基于多尺度Wiener滤波器的分形噪声滤波

针对淹没在1/f噪声中的有用信号恢复问题,本文提出了一套基于双正交小波变换与Wiener滤波的多尺度滤波算法,并设计出多尺度Wiener滤波器.首先,利用双正交小波变换将带有1/f噪声的信号分解成多尺度的子带信号,通过小波变换对1/f噪声的白化作用,消除了1/f噪声的非平稳性、自相似性和长程相关性.其次,在小波域内,利用Wiener滤波,实现了噪声和有用信号的分离,估计出了各子带中的有用信号.最后,利用双正交小波的精确重构性,较好地恢复出淹没在1/f噪声中的有用信号.仿真实验表明,该滤波器能有效的抑制分形噪声,显著地提高信噪比.     

1/f分形噪声的一种多尺度Kalman滤波方法

针对淹没在1／f分形噪声中的有用信号恢复问题，提出了一种基于小波变换与Kalman滤波的多尺度滤波算法。首先将带有1／f分形噪声的信号分解成多尺度的子带信号，通过小波变换对1／f分形噪声的白化作用，消除了1／f分形噪声的自相似性和长程相关性。然后在小波域内，利用Kalman滤波实现了噪声和有用信号的分离，估计出了各子带中的有用信号。最后进行小波重构，较好地恢复出淹没在1／f分形噪声中的有用信号。仿真实验表明，使用多尺度Kalman滤波器能有效地抑制分形噪声，显著地提高了信噪比。     

Multiscale Wiener filter for the restoration of fractal signals:wavelet filter bank approach

A filter bank design based on orthonormal wavelets and equipped with a multiscale Wiener filter is proposed in this paper for signal restoration of 1/f family of fractal signals which are distorted by the transmission channel and corrupted by external noise. First, the fractal signal transmission process is transformed via the analysis filter bank into multiscale convolution subsystems in time-scale domain based on orthonormal wavelets. Some nonstationary properties, e.g., self-similarity, long-term dependency of fractal signals are attenuated in each subband by wavelet multiresolution decomposition so that the Wiener filter bank can be applied to estimate the multiscale input signals. Then the estimated multiscale input signals are synthesized to obtain the estimated input signal. Some simulation examples are given for testing the performance of the proposed algorithm. With this multiscale analysis/synthesis design via the technique of the wavelet filter bank, the multiscale Wiener filter can be applied to treat the signal restoration problem for nonstationary 1/f fractal signals     

The time–frequency analysis approach of electric noise based on the wavelet transform

In this paper, the wavelet transform approach has been firstly introduced to analyze electric noise in a transistor. Due to the multiresolution ability of wavelet transform, we can separate noise signal into several detail signals and approximation signal which can be interpreted in terms of the noise output of a generalized constant-Q filter bank and low pass filter, respectively.Based on this approach, the fractal and chaos characteristic of 1/f noise are obtained, the smaller burst noise pulse embedded in the white noise and 1/f noise can be detected, and the noise spectrum can also be calculated from short noise data. These results demonstrate that wavelet transform approach is a useful tool for investigation of noise mechanism of a transistor.     

基于小波分析和虚拟仪器技术的1/f噪声研究

传统基于傅立叶分析和频谱分析仪的微弱信号检测方法无法对1／f噪声进行实时、高速、精确的测量与分析。本文在以虚拟仪器为平台。内嵌小波分析的低频噪声检测系统基础上对1／f噪声进行了实验和理论研究。实验结果表明，该系统能够检测到的1／f噪声幅值比传统的测试方法低2个数量，以小波理论构建的两个参量更深入细微地表征了1／f噪声特性：模极大值分布能够鉴别不同类型的1／f噪声产生机构，相似系数可描述应力对器件1／f噪声的影响。     

Deconvolution filter design for fractal signal transmissionsystems: a multiscale Kalman filter bank approach

A deconvolution filtering design is proposed for the 1/f fractal signal transmission systems, with its design philosophy being based on multiscale Kalman deconvolution filter bank equipped in the analysis/synthesis wavelet filter bank, The role of wavelet transformation for 1/f fractal signal process is exploited as a multiscale whitening filter for removing the properties of self-similarity and long-range dependence from the fractal signals     

Wavelet thresholding techniques for power spectrum estimation

Estimation of the power spectrum S(f) of a stationary random process can be viewed as a nonparametric statistical estimation problem. We introduce a nonparametric approach based on a wavelet representation for the logarithm of the unknown S(f). This approach offers the ability to capture statistically significant components of ln S(f) at different resolution levels and guarantees nonnegativity of the spectrum estimator. The spectrum estimation problem is set up as a problem of inference on the wavelet coefficients of a signal corrupted by additive non-Gaussian noise. We propose a wavelet thresholding technique to solve this problem under specified noise/resolution tradeoffs and show that the wavelet coefficients of the additive noise may be treated as independent random variables. The thresholds are computed using a saddle-point approximation to the distribution of the noise coefficients     

分形噪声中的信号检测

本文讨论了在1/f类分形噪声中的信号检测问题,利用小波变换对1/f噪声的近似白化作用,来消除1/f噪声间的相关性。文中给出了白化滤波器的传递函数,信号检测的判决规则和接收系统结构;分析了系统的接收性能;最后给出了仿真实验结果。     

小波变换在心电信号处理中的应用

在心脏病诊断过程中,心电信号的检测是重要的环节,然而心电信号的噪声很强,为了能够较好地滤除信号中的噪声,对信号的特点进行准确标定,利用基于小波变换的阈值去噪算法和基于小波的模极大值-极小值的算法进行心电信号的处理.采用MIT/BIH中的数据进行仿真调试验证,实验结果表明,被引入的几种噪声能被很好地去除,而且心电信号能较完整地保留下来,特征点能被准确地检测到,从而提高了诊断心脏等疾病的诊断效率.     

FPGA-Implementation of Discrete Wavelet Transform with Application to Signal Denoising

This paper presents new architectures for real-time implementation of the forward/inverse discrete wavelet transforms and their application to signal denoising. The proposed real-time wavelet transform algorithms present the advantage to ensure perfect reconstruction by equalizing the filter path delays. The real-time signal denoising algorithm is based on the equalized filter paths wavelet shrinkage, where the noise level is estimated using only few samples. Different architectures of these algorithms are implemented on FPGA using Xilinx System Generator for DSP and XUP Virtex-II Pro development board. These architectures are evaluated and compared in terms of reconstruction error, denoising performance and resource utilization.     

基于DM6437的压缩感知1/f噪声估计

基于压缩感知及稀疏分解的数据估计,将采集到的含高斯白噪声的1/f噪声数据信号传输至数字信号处理器TMS320DM6437系统,利用其自带小波函数进行小波分解稀疏化,通过压缩感知重构估计1/f分型信号,并尝试改变迭代次数优化估计效果,计算参数γ值并输出。仿真表明,DM6437系统可以很好地利用压缩感知及稀疏分解技术估计出1/f分型信号,大大优化了硬件检测1/f噪声的方法。     

DETECTION OF KNOWN SIGNALS IN 1/f FRACTAL NOISE

Based on the whitening property of wavelet transformation for 1/f noise, this paper addresses the problem of detecting deterministic signals in the presence of 1/f fractal noise. The transfer function of whitening filter is provided as well as the condition for whitening. The receiver structure based on Karhunen-Loeve expansion and the decision rule are also given. Finally performance of the detector is analyzed.     

压缩感知理论在语音信号去噪中的应用

针对小波阈值滤波的局限性,将压缩感知理论应用到语音信号去噪中,并与小波阈值滤波方法进行了比较,仿真实验结果表明：基于压缩感知的小波滤波方法可以有效地去除语音信号中的噪声,并且去噪效果优于传统小波阈值滤波方法,对工程中音频信号的降噪具有指导意义。     

Enhancement of bowel sounds by wavelet-based filtering

This paper evaluates the performance of an automatic method for structural decomposition, noise removal and enhancement of bowel sounds (BS), based on the wavelet transform. The proposed method combines multiresolution analysis with hard thresholding to compose a wavelet transform-based stationary-nonstationary (WTST-NST) filter, for enhanced separation of bowel sounds (BS) from superimposed noise. Quantitative and qualitative analysis of the experimental results, when applying the WTST-NST filter to BS recorded from controls and patients with gastrointestinal dysfunction, prove that the ability of the WTST-NST filter to remove noise and reveal the authentic structure of BS is excellent. By eliminating the need to record a noise reference signal, this method reduces hardware overhead when analysis of BS is the primary aim. The method is independent of subjective human judgement for selection of noise reference templates, is robust to different levels of signal interference, and, due to its simplicity, can easily be used in clinical medicine.     

On‐line wavelet filtering of narrowband noise in signal detection of spread spectrum system for location tracking

Spread spectrum signal transmitted by wireless channel for location tracking can be severely corrupted by noise due to external disturbances. Narrowband noise is the most effective interference that can make measurement signal undetected. However, the current methods for narrowband interference (NBI) suppression are either very time‐consuming or add distortion to the signal received. In this paper, an adaptive Gaussian wavelet filter with optimal time–frequency localization and variable notch depth is proposed to suppress a large number of NBIs with additive white Gaussian noise and pulsed noise that interfere with the spread spectrum communication system. The filtering of both continuous and time‐varying NBIs with fast resampling is performed in conjunction with the fast Fourier transform‐based correlation for peak detection, and is computationally efficient for real‐time operation of signal detection. The performance of the adaptive filter has been evaluated by experiments employing a reliable noise detector. Experimental results demonstrate that the proposed wavelet filter isolates the signals from the NBI in accordance with the corrupted frequency contents while preserving the desired spread spectrum signal, and improves signal to noise ratio for peak detection leading to higher accuracy of timing measurement for real‐time wireless location. Copyright © 2011 John Wiley & Sons, Ltd.     

High-order wavelet packets and cumulant field analysis

In many applications it is necessary to characterize the statistical properties of the wavelet/wavelet packet coefficients of a stationary random signal. In particular, in a stationary non-Gaussian noise scenario it may be useful to determine the high-order statistics of the wavelet packet coefficients. In this work we prove that this task may be performed through multidimensional filter banks. In particular, we show how the cumulants of the M-band wavelet packet coefficients of a strictly stationary signal are derived from those of the signal and we provide scale-recursive decomposition and reconstruction formulae to compute these cumulants. High-order wavelet packets, associated with these multidimensional filter banks, are presented along with some of their properties. It is proved that under some conditions these high-order wavelet packets allow us to define frame multiresolution analyses. Finally, the asymptotic normality of the coefficients is studied by showing the geometric decay of their polyspectra/cumulants (of order greater than two) with respect to the resolution level     

瑞利BOTDA系统的2维提升小波降噪方法

为了解决基于瑞利散射的布里渊光时域分析系统（BOTDA）中传感信号受噪声干扰严重的问题,采用2维提升小波变换算法,将测量信号从1维空间转换到2维空间,进行阈值降噪处理。通过理论分析和实验验证,取得了传统小波与2维提升小波降噪数据。结果表明,2维提升小波变换比传统小波变换信噪比提高约10dB,运算量减少了1/3;2维提升小波充分利用测量信号时间上的相关性,变换结构简单、运算速度快、降噪效果优于传统小波,适用于瑞利BOTDA系统降噪。该结果对光纤传感系统中信号降噪的研究有一定参考价值。     

基于压缩感知的大功率半导体激光器1／f噪声参数估计

根据1／f噪声结构,基于压缩感知（cs）的正交匹配追踪去噪（OMPDN）算法,以小波树结构为分解条件,提取大功率半导体激光器（LDs）中的白噪声及1／f噪声。以小波基作为稀疏基,高斯随机矩阵作为测量矩阵对信号测量并进行CS的重建,滤除白噪声后准确提取1／f噪声信号进行器件参数估计。实验结果表明,本文方法对高斯白噪声混杂...     

非平稳分形随机信号波形估计的最优门限方法

本文用基于最小均方误差准则的最优门限方法估计叠加高斯白噪声的分形布朗运动,并给出其离散小波变换分解级数确定方法.与多尺度维纳滤波相比,本方法不需估计1/f类分形信号的方差,且其离散小波变换分解级数可预先确定,因此有着更好的实用性和可操作性.     

基于小波和Context模型的海面红外弱小目标检测

红外图像中弱小目标的检测一直是图像处理领域的热点和难点.介绍了一种基于小波变换和Context模型空间自适应滤波的红外弱小目标检测算法.该方法首先利用小波滤波器抑制大部分背景杂波,然后采用基于Context模型的空间自适应滤波器对高频系数做进一步处理,提高信噪比,最后采用基于Bayes分类算法的迭代门限进行图像分割.实验结果表明,与高通滤波相比,该方法能够更有效地检测出弱小目标.