匹配付里叶变换的噪声抑制与滤波

本文讨论了匹配付里叶变换对噪声的影响,通过理论和仿真分析表明,匹配付里叶变换可以扩展有色噪声的带宽,减小所匹配信号的带宽,从而提高信号的检测性能.由于信号和噪声不同的匹配付里叶域的分布不同,则可在不同的匹配付里叶域进行滤波,进一步提高检测性能.仿真表明,在信噪比为-20dB的条件下,线性调频信号通过多次不同的匹配付里叶域滤波,可得到信号比噪声高15dB以上的效果.     

数据倒序匹配付里叶变换处理

本文讨论了改进二步匹配付里叶变换的信号分辨能力和目标信号检测能力的处理方法，文中进行了理论分析，并做了计算机仿真，结果表明：数据的正常次序和数据的倒序的二步匹配付里叶变换在目标信号分辨方面具有互补性，它们谱积具有较高的目标信号分辨力，在信噪比达-20dB的条件下，仍具有比较好的目标信号检测能力。     

基于DMFT的LFM信号参数估计

线性调频信号是低截获概率雷达常用的一种信号形式,如何在低信噪比情况下检测线性调频信号一直是人们研究的焦点之一.在离散匹配傅里叶变换的基础上对算法进行改进,并利用改进后的算法分别对单分量和多分量线性调频信号进行仿真,仿真结果表明离散匹配傅里叶变换能够在低信噪比情况下比较准确地估计出线性调频信号的参数,不存在交叉项问题.离散匹配傅里叶变换是一种针对线性调频信号有效的参数估计方法.     

基于匹配追踪的弯折离散傅里叶变换

传统WDFT利用全通弯折函数AWF（AU—pass WarpingFunction）将单位圆上均匀分布的采样点,变换成非均匀分布的采样点。然而,这种计算方式会导致不同信号分量的延迟不同。本文基于匹配追踪的信号表示思想,提出了一种新的弯折傅里叶变换方法,实验结果表明,在原子个数大于信号长度情况下,该方法获得了较传统WDFT较好的弯折频谱表示性能。基于该方法表示的弯折离散傅里叶变换更适合于语音信号处理。     

基于匹配滤波和离散分数阶傅里叶变换的水下动目标LFM回波联合检测

匹配滤波器是高斯白噪声背景下LFM回波的最优检测器,并且根据匹配滤波器输出的峰值位置可以获得目标距离的估计.有色混响噪声背景以及目标径向速度造成的回波和样本失配都将导致匹配滤波器检测性能和测距精度下降.结合匹配滤波的定位特性和分数阶傅里叶变换对LFM信号的聚焦特性,该文提出基于匹配滤波和离散分数阶傅里叶变换的联合检测方法.仿真结果表明联合检测方法性能优于单匹配滤波器,并且可以获得目标径向速度的近似估计.     

离散傅里叶变换在被采样信号频率波动时的计算结果误差原因及解决方案

在被采样信号和周期信号测量处理中,离散傅里叶变换得到广泛的应用。依据傅里叶变换相关内容可知,若采样信号持续处于有限长状态,此时频谱为无限宽。反之,若信号频谱处于有限宽状态,采用信号持续时间为无限长。文章根据离散傅里叶变换相关理论进行分析,确定产生误差的原因,从而采取恰当的处理方法,降低误差发生率。     

分数阶傅里叶变换域上带通信号的采样定理

傅里叶变换和采样定理是信号处理领域的两大基本问题,采样定理研究了傅里叶变换域上带限信号的采样和重构理论.分数阶傅里叶变换(FRFT)是傅里叶变换的一种推广,与之相应的采样理论目前还不十分完备,所以有必要从FRFT域上重新研究采样定理.本文首先得到了均匀冲激串采样信号的FRFT,然后在此基础上导出了FRFT域上带通信号和低通信号的采样定理和重构公式.这些结果是经典理论的推广,将丰富分数阶傅里叶变换的理论体系.     

基于自适应分数阶傅里叶变换的线性调频信号检测及参数估计

该文提出了一种基于最小均方算法的自适应计算分数阶傅里叶变换的方法并将该方法应用到多分量chirp信号的检测与估计之中。该方法通过对连续型分数阶傅里叶反变换进行离散化采样,得到适合数值计算的离散形式,进而通过适当的选择输入向量和目标函数构造自适应滤波器,经过最小均方算法进行训练后所得的滤波器权系数即为分数阶傅里叶变换的结果。仿真实验表明,该方法可以用来计算分数阶傅里叶变换及对chirp信号进行检测和参数估计,且计算延时相对较小。     

线性正则变换域的带限信号采样理论研究

线性正则变换是傅里叶变换、分数阶傅里叶变换的更广义形式,是一种潜在而重要的信号变换工具,但是与之相应的采样理论目前还不十分完备,所以有必要在线性正则变换域重新研究采样定理.本文从线性正则变换的定义和性质出发,首先得到时域均匀采样信号的线性正则变换;然后在此基础上导出了线性正则变换域带限信号的采样定理和重构公式;最后以chirp信号为例仿真说明了采样定理的应用.文中得出的结论是对经典采样理论的推广,将进一步丰富线性正则变换的理论体系.     

从CTFT公式出发推导周期序列的DTFT

基本的傅里叶变换有四种,学生在学习和使用过程中在连续和离散之间感觉有一些隔离而不容易将二者融会贯通起来,而是机械地记忆。在频域引入冲激函数后,周期信号/序列也有傅里叶变换,以便于将傅里叶分析方法应用到调制和采样等问题中,这体现了傅里叶变换统一的重要性。本文借助四种基本变换讨论了在连续和离散之间傅里叶变换的统一性,将连续时间和离散时间傅里叶分析联系起来,提供了一个统一的框架,以达到更好的教学效果。     

一种新的变换——匹配傅里叶变换

本文提出了非线性调制信号处理的新方法——匹配傅里叶变换.匹配傅里叶变换是对傅里叶变换的新发展,是对变采样率处理技术的概括.文中对匹配傅里叶变换进行了理论分析,论述了其与变采样率处理技术之间的关系.最后,进行了计算机仿真,仿真结果表明,匹配傅里叶变换理论是正确的.     

基于离散匹配傅立叶变换的多分量LFM信号检测和参数估计

多分量LFM信号的检测和参数估计是一个被广泛讨论的问题。本文首先介绍了离散匹配傅立叶变换的基本原理,然后结合逐次消去的思想提出了基于离散匹配傅立叶变换的多分量LFM信号检测和参数估计的原理及实现算法,并进行了计算机仿真。仿真结果验证了该算法的有效性。     

离散傅里叶变换的进一步探析

在数字信号处理领域,离散傅里叶变换是一个非常重要的术语,尤其是在他的高效算法FFT出现以后,在信号分析和处理中得到了广泛的应用。但是,人们对这个术语存在一些模糊的认识。通过对具体谱分析问题的研究,分析了连续傅里叶变换与离散傅里叶变换之间的关系,深入探讨了离散傅里叶变换的渊源,期望对离散傅里叶变换有一个清晰的认识。     

Discrete fractional Fourier transform based on orthogonalprojections

The continuous fractional Fourier transform (FRFT) performs a spectrum rotation of signal in the time-frequency plane, and it becomes an important tool for time-varying signal analysis. A discrete fractional Fourier transform has been developed by Santhanam and McClellan (see ibid., vol.42, p.994-98, 1996) but its results do not match those of the corresponding continuous fractional Fourier transforms. We propose a new discrete fractional Fourier transform (DFRFT). The new DFRFT has DFT Hermite eigenvectors and retains the eigenvalue-eigenfunction relation as a continous FRFT. To obtain DFT Hermite eigenvectors, two orthogonal projection methods are introduced. Thus, the new DFRFT will provide similar transform and rotational properties as those of continuous fractional Fourier transforms. Moreover, the relationship between FRFT and the proposed DFRFT has been established in the same way as the conventional DFT-to-continuous-Fourier transform     

Image and video processing using discrete fractional transforms

The mathematical transforms such as Fourier transform, wavelet transform and fractional Fourier transform have long been influential mathematical tools in information processing. These transforms process signal from time to frequency domain or in joint time–frequency domain. In this paper, with the aim to review a concise and self-reliant course, the discrete fractional transforms have been comprehensively and systematically treated from the signal processing point of view. Beginning from the definitions of fractional transforms, discrete fractional Fourier transforms, discrete fractional Cosine transforms and discrete fractional Hartley transforms, the paper discusses their applications in image and video compression and encryption. The significant features of discrete fractional transforms benefit from their extra degree of freedom that is provided by fractional orders. Comparison of performance states that discrete fractional Fourier transform is superior in compression, while discrete fractional cosine transform is better in encryption of image and video. Mean square error and peak signal-to-noise ratio with optimum fractional order are considered quality check parameters in image and video.     

基于LFM-BPSK 信号的距离像成像方法

针对雷达通信一体化系统中雷达成像与通信共享信号的设计,分析了常见的一体化信号设计模式。首先,利用线性调频信号相位调制传递通信信息,设计了一种基于线性调频—二进制相移键控(LFM-BPSK)调制的雷达通信一体化信号,并给出了运动扩展目标的回波信号表达式;其次,通过计算单脉冲回波信号采样的逆离散傅里叶变换或离散傅里叶变换,提出了基于一体化信号合成高分辨距离像方法;然后,依据相位因子对傅里叶变换的影响,分析了多普勒效应对一体化信号合成距离像的影响;最后,对一体化信号的雷达成像性能进行了仿真计算。     

New Realization of DFT Applied to CCITT No. 5 Telephone Signaling System

This paper describes a digital multifrequency signal receiver based on the discrete Fourier transform (DFT) principle. The new lookup table implementation for fast multiplication of an input PCM sample and a kernel sample leads to simple hardware for the operation of 128 time-multiplexed channels of the CCIT No. 5 line signal receiver. Overlap operation and guard logics are also employed to meet the signaling system requirements.     

Algebraic signal processing theory: 2-D spatial hexagonal lattice.

We develop the framework for signal processing on a spatial, or undirected, 2-D hexagonal lattice for both an infinite and a finite array of signal samples. This framework includes the proper notions of z-transform, boundary conditions, filtering or convolution, spectrum, frequency response, and Fourier transform. In the finite case, the Fourier transform is called discrete triangle transform. Like the hexagonal lattice, this transform is nonseparable. The derivation of the framework makes it a natural extension of the algebraic signal processing theory that we recently introduced. Namely, we construct the proper signal models, given by polynomial algebras, bottom-up from a suitable definition of hexagonal space shifts using a procedure provided by the algebraic theory. These signal models, in turn, then provide all the basic signal processing concepts. The framework developed in this paper is related to Mersereau's early work on hexagonal lattices in the same way as the discrete cosine and sine transforms are related to the discrete Fourier transform-a fact that will be made rigorous in this paper.     

What is the fast Fourier transform?

The fast Fourier transform is a computational tool which facilitates signal analysis such as power spectrum analysis and filter simulation by means of digital computers. It is a method for efficiently computing the discrete Fourier transform of a series of data samples (referred to as a time series). In this paper, the discrete Fourier transform of a time series is defined, some of its properties are discussed, the associated fast method (fast Fourier transform) for computing this transform is derived, and some of the computational aspects of the method are presented. Examples are included to demonstrate the concepts involved.