数字信号的模糊平滑方法
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摘要
在系统测试过程中,由于各种干扰的存在,使得测试系统采集到的数据偏离其真实值。而干扰因素不仅包括一般意义下的测量误差,还包括测量理念的差异,例如在社会经济学的统计中常出现的一种测试误差:混合数据就是由于测量理念的歧义以及测量误差共同造成的。混合数据信号造成相邻测量结果间的混叠,使得离散数据绘成的振动曲线上呈许多毛刺,很不光滑,为了消弱干扰信号的影响,提高振动曲线光滑度,常常需要对采样数据进行平滑处理。
一般较常采用的信号平滑滤波方法有:中位值滤波法、加权均值滤波法、滑动平均滤波法、防脉冲干扰平均滤波法及限幅滤波法等,这些方法各有适用的范围和优缺点。本文针对混合数据信号的特征,提出一种新的模糊平滑法,沿用加权平均的思想,对信号相邻的点之间进行加权运算。但是权因子的确立是通过建立信号尖端点的隶属度函数以此评价信号在每一点的尖端程度,更准确实际地反映信号混合的程度。另外,基于模糊变量的期望值算子做出新的评价标准用来评价信号的平均尖端度。
In testing procedure, due to the existence of various interference, experimental data records collected by system test always deviate from original true data. The interference factors do not only contain measurement errors but also contain ambiguity of measuring concepts. For example, "mixed data" is the letter condition which usually exists in human science. Mixed data make contiguous sample values be mixed up and also make data curves vibrate strongly, which will produce unexpected sharp signals. We need smooth the sharp signals in order to weaken interference factors and enhance the curve's smoothness.
Usually, we adopt the following signal smoothing filters: median filter, weighted mean filter, moving average filter, anti-pulse interference mean filter, amplitude limit filter and so on, these methods all have their own applicable scope. According to mixed data's character, this paper proposed a new fuzzy smoothing method, continuing to use weighted mean idea, sharing the neighboring samples' data value. But the weight factors are confirmed by building membership function of signal's sharp degree, more well and truly reflects mixed degree of signal. Besides, based on the expectation operator of fuzzy variable, we gain a new norm to estimate the signal's average angle.
一般较常采用的信号平滑滤波方法有:中位值滤波法、加权均值滤波法、滑动平均滤波法、防脉冲干扰平均滤波法及限幅滤波法等,这些方法各有适用的范围和优缺点。本文针对混合数据信号的特征,提出一种新的模糊平滑法,沿用加权平均的思想,对信号相邻的点之间进行加权运算。但是权因子的确立是通过建立信号尖端点的隶属度函数以此评价信号在每一点的尖端程度,更准确实际地反映信号混合的程度。另外,基于模糊变量的期望值算子做出新的评价标准用来评价信号的平均尖端度。
In testing procedure, due to the existence of various interference, experimental data records collected by system test always deviate from original true data. The interference factors do not only contain measurement errors but also contain ambiguity of measuring concepts. For example, "mixed data" is the letter condition which usually exists in human science. Mixed data make contiguous sample values be mixed up and also make data curves vibrate strongly, which will produce unexpected sharp signals. We need smooth the sharp signals in order to weaken interference factors and enhance the curve's smoothness.
Usually, we adopt the following signal smoothing filters: median filter, weighted mean filter, moving average filter, anti-pulse interference mean filter, amplitude limit filter and so on, these methods all have their own applicable scope. According to mixed data's character, this paper proposed a new fuzzy smoothing method, continuing to use weighted mean idea, sharing the neighboring samples' data value. But the weight factors are confirmed by building membership function of signal's sharp degree, more well and truly reflects mixed degree of signal. Besides, based on the expectation operator of fuzzy variable, we gain a new norm to estimate the signal's average angle.
引文
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[25]S.V.Vaseghi著,邱天爽,刘文红,郭莹,高阳译,现代数字信号处理与噪声降低,北京,电子工业出版社,2007。
[26]祁才君,数字信号处理技术的算法分析与应用,北京,机械工业出版社,2005。
[27]刘明,徐洪波,宁国勤,数字信号处理--原理与算法实现,北京,清华大学出版社,2006。
[28]程佩青,数字信号处理教程,北京,清华大学出版社,2002。
[29]张贤达,现代信号处理,北京,清华大学出版社,2002。
[30]王济,胡晓,MATLAB在振动信号处理中的应用,北京,中国水利水电出版社,2006。
[31]倪养华,数字信号处理-原理与实现,上海,上海交通大学出版社,2006。
[32]杨育霞,许珉,廖晓辉,信号分析与处理,北京,中国电力出版社,2007。
[2]A.Taguchi,A Design Method of Fuzzy Weighted Median Filters,IEEE International Conference on Image Processing,Vol.1,423-426,1996.
[3]J.M.Mendel,Uncertainty,Fuzzy Logic,and Signal Processing,Signal Processing,Vol.80,913-933,2000.
[41 B.Liu,Uncertainty Theory,Springer-Verlag Berlin,2nd Edition,2007.
[5]C.S.Lee,Y.H.Kuo,P.T.Yau,Weighted Fuzzy Mean Filter for Image Processing,Fuzzy Sets and Systems,Vol.89,157-180,1997.
[6]A.Savitzky,M.J.E.Golay,Smoothing and Differentiation of Data by Simplified Least Squares Procedures Analytical Chemistry,Vol.36,1627-1639,1964.
[7]Y.H.Kuo,C.S.Lee,C.L.Chen,High-stability AWFM Filter for Signal Restoration and Its Hardware Design,Fuzzy Sets and Systems,Vol.114,185-202,2000.
[8]J.S.Lee,Digital Image Smoothing and the Sigma Filter,Computer Vision,Graphics,and Image Processing,vol.24,255-269,1983.
[9]Y.Chen,S.Broschat,P.Flynn,Phase Insensitive Homomorphic Image Processing for Speckle Reduction,Ultrasonic Imaging,Vol.18,122-139,1996.
[10]Y.R.Hwang,M.Tomizuka,Fuzzy Smoothing Algorithms for Variable Structure Systems,IEEE Transactions on Fuzzy Systems,Vol.2,277-284,1994.
[11]A.Ferrero,S.Salicone,An Original Fuzzy Method for the Comparison of Measurement Results Represented as Random-Fuzzy Variables,IEEE Transactions on Instrumentation and Measurement,Vol.56,No.4,1292-1299,2007.
[12]F.Beritelli,A Multichannel Speech/Silence Detector Based on Time Delay Estimation and Fuzzy Classification,IEEE International Conference on Acoustics,Speech and Signal Processing,Vol.1,93-96,1999.
[13]I.Pitas,A.N.Venetsanopoulos,Nonlinear Digital Filters:Principles and Applications,Kluwer Academic Publishers,1990.
[14]J.Glasa,G.Podhajecky,On Digital Signal Smoothing by Orthogonal Polynomials,Proceedings of the 2nd International Symposium on Image and Signal Processing and Analysis,429-434,2001.
[15]A.Imiya,T.Sasaki,H.Ogawa,Generalized Lanczos Method for Signal Smoothing,IEEE International Conference on Acoustics,Speech,and Signal Processing,Vol.11,285-288,1986.
[16]A.Abdulrahim,T.P.Dobrowiecki,Knowledge-based Approach to Signal Smoothing,Intelligent Systems Engineering,Vol.1,63-75,1992.
[17]M.Zerbo,C.Thiffault,P.Sicard,Hand-Shake Filters for Signal Smoothing in a Switching Induction Machine Drive,IEEE International Symposium on Industrial Electronics,Vol.3,2389-2394,2006.
[18]O.Vainio,S.J.Ovaska,A Class of Predictive Analog Filters for Sensor Signal Processing and Control Instrumentation,IEEE Transactions on Industrial Electronics,Vol.44,565-570,1997.
[19]M.A.Khojastepour,B.Aazhang,R.G.Baraniuk,Contraction,Smoothness,and Lowpass Filtering,IEEE International Conference on Acoustics,Speech,and Signal Processing,Vol.2,897-900,2004.
[20]P.T.Harju,S.J.Ovaska,V.Valimaki,Delayless Signal Smoothing Using a Median and Predictive Filter Hybrid,3rd International Conference on Signal Processing,Vol.1,87-90,1996.
[21]N.akagi,M.Oya,T.Q.W.Kobayashi,An Adaptive Controller to Realize Smooth Input for Systems With Relative Degree Less than 3,SICE Annual Conference,830-835,2008.
[22]M.Niedzwiecki,W.A.Sethares,Smoothing of Discontinuous Signals:the Tompetitive Approach,IEEE Transactions on Signal Processing,Vol.43,1-13,1995.
[23]杨西侠,柯晶,信号分析与处理,北京,机械工业出版社,2007。
[24]张旭东,陆明泉,离散随机信号处理,北京,清华大学出版社,2005。
[25]S.V.Vaseghi著,邱天爽,刘文红,郭莹,高阳译,现代数字信号处理与噪声降低,北京,电子工业出版社,2007。
[26]祁才君,数字信号处理技术的算法分析与应用,北京,机械工业出版社,2005。
[27]刘明,徐洪波,宁国勤,数字信号处理--原理与算法实现,北京,清华大学出版社,2006。
[28]程佩青,数字信号处理教程,北京,清华大学出版社,2002。
[29]张贤达,现代信号处理,北京,清华大学出版社,2002。
[30]王济,胡晓,MATLAB在振动信号处理中的应用,北京,中国水利水电出版社,2006。
[31]倪养华,数字信号处理-原理与实现,上海,上海交通大学出版社,2006。
[32]杨育霞,许珉,廖晓辉,信号分析与处理,北京,中国电力出版社,2007。