一种基于FIR滤波器的非均匀小波周期采样方法

针对Shannon采样定理只能处理带限信号和要求采样率不低于Nyquist率的缺陷,研究了小波空间中的一种非均匀周期采样理论,给出了定理成立的条件及其突破Nyquist率限制的理论依据,将采样理论扩展到了非带限信号领域。对于紧支尺度函数张成的子波空间中的任意信号,可以利用非均匀周期采样所得的样本以及正交镜像滤波器理论求出其小波系数的估计值,进而得到信号的重建表达式。该方法在信号重建的过程中用到的全是有限冲击响应滤波器,避免了无限冲击响应滤波器的出现,降低了实际物理实现的难度。计算机仿真结果表明该方法是切实有效的,信号重建的相对误差小于1%。     

平移不变空间中信号的min-max插值重建方法

在一般平移不变子空间框架下讨论信号的有限非一致采样重建的问题.基于信号的子空间表示,本文给出一般信号在min-max插值准则下的最优插值方法以及相应的非迭代算法.该方法可以导出著名带限信号的Yen插值.数值实验表明所给方法能十分有效地重建信号.     

一种基于有限更新率的非带限信号采样方法

针对Shannon采样定理只能处理带限信号的缺陷,推导论证了一种基于有限更新率的非带限信号采样方法.该方法处理的是更新率有限的信号,先将信号经过一个采样核滤波,然后以不低于信号更新率的采样率对其采样,就可以借助抵消滤波器和范德蒙方程从采样点中重建出原信号.计算机仿真结果表明,该方法重建原信号的精确度较高,并且具有较好的抗噪声性能,信噪比为20dB时信号估计值的均方差只有10-5的数量级,完全能满足实际工程的需求.     

一种基于小波的导数采样算法

研究了小波空间中的一种导数采样理论,给出了定理成立的条件及其突破Nyquist率限制的理论依据,将采样理论扩展到了非带限信号领域。对于紧支尺度函数张成的子波空间中的任意信号,可以利用对信号及其导数采样所得的样本求出其小波系数的估计值,进而得到信号的重建表达式。在信号重建的过程中用到的全是有限冲击响应滤波器,降低了实际物理实现的难度。计算机仿真结果表明该方法是切实有效的,信号重建的相对误差小于0．11％。     

小波空间中采样理论研究

本文研究了小波理论在非带限信号采样中的应用，分析了Walter子波空间采样定理及其突破Nyquist率限制的理论依据；介绍了在信号恢复的过程中可以避免无限冲激响应滤波器出现的周期性非均匀采样及导数采样理论，并以紧支信号为例分别进行了仿真验证。     

基于奇异值分解的非带限信号采样算法

本文借助奇异值分解技术,研究了对狄拉克流这类特殊非带限信号的采样与重建算法。先对信号的采样点进行离散傅里叶变换,并用生成的系数形成Hankel矩阵,然后对Hankel矩阵进行奇异值分解,求取狄拉克流的位置信息,再解范德蒙方程组求得狄拉克流的权信息,重建出原信号。该算法具有计算量小、信号恢复精确率高和抗噪声能力强的特点。     

RFRFT域非均匀采样信号重构算法研究

讨论了非均匀采样信号简化分数阶傅立叶变换（RFRFT）域频谱重构的方法,推导了利用原信号的连续频谱无偏估计重构信号的算法,并得到了重构公式,验证了RFRFT域非均匀采样信号重构的可实现性.同时仿真了RFRFT域上非均匀采样信号的重构实施例,验证了该方法在RFRFT域上非均匀采样信号重构的准确性和稳定性.     

软件无线电中的带通采样分析

近年来,软件无线电技术以其强大的通用性和灵活性得到了广泛发展和应用。研究了软件无线电中广泛采用的带通采样技术。在给出带通采样定理一般结论的基础上,重点分析了实现无混叠带通采样的条件,得到了边界频率点上4种不同取值情况下带通采样频率的取值范围,并利用时域内插进行了带通采样信号的完全重建。最后,采用Matlab进行了仿真验证。     

周期非均匀采样多带信号时最优参数的确定方法

 以采样完全重构为基础,提出了一种周期非均匀采样多带信号时的采样阶数、单通道采样周期等参数最优值的确定方法;同时以此方法的构建思想作为指导,推导出了采样阶数固定时最优单通道采样周期以及单通道采样周期固定时最优采样阶数等确定方法.最后,通过实例验证了通过该方法确定参数可保证周期非均匀采样多带信号时的采样频率降到最低.     

基于伪非均匀采样的高精度时间间隔测量方法

为提高脉冲激光测距的精度,采用一种新的高精度时间间隔测量方法。在脉冲计数法的基础上,利用温补晶振生成与计时量化时钟同步同频率的参考正弦波信号,将提高时间间隔测量精度问题转化为初始相位估计;通过伪非均匀采样方法对参考正弦波信号采样,并针对研究中所采用的伪非均匀采样方法推导出相应的理论公式,然后利用最小二乘法对采样数据进行曲线拟合,将伪非均匀采样信号还原成被采样的参考信号,实现相位估计,从而实现高精度时间间隔测量。将本文方法应用于脉冲激光测距仪中,实验表明,测距仪的测距精度优于±5mm。     

Reconstruction of nonuniformly sampled time-limited signals using prolate spheroidal wave functions

Shannon's sampling theory is based on the reconstruction of bandlimited signals which requires infinite number of uniform time samples. Indeed, one can only have finite number of samples for numerical implementation. In this paper, as a dual of the bandlimited reconstruction, a solution for time-limited signal reconstruction from nonuniform samples is proposed. The system model we present is based on the idea that time-limited signals which are also nearly bandlimited can be well approximated by a low-dimensional subspace. This can be done by using prolate spheroidal wave functions as the basis. The order of the projection on this basis is obtained by means of the time–frequency dimension of the signal, especially in the case of non-stationary signals. The reconstruction requires the estimation of the nonuniform sampling times by means of an annihilating filter. We obtain the reconstruction parameters by solving a linear system of equations and show that our finite-dimensional model is not ill-conditioned. The practical aspects of our method including the dimensionality reduction are demonstrated by processing synthetic as well as real signals.     

Sampling random signals in a fractional Fourier domain

In this paper, we consider the sampling and reconstruction schemes for random signals in the fractional Fourier domain. We define the bandlimited random signal in the fractional Fourier domain, and then propose the uniform sampling and multi-channel sampling theorems for the bandlimited random signal in the fractional Fourier domain by analyzing statistical properties of the input and the output signals for the fractional Fourier filters. Our formulation and results are general and include derivative sampling and periodic nonuniform sampling in the fractional Fourier domain for random signals as special cases.     

Nonuniform sampling and antialiasing in image representation

A unified approach to the representation and processing of a class of images which are not bandlimited but belong to the space of locally bandlimited signals is presented. A nonuniform sampling theorem (Clark et al, 1985) for functions belonging to this space is extended, and a class of nonstationary stochastic processes is considered. The space of locally bandlimited signals is shown to be a reproducing-kernel space. A generalized projection theorem can therefore be applied, yielding either a continuous or a discrete projection filter. The former can be used for image conditioning prior to nonuniform sampling, while the latter provides a general tool for image representation by nonuniform sampling schemes. The problem of finding the local bandwidth of a given signal, in order to generate an optimal sampling scheme, is addressed in the context of signal representation in the combined position-frequency space. The stochastic estimation of parameters which characterize the local bandwidth is discussed. Bounds on the error resulting from the utilization of nonexact position-varying signal parameters are derived     

分数阶Fourier域上非均匀采样信号的频谱重构研究

 本文研究了分数阶Fourier变换域上非均匀采样信号的重构问题.首先得到周期非均匀采样信号经非均匀分数阶Fourier变换后的频谱表达式,研究了该分数阶频谱和信号连续分数阶频谱之间的关系,并基于该关系式提出了一种分数阶Fourier域周期非均匀采样信号的频谱重构算法;其次,讨论了分数阶Fourier变换域上更加一般情况下非均匀采样信号重构问题;最后,给出了周期非均匀采样信号频谱重构的仿真结果.     

Analysis and recovery of sample-and-hold and linearly interpolatedsignals with irregular samples

A modular method is suggested to recover a bandlimited signal from the sample-and-hold and linearly interpolated (or, in general, an n th-order hold) version of the irregular samples. The approach is an extension of work for the sample-and-hold signals with uniform samples. A coordinate transform technique is applied to show a practical way of finding an approximate inverse coordinate mapping. As a byproduct, some sufficient conditions on the nonuniform samples for the modular technique to the valid are derived     

Sampling of Bandlimited Signals in Fractional Fourier Transform Domain

Fractional Fourier transformed bandlimited signals are shown to form a reproducing kernel Hilbert space. Basic properties of the kernel function are applied to the study of a sampling problem in the fractional Fourier transform (FRFT) domain. An orthogonal sampling basis for the class of bandlimited signals in the FRFT domain is then given. A nonuniform sampling theorem for bandlimited signals in the FRFT domain is also presented. Numerical experiments are given to demonstrate the effectiveness of the proposed nonuniform sampling theorem.     

A Versatile Iterative Framework for the Reconstruction of Bandlimited Signals from Their Nonuniform Samples

In this paper, we study a versatile iterative framework for the reconstruction of uniform samples from nonuniform samples of bandlimited signals. Assuming the input signal is slightly oversampled, we first show that its uniform and nonuniform samples in the frequency band of interest can be expressed as a system of linear equations using fractional delay digital filters. Then we develop an iterative framework, which enables the development and convergence analysis of efficient iterative reconstruction algorithms. In particular, we study the Richardson iteration in detail to illustrate how the reconstruction problem can be solved iteratively, and show that the iterative method can be efficiently implemented using Farrow-based variable digital filters with few general-purpose multipliers. Under the proposed framework, we also present a completed and systematic convergence analysis to determine the convergence conditions. Simulation results show that the iterative method converges more rapidly and closer to the true solution (i.e. the uniform samples) than conventional iterative methods using truncation of sinc series.     

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.     

Peak value estimation of bandlimited signals from their samples, noise enhancement, and a local characterization in the neighborhood of an extremum

The paper addresses the problem of estimating the peak value of bandlimited signals from their samples with and without oversampling. This problem has significant relevance to orthogonal frequency-division multiplexing (OFDM) signal processing and system design. In particular, an upper bound on the peak value is established given the peak value of the samples and the oversampling rate. Moreover, it is shown that the bounds are sharp for all practical rates by constructing bandlimited signals taking on this bound. The proof also provides a local characterization of bandlimited signals in the neighborhood of an extremum. A different analysis examines the effect of small errors in the samples. It is shown that oversampling can provide robust recovery in the sense that small errors in the samples lead to small errors in the reconstructed signal. Again, an upper bound is derived relating the peak error in the samples and the peak error in the signals. Furthermore, both problems are shown to be coupled and put in a unifying context. The bounds are compared and applied to problems concerning OFDM.