Resolution measure criteria for the objective assessment of the performance of quadratic time-frequency distributions

This paper presents the essential elements for developing objective methods of assessment of the performance of time-frequency signal analysis techniques. We define a measure for assessing the resolution performance of time-frequency distributions (TFDs) in separating closely spaced components in the time-frequency domain. The measure takes into account key attributes of TFDs, such as components mainlobes and sidelobes and cross-terms. The introduction of this measure allows to quantify the quality of TFDs instead of relying solely on visual inspection of their plots. The method of assessment of performance of TFDs also allows the improvement of methodologies for designing high-resolution quadratic TFDs for time-frequency analysis of multicomponent signals. Different TFDs, including the modified B distribution, are optimized using this methodology. Examples of a performance comparison of quadratic TFDs in resolving closely spaced components in the time-frequency domain, using the proposed resolution measure, are provided.     

Filterbänke mit Überabtastung

Oversampled filter banks offer more design freedom, better numerical stability, and less sensitivity to quantization noise as compared to critically sampled filter banks. These advantages come at the cost of increased computational complexity. Therefore, oversampled modulated filter banks allowing a particularly efficient implementation are of practical interest. Furthermore, in certain applications (such as image coding) it is important to have linear phase filters in all channels of the filter bank. In this paper we discuss oversampled filter banks with emphasis on cosine-modulated filter banks and linear phase filters. We establish a relation of oversampled filter banks with redundant signal expansions. We also perform an analysis of the numerical sensitivity of oversampled filter banks. The increased design freedom in oversampled filter banks is demonstrated both theoretically and by means of simulation examples. Finally, we present a unified theory of cosine-modulated filter banks.     

Parallelizable Bayesian tomography algorithms with rapid,guaranteed convergence

Bayesian tomographic reconstruction algorithms generally require the efficient optimization of a functional of many variables. In this setting, as well as in many other optimization tasks, functional substitution (FS) has been widely applied to simplify each step of the iterative process. The function to be minimized is replaced locally by an approximation having a more easily manipulated form, e.g., quadratic, but which maintains sufficient similarity to descend the true functional while computing only the substitute. We provide two new applications of FS methods in iterative coordinate descent for Bayesian tomography. The first is a modification of our coordinate descent algorithm with one-dimensional (1-D) Newton-Raphson approximations to an alternative quadratic which allows convergence to be proven easily. In simulations, we find essentially no difference in convergence speed between the two techniques. We also present a new algorithm which exploits the FS method to allow parallel updates of arbitrary sets of pixels using computations similar to iterative coordinate descent. The theoretical potential speed up of parallel implementations is nearly linear with the number of processors if communication costs are neglected.     

修正自适应Chirplet分解法及其快速实现

为克服时频关系为线性的基函数的不足,该文提出一种新的信号分解算法修正自适应Chirplet分解法,将Chirplet基函数推广到三次相位信号的形式,因此可以逼近信号中的非线性时变结构成分。同时提出了一种快速分解算法,该算法通过计算信号的三次相位函数,可得到其能量分布集中于信号的瞬时频率变化率曲线上的结论,此时通过谱峰检测可同时获得基函数的二、三次相位系数,时间中心以及幅度的估计;进而通过解调频技术获得其初始频率和时间宽度的估计。文中给出了实现该方法的具体步骤,并分别以仿真信号和蝙蝠回声定位信号为例验证了该算法的有效性。     

Joint time-frequency analysis

It has been well understood that a given signal can be represented in an infinite number of different ways. Different signal representations can be used for different applications. For example, signals obtained from most engineering applications are usually functions of time. But when studying or designing the system, we often like to study signals and systems in the frequency domain. Although the frequency content of the majority of signals in the real world evolves over time, the classical power spectrum does not reveal such important information. In order to overcome this problem, many alternatives, such as the Gabor (1946) expansion, wavelets, and time-dependent spectra, have been developed and widely studied. In contrast to the classical time and frequency analysis, we name these new techniques joint time-frequency analysis. We introduce the basic concepts and well-tested algorithms for joint time-frequency analysis. Analogous to the classical Fourier analysis, we roughly partition this article into two parts: the linear (e.g., short-time Fourier transform, Gabor expansion) and the quadratic transforms (e.g., Wigner-Ville (1932, 1948) distribution). Finally, we introduce the so-called model-based (or parametric) time-frequency analysis method     

Two-Dimensional DOA Estimation by?Cross-Correlation Matrix Stacking

In this paper, we present a novel scheme to improve the two-dimensional (2-D) direction-of-arrival (DOA) estimation performance for narrowband signals impinging on two orthogonal uniform linear arrays (ULAs). The proposed scheme exploits the cross-correlation matrix information between subarray data to construct a stacking matrix and derive an expanded signal subspace representation through the singular value decomposition (SVD). This method enables the alleviation of the effects of additive noise. In particular, 2-D DOA estimation can be achieved by computing two rotation matrices with the same set of eigenvectors obtained by partitioning the expanded signal subspace. The pair matching procedure for elevation and azimuth angles is implemented by permutation test. Simulation results demonstrate that the proposed method performs better than the existing techniques in DOA estimation as well as the detection of successful pair matching.     

基于Radon-Ambiguity变换的LFM信号时/频差快速联合估计

提出了一种基于Radon-Ambiguity变换(Radon-Ambiguity Transform, RAT)的线性调频(Linear Frequency Modulated, LFM)信号时/频差快速联合估计的算法.根据LFM信号在多个不同角度上的RAT峰值位置建立一组以信号间时差和频差为未知量的方程组,求解方程组即可得到时/频差的估计值.对于存在噪声的信号,RAT误差会导致方程组不能直接求解,为了抑制噪声干扰,采用最小二乘法估计时/频差.本文算法无需计算二维平面上各点的模糊函数值,并且由于离散RAT可以通过快速傅里叶变换快速实现,具有所需运算量低的优点.仿真实验表明,相比于常见的基于模糊函数峰值搜索的时/频差估计算法,本文算法在保证时/频差估计精度的同时能够显著提高运算效率.     

Design of NPR DFT-Modulated Filter Banks via Iterative Updating Algorithm

In this paper, an efficient algorithm is proposed to design nearly-perfect-reconstruction (NPR) DFT-modulated filter banks. First, the perfect-reconstruction (PR) condition of the oversampled DFT-modulated filter banks in the frequency domain is transformed into a set of quadratic equations with respect to the prototype filter (PF) in the time domain. Second, the design problem is formulated as an unconstrained optimization problem that involves PR condition and stopband energy of the PF. With the gradient vector of the objective function, an efficient iterative algorithm is presented to design the PF, which is updated with linear matrix equations at each iteration. The algorithm is identified as a modified Newton’s method, and its convergence is proved. Numerical examples and comparison with many other existing methods are included to demonstrate the effectiveness of the proposed method.     

Robustness of oversampled Gabor transient detectors: a comparisonof energy and known location detectors

This correspondence provides a “context” for previous studies on the use of linear time-frequency transforms for transient signal detection in the case where signal component locations are assumed to be known. The robustness of a known-location detector (KLD) based on the oversampled Gabor transform is compared with that of the corresponding energy detector in the Gabor domain. As expected, the KLD was sensitive to location mismatch; unexpectedly, it was extremely sensitive to location mismatch     

Three-component signal recognition using time, time-frequency, andpolarization information-application to seismic detection of avalanches

A method for automatic signal recognition, applied to seismic signals classification, is presented. It is based on the fusion of data derived from the analysis of the signal in three domains: time, time-frequency, and polarization. In the time domain, two techniques are used for envelope shape parametrization. In the time-frequency domain, the autoregressive and Capon (ARCAP) time-frequency method is used on a gliding time-window to estimate the spectral components of the signal versus time. For each window, the frequencies are estimated using AR modelization. The power at each frequency and the corresponding filtered signal are estimated using Capon's (1969) method. A comparison with Fourier's narrow-bandpass filtering shows that Capon's method produces a better filtering. In the polarization domain, two original methods are proposed: one for checking the linear polarization of a signal and one for localizing the linear waves in the time-frequency plane. A system for automatic recognition of seismic signals associated with avalanches is then presented as an application. Signal features are derived from the analysis to sum up the characteristics of the signal in each domain. These features are combined using fuzzy logic and credibility factors, according to rules derived from physical knowledge (generating processes and propagation rules), in order to decide whether a signal comes from an avalanche or not. The global rate of correct recognition is over 90% for that first version of the system     

基于时频分布的多分量LFM信号检测

采用二次型时频分析方法对多分量线性调频信号进行分析,获取信号的时频域能量分布。首先讨论了线性调频信号的两种二次型时频分布：魏格纳-威尔分布及其改进形式——重排魏格纳-威尔分布;在此基础上,进一步对比验证了霍夫变换和若当变换对线性调频信号时频域能量的积累效果,以实现噪声背景中的多分量线性调频信号检测。仿真结果显示基于二次型时频分布的处理是实现多分量线性调频信号检测的一个有效方法。     

Positive Time-Frequency Distributions via Quadratic Programming

A new method for computing positive time-frequency distributions (TFDs) for nonstationary signals is presented. This work extends the earlier work of the author and his colleagues in computing positive TFDs [8,11]. This paper describes a general quadratic programming approach to the problem of computing these signal-dependent distributions. The method is based on an evolutionary spectrum formulation of positive TFDs. The minimization problem reduces to a linearly-constrained quadratic programming problem, for which standard solutions are widely available.     

Time-frequency formulation, design, and implementation oftime-varying optimal filters for signal estimation

This paper presents a time-frequency framework for optimal linear filters (signal estimators) in nonstationary environments. We develop time-frequency formulations for the optimal linear filter (time-varying Wiener filter) and the optimal linear time-varying filter under a projection side constraint. These time-frequency formulations extend the simple and intuitive spectral representations that are valid in the stationary case to the practically important case of underspread nonstationary processes. Furthermore, we propose an approximate time-frequency design of both optimal filters, and we present bounds that show that for underspread processes, the time-frequency designed filters are nearly optimal. We also introduce extended filter design schemes using a weighted error criterion, and we discuss an efficient time-frequency implementation of optimal filters using multiwindow short-time Fourier transforms. Our theoretical results are illustrated by numerical simulations     

The undersampled discrete Gabor transform

Conventional studies on discrete Gabor transforms have generally been confined to the cases of critical sampling and oversampling in which the Gabor families span the whole signal space. In this paper, we investigate undersampled discrete Gabor transforms. For an undersampled Gabor triple (g,a,b), i.e. a·b>N, we show that the associated generalized dual Gabor window (GDGW) function is the same as the one associated with the oversampled (g,N/b,N/a), except for the constant factor (ab/N). Computations of undersampled Gabor transforms are made possible. By applying the methods (algorithms) developed in oversampled settings, the undersampled GDGW is determined. Then, we are able to obtain the best approximation of a signal x by linear combinations of vectors in the Gabor family     

Parallel pipeline implementation of wavelet transforms

Wavelet transforms have been one of the important signal processing developments in the last decade, especially for applications such as time-frequency analysis, data compression, segmentation and vision. Although several efficient implementations of wavelet transforms have been derived, their computational burden is still considerable. The paper describes two generic parallel implementations of wavelet transforms, based on the pipeline processor farming methodology, which have the potential to achieve real-time performance. Results show that the parallel implementation of the oversampled wavelet transform achieves virtually linear speedup, while the parallel implementation of the discrete wavelet transform (DWT) also outperforms the sequential version, provided that the filter order is large. The DWT parallelisation performance improves with increasing data length and filter order, while the frequency-domain implementation performance is independent of wavelet filter order. Parallel pipeline implementations are currently suitable for processing multidimensional images with data length at least 512 pixels     

面向海洋环境的装备选优与排序方法

针对海洋环境下的武器装备选择问题,将其转化为带方案偏好、属性权重完全未知且属性值为区间数形式的多属性决策问题。基于主观偏好与客观属性值偏差最小化的思想,提出一个单目标二次优化模型,并利用LINGO软件进行模型求解,求得属性权重。通过对属性值和属性权重的线性集结,得到排序结果。最后通过数值算例,验证了该方法的可行性和操作性。     

Cross-term elimination in Wigner distribution based on 2D signal processing techniques

An efficient method based on 2D signal processing techniques and fractional Fourier transform is presented to suppress interference terms of Wigner distribution (WD). The proposed technique computes Gabor transform (GT) of a multi-component signal to obtain a blurred time-frequency (t-f) image. Signal components in GT image are segmented using connected component segmentation and are filtered out using precise application of fractional Fourier transform. A crisp t-f representation is then obtained by computing the sum of products of WD and GT of the isolated signal components. The efficacy of the proposed technique is demonstrated using examples of synthetic signals and real-life bat signals. Proposed scheme gives satisfactory performance even when cross-terms of WD overlap auto-terms and computational cost analysis shows that it is more efficient than recent interference suppression techniques of comparable performance. Moreover, the proposed technique does not require any prior info regarding the nature of signal.     

Two-dimensional DOA estimation of coherent signals using acoustic vector sensor array

In this paper, we present two new methods for estimating two-dimensional (2-D) direction-of-arrival (DOA) of narrowband coherent (or highly correlated) signals using an L-shaped array of acoustic vector sensors. We decorrelate the coherency of the signals and reconstruct the signal subspace using cross-correlation matrix, and then the ESPRIT and propagator methods are applied to estimate the azimuth and elevation angles. The ESPRIT technique is based on the shift invariance property of array geometry and the propagator method is based on partitioning of the cross-correlation matrix. The propagator method is computationally efficient and requires only linear operations. Moreover, it does not require any eigendecomposition or singular-value decomposition as for the ESPRIT method. These two techniques are direct methods which do not require any 2-D iterative search for estimating the azimuth and the elevation angles. Simulation results are presented to demonstrate the performance of the proposed methods.     

The Wigner distribution of a linear signal space

A time-frequency representation of linear signal spaces, called its Wigner distribution (WD), is introduced. Similar to the WD of a signal, the WD of a linear signal space describes the space's energy distribution over the time-frequency plane. It is shown that the WD of a signal space can be defined both in a deterministic and in a stochastic framework, and it can be expressed in a simple way in terms of the space's projection operator and the bases. It is shown to satisfy many interesting properties which are often analogous to corresponding properties of the WD of a signal. The results obtained for some specific signal spaces are found to be intuitively satisfactory. The cross-WD of two signal spaces, a discrete-time WD version, and the extension of the WD definition to arbitrary quadratic signal representation are also discussed