信号卷积的计算方法总结

卷积是信号与系统中的一个重要概念,是线性时不变系统时域分析的重要工具。线性时不变系统的零状态响应可通过系统激励与冲激响应或脉冲响应的卷积或卷积和计算得到。针对连续和离散时间信号,总结了已有的各类卷积及卷积和的计算方法,对各类方法的基本思路和应用条件进行了梳理。     

离散时间序列卷积和的求法

卷积是“信号与系统”课程中的重要概念。连续卷积与有限长序列的卷积和在文献中给出了多种解法。文中系统介绍了求解一般离散时间信号卷积和的几种方法,包括解析法、列表法、利用卷积和性质求解及应用单位样值信号求解,并通过举例加以说明。最后,对各种解法进行了比较和讨论。     

关于线性卷积及圆周卷积的简便竖式法计算

数字信号处理课中要求学生熟练掌握掌握离散时间信号的线性卷积及圆周卷积的计算方法,而大部分书中采用的图解法存在做题费时、变换复杂、容易出错等缺点。针对这个问题,本文提出了一种简单的算法,可以高效的求解有限长离散时间信号的线性卷积和圆周卷积,帮助读者快速的掌握离散时间信号的圆周卷积和线性卷积的计算。     

基于围线积分引理的信号变换域分析方法

提出了一种直接利用连续时间信号的双边LT来计算相应样值序列的双边ZT的方法。首先,基于围线积分引理,研究了s域卷积运算问题,给出了利用区左极点或区右极点计算s域卷积的留数方法;然后,依据连续时间非周期信号的ILT导出了非周期序列的IZT,给出了利用区外极点计算有终序列的IZT及计算z域卷积的留数方法;最后,解决了利用连续时间信号的双边LT来计算时域卷积信号和乘积信号相应样值序列的双边ZT的问题。     

用MATLAB计算连续时间信号的卷积

介绍了用MATLAB软件计算连续时间信号卷积的一般方法,分析了选取的参数对卷积结果的影响。     

一种频域卷积反演的新方法

本文提出了一种卷积反演的新方法。这种方法也是通过离散傅里叶变换在频域实现的，但是避免了通常所用的离散傅里叶变换方法当位于分母位置的信号频谱有零点存在时计算失效的问题。本文讨论了新方法与普通离散傅里叶变换方法之间的关系，并且给出了计算示例。     

一种频域卷积反演的新方法

本文提出了一种卷积反演的新方法。这种方法也是通过离散傅里叶变换(DFT)在频域实现的,但是避免了通常所用的离散傅里叶变换方法当位于分母位置的信号频谱有零点存在时计算失效的问题。本文讨论了新方法与普通离散傅里叶变换方法之间的关系,并且给出了计算示例。     

盲解卷积与窄带阵列模型结合的信号分离算法

在水声制导技术中,提出了一种高效分离算法,实现了对多目标源信号的分离,为系统后端对多目标定位提供了技术支持。窄带信号条件下,把盲分离与阵列信号处理结合起来．借助阵列模型把接收的混合信号变成解析信号,然后利用瞬时复值盲分离算法进行分离获得源信号的解析信号,取实部后便是实源信号。从而将实数的卷积混合转化为复数的瞬时混合,在盲分离阵列模型的基础上,通过复数盲分离的手段完成盲解卷积。解卷积恢复的多目标源信号十分有利于多目标特征识别与定位。通过构建正弦信号盲解卷积仿真实验,对文中提出的盲解卷积方法进行了验证。结果表明了该方法的正确性。     

长序列线性卷积的数论变换算法

本文提出一种利用数论变换计算长序列线性卷积的算法。它利用较短的数论变换对长序列卷积进行分段计算,减少了数论变换处理中移位操作的位数;用适当的字长就能完成较长的卷积计算,因而显著缩短了卷积执行时间。     

长序列信号快速相关及卷积的算法研究

文章通过对快速傅立叶变换（FFT）的算法原理分析,根据线性相关和卷积的数学特征及物理含义,针对长序列信号,提出了一种基于FFT的长序列快速相关及卷积算法,用C＋＋进行了算法编程,在计算机上得到较好的实验效果,提高了运行速度,并结合算术傅立叶变换进行了改进。     

Generalized discrete Hartley transforms

The discrete Hartley transform is generalized into four classes in the same way as the generalized discrete Fourier transform. Fast algorithms for the resulting transforms are derived. The generalized transforms are expected to be useful in applications such as digital filter banks, fast computation of the discrete Hartley transform for any composite number of data points, fast computations of convolution, and signal representation. The fast computation of skew-circular convolution by the generalized transforms for any composite number of data points is discussed in detail     

Summing received signal powers with arbitrary probability density functions on a logarithmic scale

A technique is presented to calculate the probability density function (pdf) for a sum of random variables that have pdf's on a logarithmic scale. In mobile radio it is often necessary to calculate the pdf of the total received signal power, which is the power sum of a number of simultaneously received signal powers. When the signal powers are given on a linear scale (e.g. Watts) probability density functions (pdf's) of the individual signals can be convolved to give the pdf for the received power of all the signals together. When, as is usual, the signal powers are given on a logarithmic scale (e.g. dBs) this is not possible. The simple convolution for the linear domain must now be replaced by a convolution for the logarithmic domain, which is not straightforward to compute. In this paper, a method is presented to compute the pdf of a power sum of two random variables, the logarithmic convolution. The results are not in closed form, numerical integration is necessary to find the resulting pdf. The method can be applied recursively to give results for power sums of more than two random variables. Although methods exist that give solutions in a closed form, they mainly use approximations and are valid only for specific distributions. The method presented in this paper yields exact results for arbitrary distributions. The results of the logarithmic convolution are verified by Monte-Carlo simulations. Even for large numbers of random variables the power sum results are shown to be correct.     

The gridding method for image reconstruction by Fourier transformation

The authors explore a computational method for reconstructing an n-dimensional signal f from a sampled version of its Fourier transform f;. The method involves a window function w; and proceeds in three steps. First, the convolution g;=w;*f; is computed numerically on a Cartesian grid, using the available samples of f;. Then, g=wf is computed via the inverse discrete Fourier transform, and finally f is obtained as g/w. Due to the smoothing effect of the convolution, evaluating w;*f; is much less error prone than merely interpolating f;. The method was originally devised for image reconstruction in radio astronomy, but is actually applicable to a broad range of reconstructive imaging methods, including magnetic resonance imaging and computed tomography. In particular, it provides a fast and accurate alternative to the filtered backprojection. The basic method has several variants with other applications, such as the equidistant resampling of arbitrarily sampled signals or the fast computation of the Radon (Hough) transform.     

Sinc interpolation of discrete periodic signals

The paper introduces a method for the sinc interpolation of discrete periodic signals. The convolution of the sinc kernel with the infinite sequence of a periodic function is rewritten as a finite summation. The method is equivalent to trigonometrical interpolation by Fourier series expansion     

A Multiresolution Model of Transient Microwave Signals in Dispersive Chiral Media

A multiresolution in time domain method is used to model the propagation of transient signals through dispersive chiral media. The modeling of these media requires the computation of convolution integrals, whose resolution level may be increased by introducing wavelets in the time dependence of the fields.     

The discrete Zak transform application to time-frequency analysisand synthesis of nonstationary signals

Algorithms to compute coefficients of the finite double sum expansion of time-varying nonstationary signals and to synthesize them from a finite number of expansion coefficients are presented. The algorithms are based on the computation of the discrete Zak transform (DZT). Fast algorithms to compute DZT are presented. Modifications to the algorithms which increase robustness are given     

A fast algorithm for general Volterra filtering

Volterra filters are a classical instrument for nonlinear channels and systems modeling, noise and echo cancellation, signal estimation and detection, and various other applications. As is well known, the computational weight of Volterra filters exponentially grows with the nonlinearity degree. This work presents a contribution to the efficient computation of Volterra filters with generic order nonlinearity found in many telecommunication applications. Our technique rests on the interpretation of the Mth-order one-dimensional Volterra filters in terms of M-dimensional linear convolution, and it adopts a multidimensional fast convolution scheme. This makes the method applicable to any M. Interestingly enough, fast convolution based on the standard multidimensional fast Fourier transform (MD FFT) in the case of Volterra filters is outperformed by direct computation. Our method is efficient due to the use of a special MD FFT which can exploit the symmetries of the signals entering the computation of Volterra filters and which makes it superior to direct computation. The points of interests of the results presented are both the generality and the fact that they show that the well-known nonlinearity/multidimensionality tradeoff of Volterra filters can have computational implications.     

一种基于循环谱的共信道多信号调制参数估计方法

共信道多信号的调制参数估计问题已成为通信信号处理领域的一个新兴课题,在非合作通信中是调制识别、信号解调等后续处理的基础。信号经过调制、成形及采样等处理后具有循环平稳性,本文提出了一种基于循环谱和离散谱线提取的调制参数估计方法。该算法利用信号调制参数和循环频率之间的关系,通过提取信号循环谱的谱频率截面上与循环频率相对应的离散谱线,实现对时频重叠的共信道多信号中每个信号分量调制参数的精确估计,主要包括载波频率和码元速率。Matlab仿真BPSK、8QAM两种类型的混合信号结果表明该方法切实有效,可以实现载波频率相差不大时共信道多信号的调制参数估计问题,并且算法计算复杂度小、精确度高、抗噪声性能好,不受频谱重叠度的影响。