A fast refinement for adaptive Gaussian chirplet decomposition

The chirp function is one of the most fundamental functions in nature. Many natural events, for example, most signals encountered in seismology and the signals in radar systems, can be modeled as the superposition of short-lived chirp functions. Hence, the chirp-based signal representation, such as the Gaussian chirplet decomposition, has been an active research area in the field of signal processing. A main challenge of the Gaussian chirplet decomposition is that Gaussian chirplets do not form an orthogonal basis. A promising solution is to employ adaptive type signal decomposition schemes, such as the matching pursuit. The general underlying theory of the matching pursuit method has been well accepted, but the numerical implementation, in terms of computational speed and accuracy, of the adaptive Gaussian chirplet decomposition remains an open research topic. We present a fast refinement algorithm to search for optimal Gaussian chirplets. With a coarse dictionary, the resulting adaptive Gaussian chirplet decomposition is not only fast but is also more accurate than other known adaptive schemes. The effectiveness of the algorithm introduced is demonstrated by numerical simulations     

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。     

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.     

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     

Adaptive Nonlinear System Identification in the Short-Time Fourier Transform Domain

In this paper, we introduce an adaptive algorithm for nonlinear system identification in the short-time Fourier transform (STFT) domain. The adaptive scheme consists of a parallel combination of a linear component, represented by crossband filters between subbands, and a quadratic component, which is modeled by multiplicative cross-terms. We adaptively update the model parameters using the least-mean-square (LMS) algorithm, and derive explicit expressions for the transient and steady-state mean-square error (MSE) in frequency bins for white Gaussian inputs. We show that estimation of the nonlinear component improves the MSE performance only when the power ratio of nonlinear to linear components is relatively high. Furthermore, as the number of crossband filters increases, a lower steady-state MSE may be obtained at the expense of slower convergence. Experimental results support the theoretical derivations.     

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.     

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.     

Comparison of MOE and blind LMS

In this letter, we provide a rigorous analytical comparison of two blind adaptive algorithms for adjustment of the minimum mean-squared error (MMSE) filter for multiple access interference (MAI) suppression for direct-sequence code-division multiple access (DS-CDMA). In particular, we compare the popular minimum-output-energy (MOE) algorithm and the blind least-mean-square algorithm (BLMS) in terms of complexity, transient behavior, convergence, stability, and steady-state performance. We show analytically that the MOE algorithm enjoys a faster speed of convergence and has a superior steady-state performance, while the BLMS algorithm is computationally less complex.     

基于不对称高斯调制模型的超声回波参数估计

该文将用于连续函数优化的蚁群算法成功应用到超声回波参数估计中,根据不对称高斯调制模型,给出了用于超声回波估计的蚁群算法的基本原理和参数估计步骤.通过数值仿真,对不同信噪比条件下超声回波参数进行了估计.仿真结果表明,该方法不依赖于初始值的选取,可在较大范围内搜索,得到全局最优解,且估计出的超声回波参数具有较高的精度.     

Stochastic analysis of the filtered-X LMS algorithm in systems withnonlinear secondary paths

This paper presents a statistical analysis of the filtered-X LMS algorithm behavior when the secondary path (output of the adaptive filter) includes a nonlinear element. This system is of special interest for active acoustic noise and vibration control, where a saturation nonlinearity models the nonlinear distortion introduced by the power amplifiers and transducers. Deterministic nonlinear recursions are derived for Gaussian inputs for the transient mean weight, mean square error, and cross-covariance matrix of the adaptive weight vector at different times. The cross-covariance results provide improved steady-state predictions (as compared with previous results) for moderate to large step sizes. Monte Carlo simulations show excellent agreement with the behavior predicted by the theoretical models. The analytical and simulation results show that a small nonlinearity can have a significant impact on the adaptive filter behavior     

Steady-State Mean-Square Performance Analysis of a Relaxed Set-Membership NLMS Algorithm by the Energy Conservation Argument

This paper presents an analysis of the steady-state mean-square error (MSE) of the set-membership normalized least-mean square (SM-NLMS) algorithm with relaxation and regularization parameters. These parameters are introduced for the purpose of deriving in a unified way the steady-state MSE performances of the $varepsilon$-normalized least mean square ($varepsilon$-NLMS) algorithm and a special case of the adaptive parallel subgradient projection (PSP) algorithm. The approach of the paper is to employ the energy conservation relation as a starting point of our analysis. This relation enables us to avoid the transient analysis of the SM-NLMS algorithm, which is in general hard due to the nonlinearity of the SM-NLMS algorithm. As a result, a few nonlinear equations whose solutions are theoretical steady-state MSEs are derived, where two types of reasonable assumptions are introduced to overcome the nonlinearity of the SM-NLMS algorithm. Our results are generalizations of well-known results of the steady-state MSE of the $varepsilon$-NLMS. Extensive simulations show the close agreement between our theories and experiments.      

Distributed Estimation Over an Adaptive Incremental Network Based on the Affine Projection Algorithm

We study the problem of distributed estimation based on the affine projection algorithm (APA), which is developed from Newton's method for minimizing a cost function. The proposed solution is formulated to ameliorate the limited convergence properties of least-mean-square (LMS) type distributed adaptive filters with colored inputs. The analysis of transient and steady-state performances at each individual node within the network is developed by using a weighted spatial-temporal energy conservation relation and confirmed by computer simulations. The simulation results also verify that the proposed algorithm provides not only a faster convergence rate but also an improved steady-state performance as compared to an LMS-based scheme. In addition, the new approach attains an acceptable misadjustment performance with lower computational and memory cost, provided the number of regressor vectors and filter length parameters are appropriately chosen, as compared to a distributed recursive-least-squares (RLS) based method.     

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     

Robust M-estimate adaptive filtering

An M-estimate adaptive filter for robust adaptive filtering in impulse noise is proposed. Instead of using the conventional least-square cost function, a new cost function based on an M-estimator is used to suppress the effect of impulse noise on the filter weights. The resulting optimal weight vector is governed by an M-estimate normal equation. A recursive least M-estimate (RLM) adaptive algorithm and a robust threshold estimation method are derived for solving this equation. The mean convergence performance of the proposed algorithm is also analysed using the modified Huber (1981) function (a simple but good approximation to the Hampel's three-parts-redescending M-estimate function) and the contaminated Gaussian noise model. Simulation results show that the proposed RLM algorithm has better performance than other recursive least squares (RLS) like algorithms under either a contaminated Gaussian or alpha-stable noise environment. The initial convergence, steady-state error, robustness to system change and computational complexity are also found to be comparable to the conventional RLS algorithm under Gaussian noise alone     

A Novel Adaptive Antenna Array for DS/CDMA Code Acquisition

Equipped with an adaptive beamformer, existing adaptive array code acquisition still relies on the correlator structure. Due to the inherent property of the associated serial-search scheme, its mean acquisition time is large, especially in strong interference environments. In this paper, we propose a novel adaptive filtering scheme to solve the problem. The proposed scheme comprises two adaptive filters, an adaptive spatial and an adaptive temporal filter. With a specially designed structure, the spatial filter can act as a beamformer suppressing interference, while the temporal filter can act as a code-delay estimator. A mean squared error (MSE) criterion is proposed such that these filters can be simultaneously adjusted by a stochastic gradient descent method. The performance as well as the convergence behavior of the proposed algorithm are analyzed in detail. Closed-form expressions for optimum filter weights, optimum beamformer signal-to-interference-plus-noise ratio (SINR), steady-state MSE, and mean acquisition time are derived for the additive white Gaussian noise (AWGN) channel. Computer simulations show that the mean acquisition time of the proposed algorithm is much shorter than that of the correlator-based approach, and the derived theoretical expressions are accurate.     

Sequence detection and adaptive channel estimation for ISI channels under class-a impulsive noise

In this paper, sequence detection and channel estimation for frequency-selective, intersymbol interference (ISI)-producing channels under Class-A impulsive noise are considered. We introduce a novel suboptimum sequence detection (SSD) scheme and show that although SSD employs a simplified metric, it achieves practically the same performance as maximum-likelihood sequence detection (MLSD). For both SSD and MLSD, a lower bound on the achievable performance is derived, which is similar to the classical matched-filter bound for frequency-selective (fading) channels under Gaussian noise. For channel estimation, we adopt a minimum entropy criterion and derive efficient least-mean-entropy and recursive least-entropy algorithms. For both adaptive algorithms, we analyze the steady-state channel-estimation error variance. Theoretical considerations and simulation results show that in Class-A impulsive noise, the proposed sequence detection and adaptive channel-estimation schemes yield significant performance gains over their respective conventional counterparts (designed for Gaussian noise). Although the novel algorithms require knowledge of the Class-A noise-model parameters, their computational complexity is comparable to that of the corresponding conventional algorithms.     

An improved statistical analysis of the least mean fourth (LMF) adaptive algorithm

The paper presents an improved statistical analysis of the least mean fourth (LMF) adaptive algorithm behavior for a stationary Gaussian input. The analysis improves previous results in that higher order moments of the weight error vector are not neglected and that it is not restricted to a specific noise distribution. The analysis is based on the independence theory and assumes reasonably slow learning and a large number of adaptive filter coefficients. A new analytical model is derived, which is able to predict the algorithm behavior accurately, both during transient and in steady-state, for small step sizes and long impulse responses. The new model is valid for any zero-mean symmetric noise density function and for any signal-to-noise ratio (SNR). Computer simulations illustrate the accuracy of the new model in predicting the algorithm behavior in several different situations.     

基于自适应chirplet变换的ISAR瞬时成像的快速算法

在逆合成孔径雷达(ISAR)瞬时成像中,针对自适应chirplet分解方法运算量大,对信号的逼近精度有限等问题,提出了一种瞬时成像快速算法。该方法在参数粗搜索的基础上,将多维参数搜索过程转化为超越方程的求解问题。与传统方法比较,该方法不仅运算速度快,计算量小,而且参数估计精度高。仿真和真实雷达数据用此方法均能成出质量较好的ISAR图像。因而此快速算法是一种有效的ISAR瞬时成像的快速算法。     

Stochastic analysis of the least mean fourth algorithm for non-stationary white Gaussian inputs

This paper studies the stochastic behavior of the least mean fourth (LMF) algorithm for a system identification framework when the input signal is a non-stationary white Gaussian process. The unknown system is modeled by the standard random-walk model. A theory is developed which is based upon the instantaneous average power and the instantaneous average squared power in the adaptive filter taps. A recursion is derived for the instantaneous mean square deviation of the LMF algorithm. This recursion yields interesting results about the transient and steady-state behaviors of the algorithm with time-varying input power. The theory is supported by Monte Carlo simulations for sinusoidal input power variations.     

Transient analysis of data-normalized adaptive filters

This paper develops an approach to the transient analysis of adaptive filters with data normalization. Among other results, the derivation characterizes the transient behavior of such filters in terms of a linear time-invariant state-space model. The stability, of the model then translates into the mean-square stability of the adaptive filters. Likewise, the steady-state operation of the model provides information about the mean-square deviation and mean-square error performance of the filters. In addition to deriving earlier results in a unified manner, the approach leads to stability and performance results without restricting the regression data to being Gaussian or white. The framework is based on energy-conservation arguments and does not require an explicit recursion for the covariance matrix of the weight-error vector.