The adaptive chirplet transform and visual evoked potentials

We propose a new approach based upon the adaptive chirplet transform (ACT) to characterize the time-dependent behavior of the visual evoked potential (VEP) from its initial transient portion (tVEP) to the steady-state portion (ssVEP). This approach employs a matching pursuit (MP) algorithm to estimate the chirplets and then a maximum-likelihood estimation (MLE) algorithm to refine the results. The ACT decomposes signals into Gaussian chirplet basis functions with four adjustable parameters, i.e., time-spread, chirp rate, time-center and frequency-center. In this paper, we show how these four parameters can be used to distinguish between the transient and the steady-state phase of the response. We also show that as few as three chirplets are required to represent a VEP response. Compared to decomposition with Gabor logons, a more compact representation can be achieved by using Gaussian chirplets. Finally, we argue that the adaptive chirplet spectrogram gives a superior visualization of VEP signals' time-frequency structures when compared to the conventional spectrogram.     

A four-parameter atomic decomposition of chirplets

A new four-parameter atomic decomposition of chirplets is developed for compact and precise representation of signals with chirp components. The four-parameter chirplet atom is obtained from the unit Gaussian function by successive applications of scaling, fractional Fourier transform (FRFT), and time-shift and frequency-shift operators. The application of the FRFT operator results in a rotation of the Wigner distribution of the Gaussian in the time-frequency plane by a specified angle. The decomposition is realized by using the matching pursuit algorithm. For this purpose, the four-parameter space is discretized to obtain a small but complete subset in the Hilbert space. A time-frequency distribution (TFD) is developed for clear and readable visualization of the signal components. It is observed that the chirplet decomposition and the related TFD provide more compact and precise representation of signal inner structures compared with the commonly used time-frequency representations     

基于优化初值选择的自适应高斯包络线性调频基信号分解

基于高斯包络线性调频基的自适应信号分解是一种分辨力高、性能优良的时频分析算法,在语音信号、地震信号、雷达信号等可以用调频类函数进行建模的信号分析中有着广阔的应用前景。该算法在四维参数空间构造和求解超越方程,得到参数的闭式解,与传统的优化算法相比大大降低了运算量。对于由高斯包络线性调频基不相交或浅相交形成的简单信号,该算法具有非常优良的分辨性能,而对由高斯包络线性调频基深相交形成的复杂信号分解存在较大误差。本文针对这一问题进行研究,指出初值选择在该算法中的重要作用,分析了得到高精度分解结果的初值条件,提出了基于优化初值选择的高斯包络线性调频基自适应信号分解算法。通过在局部信号粗时频平面中搜索最优初值,结合自适应分解中建立和求解超越方程的方法得到参数闭式解,提高了分解精度,同时降低了运算量。对仿真信号及语音信号的分解效果验证了改进后算法的有效性和准确性。     

一种有效的基于Chirplet自适应信号分解算法

基于线性调频小波(chirplet)的自适应信号分解法,将待分析的线性调频(Chirp)信号分解成为一组chirplet基函数的线性叠加,能够更清楚地表述Chirp信号的时频特征.其中关键的问题,是如何自适应地估计与信号最匹配的chirplet,这将影响到自适应分解的效果.目前,还没有一种有效chirplet估计算法.本文提出了一种新的chirplet估计算法,该法充分利用了chirplet的特点,具有较高的参数估计精度.仿真数据的实验结果证明了该方法的有效性.     

短时高斯包络线性调频基自适应信号分解算法

作为一种参数化时频分析的方法,基于高斯包络线性调频基自适应信号分解的快速算法具有分辨力高、零交叉项和计算量小的优点,在信号时频分析中具有独特的优势和广阔的应用前景.然而该快速算法却存在由于采样点初值选择不当而造成分解失效的缺点,虽然后来的基于优化初值选择的自适应高斯包络线性调频基信号分解对初值选择算法进行了改进,提高了分解性能的稳定性,但仍存在较多的问题没有解决.本文将对这些问题进行研究和改进,并提出短时自适应高斯包络线性调频基信号分解算法.算法通过加短时窗来增强时频中心定位的准确性,通过控制采样基时宽来获取有效的初始方差取值范围,从而提高了分解的自适应性和稳定性.对仿真信号和语音信号的分解结果表明了该算法的有效性.     

Fast matching pursuit with a multiscale dictionary of Gaussianchirps

We introduce a modified matching pursuit algorithm, called fast ridge pursuit, to approximate N-dimensional signals with M Gaussian chirps at a computational cost O(MN) instead of the expected O(MN² logN). At each iteration of the pursuit, the best Gabor atom is first selected, and then, its scale and chirp rate are locally optimized so as to get a “good” chirp atom, i.e., one for which the correlation with the residual is locally maximized. A ridge theorem of the Gaussian chirp dictionary is proved, from which an estimate of the locally optimal scale and chirp is built. The procedure is restricted to a sub-dictionary of local maxima of the Gaussian Gabor dictionary to accelerate the pursuit further. The efficiency and speed of the method is demonstrated on a sound signal     

A CLOSED-FORM WIDEBAND DIRECTION-OF-ARRIVAL ESTIMATION WITH CHIRPLET-BASED ADAPTIVE SIGNAL DECOMPOSITION ALGORITHM

The Direction-Of-Arrival (DOA) estimation with Coherent Signal Subspace (CSS)is not easy to cxtend from narrowband to wideband case.Time-frequency analysis is a powerfultechnique to deal with time-variant or non-stationary signal. Its combination with CSS exploresa new field in signal processing, especially the wideband DOA estimation. The chirp function isone of the most fundamental functions in nature. Many nature events can be modeled as chirpletfunction, such as radar system or scismic exploring.Hence,the chirplet-based signal decomposi-     

Matching pursuits with time-frequency dictionaries

The authors introduce an algorithm, called matching pursuit, that decomposes any signal into a linear expansion of waveforms that are selected from a redundant dictionary of functions. These waveforms are chosen in order to best match the signal structures. Matching pursuits are general procedures to compute adaptive signal representations. With a dictionary of Gabor functions a matching pursuit defines an adaptive time-frequency transform. They derive a signal energy distribution in the time-frequency plane, which does not include interference terms, unlike Wigner and Cohen class distributions. A matching pursuit isolates the signal structures that are coherent with respect to a given dictionary. An application to pattern extraction from noisy signals is described. They compare a matching pursuit decomposition with a signal expansion over an optimized wavepacket orthonormal basis, selected with the algorithm of Coifman and Wickerhauser see (IEEE Trans. Informat. Theory, vol. 38, Mar. 1992)     

基于多尺度线性调频基信号稀疏分解的多分量LFM信号检测

该文针对传统的基于二次时频分析和原子追踪匹配方法处理多分量LFM信号时存在的时频干扰和等振幅交叉分解等问题,提出了一种基于多尺度线性调频基信号稀疏分解的多分量LFM信号检测方法,该方法采用多尺度的线调频基函数对多分量LFM信号进行投影分解,通过从不同的时间支撑区内投影系数最大的基函数中寻找出使分解信号能量最大的基元函数组合,逐次获得信号包含的能量最大的LFM信号分量,从基元函数连接形成的频率曲线即可获得LFM信号分量瞬时频率的估计,再对分量瞬时频率求起始时间点的频率值和曲线斜率便可得到该LFM分量的中心频率及调频斜率,仿真试验表明该文方法能精确地提取等振幅多分量LFM信号的瞬时频率,并具有很强的抗噪声干扰能力。     

由时频分布引导的四参数子空间匹配追踪算法

为了克服四参数匹配追踪计算量巨大的缺点,本文提出了一种由时频分布引导的四参数子空间匹配追踪算法.该算法由引导时频分布确定chirp原子的时频中心,然后用模板匹配方法搜索原子的尺度和调频率(chirp rate).这样,一个高计算复杂度的四维搜索问题被转化为两个相对简单的二维搜索问题.为有效利用时频分布,每次搜索多个时频原子,这些原子不再相互正交.为此,我们利用最小二乘方法计算信号(或残差信号)在相应子空间上的正交投影.同快速脊追踪算法相比,四参数子空间匹配追踪需要更少的原子逼近信号,对实测语音信号的数值计算也证实了这点.     

基于先验估计的自适应Chirplet信号展开

该文提出一种新的时频表示方法--自适应线性调频小波(Chirplet)信号展开算法。算法基于信号本征空间,融参数的初值估计和精确估计于一体,利用匹配追踪算法将信号自适应地展开在高斯线性调频小波基函数集上。通过展开系数和基函数参数获得信号的时频分布,其时频聚集性、抗噪性和时频分辨率不仅优于一般的时频分布而且优于已有的自适应时频分布,可以更好地刻画信号的本质。应用数值仿真检验了算法的有效性和时频分布的优良性能。     

基于子空间的三阶多项式相位信号快速稀疏分解算法

针对稀疏分解冗余字典中原子数量庞大的缺点,该文提出一种三阶多项式相位信号的快速稀疏分解算法。该算法根据三阶多项式相位信号的特点,把原有信号变换成两个子空间信号,并根据这两个子空间信号构建相应的冗余字典,然后采用正交匹配追踪法来完成其稀疏分解,最后利用稀疏分解原理完成原有信号的稀疏分解。该算法把原有信号变换成两个不同子空间信号,构建了两个不同的冗余字典,对比采用一个冗余字典库,这种采用两个冗余字典的算法大大减少了原子数量,并且通过快速傅里叶变换,在一个冗余字典进行稀疏分解时,同时找到另一个冗余字典中的最匹配的原子。因此该算法通过减少原子数量和采用快速傅里叶变换大大加快了稀疏分解速度。实验结果表明,相比于采用Gabor原子构建的冗余字典,采用匹配追踪算法与遗传算法及最近提出的基于调制相关划分的快速稀疏分解,它的稀疏分解速度更快,并且具有更好的收敛性。     

Dopplerlet based time-frequency representation via matching pursuits

A new time-frequency representation called Dopplerlet transform, which uses the dilated, translated and modulated windowed Doppler signals as its basis functions, is proposed, and the Fourier transform, short-time Fourier transform (including Gabor transform), wavelet transform, and chirplet transform are formulated in one framework of Dopplerlet transform accordingly. It is proved that the matching pursuits based on Dopplerlet basis functions are convergent, and that the energy of residual signals yielded in the decomposition process decays exponentially. Simulation results show that the matching pursuits with Dopplerlet basis functions can characterize compactly a nonstationary signal.     

基于迭代自适应稀疏分解的雷达信号去噪

稀疏分解能有效分离信号和噪声,因此适用于信号去噪.文中构造了雷达回波稀疏表示的冗余字典,字典原子与目标回波波形匹配,基于该字典的雷达回波信号稀疏度就是目标数.针对稀疏度自适应匹配追踪算法进行低信噪比信号稀疏分解时的不足,提出了一种迭代自适应匹配追踪算法,采用规范化的残差之差作为迭代终止条件,使得稀疏分解过程能依据噪声水平自适应终止,以逐次逼近方式估计信号稀疏度,改善了稀疏分解的精度.仿真实验结果表明,该算法在低信噪比以及稀疏度未知的条件下,实现了雷达回波信号的准确稀疏分解,极大地提高了信噪比.     

Investigation of short-term changes in visual evoked potentials with windowed adaptive chirplet transform

We propose a new application of the adaptive chirplet transform that involves partitioning signals into non-overlapping sequential segments. From these segments, the local time-frequency structures of the signal are estimated by using a four-parameter chirplet decomposition. Entitled the windowed adaptive chirplet transform (windowed ACT), this approach is applied to the analysis of visual evoked potentials (VEPs). It can provide a unified and compact representation of VEPs from the transient buildup to the steady-state portion with less computational cost than its non-windowed counterpart. This paper also details a method to select the optimal window length for signal segmentation. This approach will be useful for long-term signal monitoring as well as for signal feature extraction and data compression.     

Joint time-frequency analysis for radar signal and image processing

The Fourier transform has been widely used in radar signal and image processing. When the radar signals exhibit time- or frequency-varying behavior, an analysis that can represent the intensity or energy distribution of signals in the joint time-frequency (JTF) domain is most desirable. In this article, we showed that JTF analysis is a useful tool for improving radar signal and image processing for time- and frequency-varying cases. We applied JTF analysis to radar backscattering and feature extraction; we also examined its application to radar imaging of moving targets. Most methods of JTF analysis are non-parametric. However, parametric or model-based methods of time-frequency analysis, such as adaptive Gaussian and chirplets, are more suitable for radar signals and images     

基于压缩感知的MIMO-OFDM系统自适应信道估计

针对超密集组网中导频复用将产生导频干扰,严重影响移动用户下行链路信道估计准确性的问题,提出了一种使用短导频的幂函数稀疏度自适应匹配追踪(Power Sparsity Adaptive Matching Pursuit,PSAMP)算法.该算法由稀疏度预估计和追踪重构两部分构成.首先通过幂函数试探得到一个略小于真实稀疏度的预估值,再通过压缩采样匹配追踪重构信号,改善估计结果;若不能成功重构,则逐渐增加信号原子数量.仿真结果表明,相较于传统自适应压缩感知重建算法,所提的P SAMP算法在高信噪比区域具有更好的信道估计性能.     

基于多尺度线调频基信号稀疏分解的 信号分离和瞬时频率估计

提出了一种基于多尺度线调频基信号稀疏分解的多分量多项式相位信号分离和瞬时频率估计方法.该方法采用多尺度的线调频基函数对多分量多项式相位信号进行投影分解,通过从不同的时间支撑区内投影系数最大的基函数中寻找出使分解信号能量最大的基元函数组合,逐次获得信号包含的能量最大的多项式相位信号分量,从而实现多分量多项式相位信号的分离,而从基元函数连接形成的频率曲线则可获得多项式相位信号分量瞬时频率的估计.仿真信号分析表明,本文方法能在信噪比较低情况下有效分离多分量多项式相位信号中包含的多项式相位信号分量,准确地估计其瞬时频率.     

Harmonic decomposition of audio signals with matching pursuit

We introduce a dictionary of elementary waveforms, called harmonic atoms, that extends the Gabor dictionary and fits well the natural harmonic structures of audio signals. By modifying the "standard" matching pursuit, we define a new pursuit along with a fast algorithm, namely, the fast harmonic matching pursuit, to approximate N-dimensional audio signals with a linear combination of M harmonic atoms. Our algorithm has a computational complexity of O(MKN), where K is the number of partials in a given harmonic atom. The decomposition method is demonstrated on musical recordings, and we describe a simple note detection algorithm that shows how one could use a harmonic matching pursuit to detect notes even in difficult situations, e.g., very different note durations, lots of reverberation, and overlapping notes.     

ISAR机动目标的平动补偿和瞬时成像研究

机动目标成像近年来受到广泛注意.本文首先讨论平动补偿,它通常可以分解为两步进行──包络对齐和自聚焦,分析表明,针对平稳目标的包络对齐方法仍然适用于机动目标,而根据相干积累原理,已有的自聚焦方法从理论上和实际上都不是最优的,我们提出适用于机动目标和平稳目标的迭代相干积累自聚焦(ICSA)算法,PGA(相位梯度算法)是ICSA算法的一个特例; 然后,本文讨论机动目标的瞬时成像,它实际上是一个瞬时谱估计问题,已有的一些瞬时成像方法只适用于散射点子回波为线性调频信号(多普勒分布为直线).针对时频分布为非直线的情况,我们提出用自适应窗短时chirplet分解方法估计信号的瞬时频率和瞬时幅度,并结合"洁净"技术,提出了快速自适应窗短时chirplet分解成像(ACDI)算法.实测数据的处理表明本文提出ICSA算法和ACDI算法是有效的.