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.     

基于测量多分辨预处理的信号去噪方法

该文将多分辨分析方法与传统Kalman滤波方法相结合,以离散小波变换为工具,建立了一种基于测量多分辨预处理的信号去噪新方法。由于小波变换特有的低通滤波特性,能有效的抑制测量噪声,相应提高了测量信号的信噪比,从而获得比原来仅在单一尺度上进行信号处理获得好的处理效果。计算机仿真验证了算法的有效性。     

莫奈特子波变换分析信号奇点

用原函数为光滑曲线的子波变换(简称莫奈特子波变换)检测信号波形奇点的方法是建立在信号奇异性与李普西兹正则性关系基础上的。该方法的基本原理是信号子波变换Wψ(a,t)等价于信号光滑版s(t)θa(t)的1阶导数,当s(t)θa(t)为尖锐变化时,必然对应其导数的模的极大值,只要检测到子波变换模的极大值,就能检测到信号s(t)的奇点。仿真表明,莫奈特子波变换能准确检测出信号奇点。     

小波变换及其在信号去噪中的应用

介绍了小波变换理论及基于小波变换去除信号噪声的基本原理和方法.研究利用小波变换技术对噪声进行阈值处理和去除非平稳信号的噪声,并应用Matlab软件实现了小波去噪的计算机仿真,仿真结果表明小波变换去除噪声的效果优于传统的Fourier变换.     

斜坡类信号频谱分析时应注意的一个问题

斜坡类信号属功率无限信号,针对常见于各种复变函数与积分变换类教科书中此类信号的傅里叶变换结果提出了质疑,认为以傅里叶变换所体现的此类信号的频谱特性不具有实际意义或应用背景。通过对傅里叶变换基本定义、运算性质、物理意义以及斜坡信号频谱特性的分析,表明在信号频谱分析过程中,傅里叶变换这一频谱分析工具不一定适用于功率无限信号。     

基于小波变换和支持矢量机的调制信号识别

提出一种基于小波变换和支持矢量机的数字信号自动调制识别新方法，即将信号小波变换后提取各尺度上的能量峰值作为特征向量，利用支持矢量机把分类特征向量映射到一个高维空间，并在高维空间中构造最优分类超平面以实现信号分类。这种方法对高斯噪声具有良好的稳健性，并避免了神经网络中的过学习和局部极小点等缺陷。计算机仿真结果表明，这种方法具有很高的分类性能和良好的稳健性。     

Construction of sparse signal representations with adaptive multiscale orthogonal bases

We propose a new approach to construct adaptive multiscale orthonormal (AMO) bases of R^N that provide highly sparse signal representations. Our new multilayer AMO basis design produces a high proportion of small scale vectors. The basis vectors are built from small scale to large scales, layer by layer. For each layer, the basis vector maximizes a p-norm measure of sparsity. We compare the sparsity ratios SR (i.e. the percentage of negligibly small coefficients) obtained with AMO and Daubechies wavelet bases for seven families of piecewise smooth signals with randomly located discontinuities. The signals are composed of polynomial, sinusoidal and exponential pieces. In all cases, AMO bases produce a SR increase ranging from 6% to 37%. AMO bases have three main advantages over wavelets. First, they are found automatically by solving a sequence of optimization problems, which eliminates the problem of selecting a wavelet for a given signal. Second, they can provide a significantly sparser representation. Finally, they have the ability to produce zero coefficients for a larger family of piecewise smooth signals. The drawbacks of AMO bases are computational: the basis computation is more expensive, the basis vectors require storage space and no fast transform is known.     

傅里叶变换与小波变换在信号去噪中的应用

对于高频信号和高频噪声干扰相混叠的信号,采用小波变换去除噪声可以避免用傅里叶变换去噪带来的信号折损。对于噪声频率固定的平稳信号,在对信号进行傅里叶变换后使用滤波器滤除噪声。对高频含噪信号则采用正交小波函数sym4对信号分解到第4层,利用极大极小值原则选择合适的阈值进行软阈值处理,最后利用处理后的小波系数进行重构。实验结果表明,对于高频含噪信号傅里叶去噪会出现严重的信号丢失现象,使用极大极小值原则选择阈值进行小波去噪可以有效地保留高频部分的有用信号。     

Wavelets and signal processing

A simple, nonrigorous, synthetic view of wavelet theory is presented for both review and tutorial purposes. The discussion includes nonstationary signal analysis, scale versus frequency, wavelet analysis and synthesis, scalograms, wavelet frames and orthonormal bases, the discrete-time case, and applications of wavelets in signal processing. The main definitions and properties of wavelet transforms are covered, and connections among the various fields where results have been developed are shown     

脉搏信号滤波方法研究

为了降低噪声对人体脉搏信号的干扰、提高采集精度,提出了一种改进的滤波算法。从脉搏信号及其噪声特点出发,采用与经验模态分解法结合的方法,选择适当的小波基并改进小波阈值函数,构造模态系数对脉搏信号进行滤波。经过理论分析与实验验证,取得了理想的实验数据。结果表明,改进的阈值算法不仅克服了软、硬阈值的局限性,并能有效克服傅里叶变换后产生的边缘效应问题;同时,与经验模态分解法相结合,削弱了低频噪声滤除的误差,增强了小波变换的自适应性,较传统的滤波方法能更好地抑制噪声,有助于提高信噪比。     

Robust L-estimation based forms of signal transforms and time-frequency representations

The L-estimation based signal transforms and time-frequency (TF) representations are introduced by considering the corresponding minimization problems in the Huber (1981, 1998) estimation theory. The standard signal transforms follow as the maximum likelihood solutions for the Gaussian additive noise environment. For signals corrupted by an impulse noise, the median-based transforms produce robust estimates of the non-noisy signal transforms. When the input noise is a mixture of Gaussian and impulse noise, the L-estimation-based signal transforms can outperform other estimates. In quadratic and higher order TF analysis, the resulting noise is inherently a mixture of the Gaussian input noise and an impulse noise component. In this case, the L-estimation-based signal representations can produce the best results. These transforms and TF representations give the standard and the median-based forms as special cases. A procedure for parameter selection in the L-estimation is proposed. The theory is illustrated and checked numerically.     

Young’s modulus evaluation by SAWs for porous silica low-k film with cesium doping

Young’s moduli of porous silica low-k films with cesium (Cs) doping are determined by surface acoustic waves (SAWs) in this study. Four low-k samples doped with 0-30 ppm wt% Cs in the precursor solution are investigated to check the mechanical promotion of the porous silica films. The SAW determination process is performed on these ultra-thin porous films. The detected signals with the signal-to-noise ratio of 50:1 are achieved in our measurements. The signal process with combination of wavelet and FIR filter is proposed to effectively restrain the high and low frequency noises and the “Gibbs effect” of the detected signals. The smooth experimental dispersive curves with frequency range from 20 to 150 MHz, which is qualified for the data fitting process with the theoretical dispersion curves, are obtained for these detected thin low-k films. The determination results show that the mechanical property is improved with the pretreatment of cesium doping, which confirms that the degree of siloxane cross-linkage of the porous silica film is promoted by cesium doping.     

A translation-invariant wavelet representation algorithm withapplications

We address the time-varying problem of wavelet transforms, and a new translation-invariant wavelet representation algorithm is proposed. Using the algorithm introduced by Beylkin (see SIAM J. Numer. Anal., vol. 29, p.1716-1740, 1992), we compute the wavelet transform for all the circular time shifts of a length-N signal in O(N log N) operations. The wavelet coefficients of the time shift with minimal cost are selected as the best representation of the signal using a binary tree search algorithm with an appropriate cost function. We apply the translation-invariant representation algorithm to a geoacoustic data compression application. The results show that the new algorithm can reduce the distortion (the squared error in our case) substantially, if the input signals are transients that are sensitive to time shifts     

Analysis of the suppression of nonlinear distortions in amplifiers using the envelope signal

The suppression of the nonlinear distortions in amplifier using the effect of the envelope signal of the amplified HF oscillations on the amplifier parameters is analyzed. A slow (on the time scale of the HF oscillations) variation in the parameters gives rise to additional frequency components of oscillations that compensate for the nonlinear distortions of the original signal. Several variants to employ the compensating signal using the feedback circuits in the transistor amplifiers and variations in the electron-beam current in TWT in the absence of such circuits are considered. The suppression of the nonlinear intermodulation distortions (IMDs) of the test two-frequency signal is studied for the above variants and the suppression of the third-order IMD by 6–19 dB corresponds to the known experimental data on the microwave transistor amplifier. The generalization of the quasi-stationary method for the analysis of the nonlinear transformation of signals allows the analysis of the amplification and suppression of IMD for more complicated multifrequency signals that are used in radio systems.     

A noise reduction technique of speech signal using ICA and spectral analysis

This paper discusses the new method on noise reduction exploiting the combined effects of wavelet decomposition, ICA and spectral analysis on noisy speech. The input noisy speech is wavelet decomposed into two signals. Wavelet entropy is computed based on the modified probability density function for the signal derived from the approximation coefficients during wavelet decomposition. By proper entropy comparison, the starting frame is detected. Between the two signals obtained from the wavelet decomposition, one is speech combined with noise and another one is noise alone. These two signals are analysed in independent component analysis (ICA) domain, in order to generate an enhanced speech. Zero-crossing rate is computed and used to discriminate between speech and noise. Then, spectral analysis is performed on the noise prior to starting frame and noisy speech. Elimination of noise frequencies in the noisy speech leads to noise reduced speech. Subjective analysis and experimental results show the considerable noise reduction capability of the proposed algorithm.     

基于小波变换的信号断点检测

小波分析是近15年来发展起来的一种新的时频分析方法,其在信号处理中有着广泛的应用。在很多情况下单单分析其时域或频域的性质是不够的,比如在电力监测系统中,即要监控稳定信号的成分,又要准确定位故障信号,这就需要引入新的时频分析方法。小波分析正是由于这种需求而发展起来的通过小波变换来精确地检测信号发生变化的时刻,构造一个信号模型,由一个低频正弦波信号连接一个高频正弦波信号,利用小波工具可以检测出信号发生不连续的间断点的位置。     

信号的一种快速子波分解

本文提出一种分析子波ｇ（ｔ），并在此基础上讨论了子波变换的性质和特点，提出复信号的正交子波变换与反变换并讨论了复信号的正交子波分解与恢复，最后给出一种快速算法。     

基于小波变换的信号调制方式的识别研究

根据小波理论,利用小波变换的尺度分解和局部放大的能力,对调制信号进行小波变换和分解,挖掘调制信号在间断点的瞬态特性,成功建立了不同调制方式和其调制特征间的对应关系。在不需要同步和符号速率等先验知识的情况下,实现了对MASK、MFSK、MPSK、MQAM等数字调制方式的完全识别。通过理论分析和计算机仿真验证了所提方法的有效性和实用性,具有很高的应用价值。     

Microarray image enhancement by denoising using decimated and undecimated multiwavelet transforms

In this paper, we present a new approach to deal with the noise inherent in the microarray image processing procedure. We use the denoising capabilities of decimated and undecimated multiwavelet transforms, DMWT and UMWT respectively, for the removal of noise from microarray data. Multiwavelet transforms, with appropriate initialization, provide sparser representation of signals than wavelet transforms so that their difference from noise can be clearly identified. Also, the redundancy of the UMWT transform is particularly useful in image denoising in order to capture the salient features such as noise or transients. We compare this method with the discrete and stationary wavelet transforms, denoted by DWT and SWT, respectively, and the Wiener filter for denoising microarray images. Results show enhanced image quality using the proposed approach, especially in the undecimated case in which the results are comparable and often outperform that of the stationary wavelet transform. Both multiwavelet transforms outperform the DWT and the Wiener filter.     

Oscillatory-Plus-Transient Signal Decomposition Using TQWT and MCA

This paper describes a method for decomposing a signal into the sum of an oscillatory component and a transient component. The process uses the tunable Q-factor wavelet transform (TQWT): The oscillatory component is modeled as a signal that can be sparsely denoted by high Q-factor TQWT; similarly, the transient component is modeled as a piecewise smooth signal that can be sparsely denoted using low Q-factor TQWT. Since the low and high Q-factor TQWT has low coherence, the morphological component analysis (MCA) can effectively decompose the signal into oscillatory and transient components. The corresponding optimization problem of MCA is resolved by the split augmented Lagrangian shrinkage algorithm (SALSA). The applications of the proposed method to speech, electroencephalo-graph (EEG), and electrocardiograph (ECG) signals are included.