周期非均匀采样信号的重建中的优化子频带划分

对于周期非均匀采样,由于每个均匀采样流的采样率通常都是小于Nyquist率的,因此,采样信号频谱中会发生频率混叠。这表明在采样信号的重建频带内将会有多于1的谱分量。因为不是所有的与重建频带相交的谱分量都会覆盖整个重建频带,所以有必要将重建频带分成若干个子频带进行分析,构造内插函数,这样有利于减小重建所必需的最小采样率。本文提出一种优化的子频带划分方法,通过该方法在重建频带上定义子频带,能在保证重建所需的采样率最低的情况下使子频带的个数最少,这对于简化内插滤波器的结构有重要的意义。     

Functionally Weighted Lagrange Interpolation of Band-Limited Signals From Nonuniform Samples

A modification of the conventional Lagrange interpolator is proposed in this paper, that allows one to approximate a band-limited signal from its own nonuniform samples with high accuracy. The modification consists in applying the Lagrange method to the signal, but pre-multiplied by a fixed function, and then solving for the desired signal value. Its efficiency lies in the fact that the fixed function is independent of the sampling instants. It is shown in this paper that the function can be selected so that the interpolation error decreases exponentially with the number of samples, for the case in which the sampling instants have a maximum deviation from a uniform grid. This paper includes a low-complexity recursive implementation of the method. Its accuracy is validated in the numerical examples by comparison with several interpolators in the literature, and by deriving upper and lower bounds for its maximum error.     

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.     

Reconstruction of Multidimensional Signals From Irregular Noisy Samples

We focus on a multidimensional field with uncorrelated spectrum and study the quality of the reconstructed signal when the field samples are irregularly spaced and affected by independent and identically distributed noise. More specifically, we apply linear reconstruction techniques and take the mean-square error (MSE) of the field estimate as a metric to evaluate the signal reconstruction quality. We find that the MSE analysis could be carried out by using the closed-form expression of the eigenvalue distribution of the matrix representing the sampling system. Unfortunately, such distribution is still unknown. Thus, we first derive a closed-form expression of the distribution moments, and we find that the eigenvalue distribution tends to the MarČenko–Pastur distribution as the field dimension goes to infinity. Finally, by using our approach, we derive a tight approximation to the MSE of the reconstructed field.      

High-Rate Interpolation of Random Signals From Nonideal Samples

We address the problem of reconstructing a random signal from samples of its filtered version using a given interpolation kernel. In order to reduce the mean squared error (MSE) when using a nonoptimal kernel, we propose a high rate interpolation scheme in which the interpolation grid is finer than the sampling grid. A digital correction system that processes the samples prior to their multiplication with the shifts of the interpolation kernel is developed. This system is constructed such that the reconstructed signal is the linear minimum MSE (LMMSE) estimate of the original signal given its samples. An analytic expression for the MSE as a function of the interpolation rate is provided, which leads to an explicit condition such that the optimal MSE is achieved with the given nonoptimal kernel. Simulations confirm the reduction in MSE with respect to a system with equal sampling and reconstruction rates.      

基于双谱的谐波信号相位重构

本文提出了一种基于双谱分析的谐波信号相位精确重构方法.该方法通过在被测信号中加入一相位为零的半基频信号,并对该合成信号进行双谱分析,实现了被测信号的相位精确求解,解决了已有基于双谱的信号相位估计方法中所存在的相对相移问题.仿真结果验证了该方法的有效性.     

Error Analysis of Frame Reconstruction From Noisy Samples

This paper addresses the problem of reconstructing a continuous function defined on R^d from a countable collection of samples corrupted by noise. The additive noise is assumed to be i.i.d. with mean zero and variance sigma². We sample the continuous function / on the uniform lattice (1/m)Z^d, and show for large enough m that the variance of the error between the frame reconstruction f_epsiv,m from noisy samples of f and the function f satisfy var(f_epsiv,m(x) - f(x)) ap(sigma²/m^d)C_x where C_x is the best constant for every x isin R^d. We also prove a similar result in the case that our data are weighted-average samples of / corrupted by additive noise.     

Hybrid Temporal Error Concealment Methods for Block-Based Compressed Video Transmission

Boundary matching algorithm (BMA) and decoder motion vector estimation (DMVE) are two well-known temporal error concealment methods using the matching-based approach. In these two methods, the motion vector of each missing block is estimated by choosing one among candidate motion vectors which minimizes a sum of absolute differences (SAD) between boundary pixels of the corrupted macroblock. In general, the performance of DMVE is better than that of BMA. However, depending on the location or pattern of the corrupted block, BMA produces higher visual quality than DMVE. In this paper, we propose two types of hybrid error concealment methods; switching method and blending method. The switching method chooses one of two results obtained by BMA and DMVE based on the normalized SAD values. In the blending method, the weighted sum of the results concealed by the aforementioned two methods is utilized to improve the performance of error concealment. In order to reduce blocking artifacts further, the modified overlapped-block motion compensation is adaptively applied to the concealed blocks. Simulation results show that the proposed methods outperform other techniques in terms of subjective visual quality as well as PSNR performance.     

A Reconstruction Algorithm for Photoacoustic Imaging Based on the Nonuniform FFT

Fourier reconstruction algorithms significantly outperform conventional backprojection algorithms in terms of computation time. In photoacoustic imaging, these methods require interpolation in the Fourier space domain, which creates artifacts in reconstructed images. We propose a novel reconstruction algorithm that applies the one-dimensional nonuniform fast Fourier transform to photoacoustic imaging. It is shown theoretically and numerically that our algorithm avoids artifacts while preserving the computational effectiveness of Fourier reconstruction.      

Nonuniform Interpolation of Noisy Signals Using Support Vector Machines

The problem of signal interpolation has been intensively studied in the information theory literature, in conditions such as unlimited band, nonuniform sampling, and presence of noise. During the last decade, support vector machines (SVM) have been widely used for approximation problems, including function and signal interpolation. However, the signal structure has not always been taken into account in SVM interpolation. We propose the statement of two novel SVM algorithms for signal interpolation, specifically, the primal and the dual signal model based algorithms. Shift-invariant Mercer's kernels are used as building blocks, according to the requirement of bandlimited signal. The sine kernel, which has received little attention in the SVM literature, is used for bandlimited reconstruction. Well-known properties of general SVM algorithms (sparseness of the solution, robustness, and regularization) are explored with simulation examples, yielding improved results with respect to standard algorithms, and revealing good characteristics in nonuniform interpolation of noisy signals.     

基于非均匀FFT的压缩感知雷达信号快速重构方法

雷达处理是压缩感知理论重要的应用方向之一,基于压缩感知的雷达处理可以降低对回波信号的采样速率要求,并且在部分应用中也可改善处理性能。然而,压缩感知重构算法的计算复杂性限制了压缩感知理论在实际雷达信号处理中的应用,尤其是大尺度雷达数据的处理。本文提出了一种基于压缩感知的雷达信号快速重构方法,利用均匀和非均匀快速傅里叶变换运算实现了常规压缩感知重构算法中的矩阵-向量乘法运算,有效降低了重构算法的计算复杂度,加快了压缩感知雷达信号的重构速度。同时,由于引入了快速傅里叶变换运算,该方法消除了大多数常规重构算法对感知矩阵的存储需求。仿真实验验证了该方法的可行性和高效性。      

基于小波变换的非均匀采样信号频谱的研究

该文提出基于小波变换的非均匀采样信号频谱的检测方法,给出变换函数关系使得非均匀采样信号满足小波变换的两个基本条件。文中说明了小波的非均匀化过程,从均匀小波得到非均匀小波,以非均匀小波分析非均匀采样信号,得到非均匀采样信号的频谱。文中还说明了非均匀小波变换的抗混叠的原理以及对信号频谱的检测方法,最后给出实验结果。理论和实验表明,非均匀采样信号的小波变换方法是一种行之有效的非均匀采样信号的频率检测方法,使用该方法处理信号可以得到准确的频率估计效果。     

离散光电信号的自适应重构方法

采集雷达信号数据源发射的电磁信号以后,对其进行时域至频域的变换即离散傅里叶变换、自适应幅度波束成形使得信号频率得到补偿,并对重构信号的波形进行分析和比较.通过重新定义的模型进行表征,使得可见光、红外、雷达频谱等波段数据不损失自身所携带信息情况下,减少时变时间函数和选择性积分在检测性能方面遭受大的损失.计算得到重构信号和...     

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。     

Recovery of Bandlimited Signals from Unequally Spaced Samples

A method of recovering bandlimited signals from unequally spaced samples is described. The method uses an iterative procedure which requires low pass filtering of the unequally spaced sample pulses. This is followed by resampling at the same unequally spaced times and again low pass filtering to obtain a correction signal. Repeated application of this process is shown to converge to the original signal. These results are obtained by slight modifications of the analysis in Reference 2.     

Robust Quantization of Discrete-Time Signals with Independent Samples

TheN-level uniform quantizer on[-c,c]plus the assignment ofy_{0}deg = -(a _{s}+ c)/2andy_{N+1}deg = (a_{s}+ c)/2to signal values falling in the saturation regions[-a_{s},- c) and (c,a_{s}], respectively, is shown to be the minimax(N + 2)-level quantizer with a nonsaturating input range[-c,c]. The performance criterion considered is the mean weighted quantization error and the input signals are only required to be amplitude bounded bypm a_{s}wherea_{s} > c > 0. The worst case input signal marginal probability distributions are shown to be discrete. From the derivation of this result, the minimax error can be computed. An example is given which illustrates the performance of the minimax quantizer for several input ranges against different input signal probability distributions.     

产生受锁彩场信号的多种方法

本文提出了产生被录像信号同步锁相彩场信号的多种方法,并对其实际电路进行详细的分析。     

基于非均匀采样的信号频率和到达角联合估计

利用阵列中每个阵元有不同采样频率的非均匀采样特性,可以等效得到时变的虚拟非均匀线阵,然后采用经典的子空间法中的MUSIC测向法,通过网格搜索实现对信号频率和DOA联合估计;并且通过合理设置各阵元间的采样率,有效提高空间谱估计的分辨率和精度,还可避免测向角度模糊。该算法采用网格搜索法,明显减少了计算量。计算机仿真结果证明该方法的有效性和正确性。     

气泡激光散射信号处理方法

提出了阈值检测、降噪处理和功率谱估计三种分析和处理水中气泡激光散射信号的方法.利用这三种方法分别对不同散射角时的测量信号进行了处理,得到了水中气泡激光散射强度随散射角的分布特性.并将实验结果与米氏(Mie)理论结果及水的散射强度进行了对比,比较和分析了三种方法的优劣.阈值检测法和降噪处理法分别以平均值和绝对偏差为中心来估计气泡散射强度,它们不能隔离直流分量.功率谱估计法处理得到的气泡角散射特性与Mie理论结果一致,能够区别开气泡散射和水的散射,两者相差近1个数量级.实验结果表明功率谱估计法是最合理的处理气泡激光散射信号的方法.     

Novel Sampling and Reconstruction Method for Non-Bandlimited Impulse Signals

To sample non-bandlimited impulse signals, an extremely high-sampling rate analog-todigital converters （ADC） is required. Such an ADC is very difficult to be implemented with present semiconductor technology. In this paper, a novel sampling and reconstruction method for impulse signals is proposed. The required sampling rate of the proposed method is close to the signal innovation rate, which is much lower than the Nyquist rate in conventional Shannon sampling theory. Analysis and simulation results show that the proposed method can achieve very good reconstruction performance in the presence of noise.