Vector Hartley transform

The fast Hartley transform provides the same information as the fast Fourier transform (FFT) but with greater speed and efficiency when the input data are real. An algorithm for taking the Hartley transform of a long sequence on a multiprocessor machine by simultaneously transforming short subsequences does not require complex arithmetic and is faster than analogous techniques which use the Fourier transform.<>     

A three-dimensional DFT algorithm using the fast Hartley transform

A three-dimensional (3-D) Discrete Fourier Transform (DFT) algorithm for real data using the one-dimensional Fast Hartley Transform (FHT) is introduced. It requires the same number of one-dimensional transforms as a direct FFT approach but is simpler and retains the speed advantage that is characteristic of the Hartley approach. The method utilizes a decomposition of the cas function kernel of the Hartley transform to obtain a temporary transform, which is then corrected by some additions to yield the 3-D DFT. A Fortran subroutine is available on request.     

Parallel vector processing of multidimensional orthogonal transforms for digital signal processing applications

This paper presents vector and parallel algorithms and implementations of one- and two-dimensional orthogonal transforms. The speed performances are evaluated on Cray X-MP/48 vector computer. The sinusoidal orthogonal transforms are computed using fast real Fourier transform (FFT) kernel. The non-sinusoidal orthogonal transform algorithms are derived by using direct factorizations of transform matrices. Concurrent processing is achieved by using the multitasking capability of Cray X-MP/48 to transform long data vectors and two-dimensional data vectors. The discrete orthogonal transforms discussed in this paper include: Fourier transform (DFT), cosine transform (DCT), sine transform (DST), Hartley transform (DHT), Walsh transform (DWHT) and Hadamard transform (DHDT). The factors affecting the speedup of vector and parallel processing of these transforms are considered. The vectorization techniques are illustrated by an FFT example.This work is supported in part by the National Science Foundation, Pittsburgh Supercomputing Center (grant number ECS-880012P) and by the PEW Science Education Program.     

Basefield transforms with the convolution property

We present a general framework for constructing transforms in the field of the input which have a convolution-like property. The construction is carried out over the reals, but is shown to be valid over more general fields. We show that these basefield transforms can be viewed as “projections” of the discrete Fourier transform (DFT). Furthermore, by imposing an additional condition on the projections, one may obtain self-inverse versions of the basefield transforms. Applying the theory to the real and complex fields, we show that the projection of the complex DFT results in the discrete combinational Fourier transform (DCFT) and that the imposition of the self-inverse condition on the DCFT yields the discrete Hartley transform (DHT). Additionally, we show that the method of projection may be used to derive efficient basefield transform algorithms by projecting standard FFT algorithms from the extension field to the basefield. Using such an approach, we show that many of the existing real Hartley algorithms are projections of well-known FFT algorithms     

Hartley transforms over finite fields

A general framework is presented for constructing transforms in the field of the input which have a convolution-like property. The construction is carried out over finite fields, but is shown to be valid over the real and complex fields as well. It is shown that these basefield transforms can be viewed as “projections” of the discrete Fourier transform (DFT) and that they exist for all lengths N for which the DFT is defined. The convolution property of the basefield transforms is derived and a condition for such transforms to have the self-inverse property is given. Also, fast algorithms for these basefield transforms are developed, showing gains when compared to computations using the FFT. Application of the methodology to Hartley transforms over R leads to a simple derivation of fast algorithms for computing real Hartley transforms     

Application of running Hartley transform in adaptive digitalfiltering

A transform-domain adaptive digital filtering technique based on the concept of the running discrete Hartley transform (RDHT) is presented, with an application. This Hartley implementation is shown to have a speed advantage over the running FFT approach proposed and implemented recently. Possible implementation of the RDHT in various applications is outlined. Particular attention is given to implementation of the RDHT in the adaptive nonrecursive LMS algorithm     

由FFT芯片构成的并行FFT结构

快速傅立叶变换（ＦＦＴ）在计算机层析影象技术,语间识别,图像处理等域得了广泛的应用。随着计算机应用的发展,越来越需要对大规模的数据进行变换。并行ＦＦＴ是完成快速数据变换的一种方法。本文提出一咱由小规模ＦＦＴ芯片构成并行ＦＦＴ的方法,楞用于大规模数据的变换,并对其并行结构的面积和执行时间进行了探讨,还提出了具有容错功能的并行ＦＦＴ网络。     

多重频解模糊中降低频道量化误差的新方法

针对工程应用中采用重频参差法解脉冲多普勒雷达的速度模糊存在频道量化误差问题,提出了一种提高频率估计精度的综合方法。该方法首先将目标所在距离单元相参积累后的频域数据,通过傅里叶反变换为原始数据,然后补零FFT,在此基础上运用二次函数拟合,进一步提高频率估计精度。它有效结合了补零FFT和二次函数拟合两种方法的优点,弥补了二者的不足。仿真结果表明,该方法在运算量不大的情况下,即可很好地降低频道量化误差。     

Updating the power spectrum of real data by the Hartley method

A general technique for updating a previously calculated power spectrum upon the reception of a new real data sample is presented. The technique is based on the Hartley transform which provides a fast and simple technique for the updating. Only N real multiplications and 2N + 1 real additions are needed for each update.     

多载波中的实数FFT及其离散Hartley变换实现

在OFDM／DMT多载波调制中，FFT为实数FFT（Real—Valued FFT），输入全部为实数，变换后的输出为偶函数即具有一定的共轭特性。相应地，IFFT为实数FFT的逆过程。实数FFT的实现与复数FFT具有很大的不同，文中提出了一种基于离散Hartley变换的实现方法，运算过程全部为实数过程，与复数FFT相比，所需的乘法、加法运算以及RAN的开销均大幅度降低。     

基于DHT的光OFDM系统PAPR抑制算法

针对光OFDM系统存在高峰均功率比(PAPR),提出了一种基于离散哈特利变换(DHT)的选择映射抑制算法。采用快速哈特利逆变换(IFHT)代替传统的快速傅立叶逆变换(IFFT)和Hermi t i an对称算法,并结合非对称限幅法产生满足光OFDM系统要求的正、实值信号送入光纤信道。     

基于FFT的多周期噪声的滤波-X算法研究

为了弥补已有消噪技术的缺陷及不足,结合实际应用对有源噪声控制技术及针对多周期低频噪声主动控制进行深入的研究,根据快速傅里叶算法(FFT)和凹槽滤波器的工作原理,系统地研究并设计滤波-X算法,进行相关计算机仿真出结果分析;运用快速傅里叶变换(FFT)的方法,将多周期信号从时域变换到频域,从而达到对多周期噪声消噪的目的。     

Comment on 'Vector Hartley transform'

The vector Hartley transform algorithm was recently proposed for efficient transformation of real data by J.D. Villasenor and R.N. Bracewell. It maps a very long one-dimensional input into a multidimensional array by an index mapping. However, this index mapping results in a complicated expression; also, multiplying each element of the intermediate array by an appropriate factor is necessary. This 'Comment' is to point out that these multiplications are unnecessary, and can be eliminated by a proper prime-factor mapping technique. The authors reply that the use of prime factor decomposition is well known in Fourier transformation as providing very efficient operation, and the same may be expected for the Hartley transform. The reduction of the argument of the cas function from three to two terms is clearly very helpful. However, the gain in speed is dependent on the prime factors that are chosen, and needs to be checked in a given environment by overall timing.<>     

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.     

一种改进的滑动窗FFT递推算法

在信号谱线分析中,经常用到滑动窗的FFT计算,由于传统的FFT在N值较大和滑动步进较小时,计算量较大,在实时通信系统中难以实现,本文提出一种连续滑动窗的递推FFT算法,该算法充分利用了前窗的计算结果并将输入序列转换为一个输入端仅有少数非零点的特殊序列,不仅降低了计算量,而且提高了使用的灵活性和实时性。     

基于CompuScope 82G型高速数据采集卡的虚拟示波器设计

基于PCI接口的CompuScope 82G型高速数据采集卡和Visual C 编程工具,设计了一种快速虚拟示波器试验系统,为了保证数据采集和波形显示的实时性,设计中采用了多线程技术.该系统集波形采集、数据分析、输出、显示为一体,实现了高速数据的采集和动态波形的显示,并且在此基础上实现了传统示波器无法实现的频谱分析和数字滤波功能.     

Basis-vector-decomposition based two-stage computational algorithmsfor DFT and DHT

Discrete Fourier transform (DFT)/discrete Hartley transform (DHT) algorithms based on the basis-vector decomposition of the corresponding transform matrices are derived. The computations of DFT are divided into two stages: an add/subtract preprocessing and a block-diagonal postprocessing. Both stages can be computed effectively. It can be proved that the computational complexity of the proposed DFT algorithm is identical to that of the most popular split-radix FFT, yet requires real number arithmetics only. Generation and storage of the real multiplicative coefficients are easier than that in conventional FFTs. Connections of the proposed approach with several well-known DFT algorithms are included. Furthermore, many variations of the proposed algorithm are also pointed out     

在OFDM系统中采用余弦变换的信道估计

提出在OFDM通信系统中采用余弦变换(DCT)实现信道内插估计,同时讨论离散傅氏变换(DFT)、离散哈特莱(DHT)、Hadamard变换等数学方法用于采用导引信号下的信道估计。无需知道信道阶数、噪声功率、多谱勒频移等信道统计特性仍能达到较好的信道估计性能,计算简单。仿真结果表明,余弦变换算法的信道估计在多径干扰、多谱勒频移较大时,仍能正常工作,性能稳定,达到较好的信道估计效果。     

宽带机动目标检测

该文提出了一种高机动目标宽带信号检测与运动参数估计方法,即先通过相邻相关对目标回波进行降阶处理,然后将其变换到距离频域,利用广义二阶keystone变换去除距离弯曲,接着对一个距离单元信号进行时间调频率变换并估计方位向的调频率,构造相位补偿函数,对广义二阶keystone变换后的信号进行补偿,再进行第二次广义二阶keystone变换,最后通过距离IFFT和方位FFT对目标进行检测,通过估计的参数可以获得目标的运动参数。仿真和实测数据验证了该方法的有效性。     

基于FPGA的二维FFT算法在LFMCW雷达信号处理中的应用

线性调频连续波( LFMCW)检测运动目标存在一定难度,利用二维FFT处理技术对目标回波信号相位信息进行提取,可有效抑制固定杂波,实现对运动目标的检测。介绍了线性调频连续波( LFMCW)雷达信号进行多普勒处理的原理以及利用单片FPGA实现多普勒测速雷达信号处理的过程,详细说明了数据的缓存、实数序列FFT的快速算法以及希尔伯特变换等步骤的FPGA实现,最后测试结果表明二维FFT算法能很好的提取出目标的距离和速度。