐point FFT architectures.     

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.     

Algebraic Signal Processing Theory: Cooley–Tukey Type Algorithms for Real DFTs

In this paper, we systematically derive a large class of fast general-radix algorithms for various types of real discrete Fourier transforms (real DFTs) including the discrete Hartley transform (DHT) based on the algebraic signal processing theory. This means that instead of manipulating the transform definition, we derive algorithms by manipulating the polynomial algebras underlying the transforms using one general method. The same method yields the well-known Cooley-Tukey fast Fourier transform (FFT) as well as general radix discrete cosine and sine transform algorithms. The algebraic approach makes the derivation concise, unifies and classifies many existing algorithms, yields new variants, enables structural optimization, and naturally produces a human-readable structural algorithm representation based on the Kronecker product formalism. We show, for the first time, that the general-radix Cooley-Tukey and the lesser known Bruun algorithms are instances of the same generic algorithm. Further, we show that this generic algorithm can be instantiated for all four types of the real DFT and the DHT.