短时傅里叶变换和提升小波变换在脉象信号分析中的应用
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摘要
中医独特的诊断方法及治病的疗效是有目共睹的。随着传感器技术和计算机处理技术的发展,人们开始致力于脉诊的客观化研究,希望用现代科学技术的方法和仪器,推进中医脉诊的现代化,这也是本文进行研究的目的。
短时傅里叶变换(Short-Time Fourier Transform, STFT)和小波变换是目前最常用的时频分析方法。本文对短时傅里叶变换和小波变换的基本概念和基本理论进行了详细的阐述,并探讨了其物理意义;
短时傅里叶变换的基本思想是:把信号划分成许多小的时间间隔,用傅里叶变换分析每个时间间隔内的信号,以便确定在该间隔内信号的频谱信息。本文应用全极点滑动窗递归算法,分析了15例吸毒者和22例正常人脉象信号的离散短时傅里叶变换,再通过提取出特定频率段的平均频率和频率中心进行分析,发现吸毒者的最小平均频率值和最大频率中心值均低于正常人,因此当选取最小平均频率值时,20例正常人和14例吸毒者被检测出来,而吸毒者B13,正常人Z05和Z06被误判;当选取最大频率中心值时,21例正常人和15吸毒者被检测出来,正常人Z17被误判。最后以这两个值作为二维特征向量,初步提出了用于划分吸毒者和正常人的临界参数方程,根据该方程,正常人和吸毒者全部被检测出来。
小波分析是一种在时域和频域均具有良好局域性的分析方法,尤其适用于非平稳信号的处理,而本文更是在传统小波的基础上,提出了不依赖傅立叶变换,不必通过对一个函数的伸缩和平移来构造小波的小波提升算法。本文利用db4正交小波进行提升小波变换分析了37例样本的脉象信号,通过提取第三层小波系数的第8个分量和第三层尺度系数的第2个分量,构成二维特征向量,找出了吸毒者与正常人脉象信号之间的显著差异,初步提出了用于划分吸毒者和正常人的判据,根据该判据,Z01发生了错判。
最后针对这两种方法提取出的二维特征向量,应用概率神经网络算法进行了脉象信号的分类识别,发现网络的训练速度快,聚类效应好,对吸毒者和正常人的脉象信号的网络识别率也分别达到了97%和100%。
Traditional Chinese medicine all along receives publicity for its unique diagnostic method and particularly curative effects. With the development of sensor and computer technology, people hope to apply modern technology to human pulse diagnosis to reveal the essence and features of pulse phenomena scientifically, which is the main research aspect in this paper.
Short-time Fourier transform (STFT) and Wavelet transform are most commonly used in the time-frequency representation of signals. This paper deduced the theorems and formulas of the Short-time Fourier transform and wavelet transform, and discussed the physics meaning of them.
The basic idea of short-time Fourier transfom is to divide signal into many small time interval, using Fourier transform to analyse the each time interval in order to determine the spectrum information of the interval. In this paper,an efficient recursive algorithm with all-pole moving-windows is used to analyze the discrete short-time power spectra of pulse signals for 15 heroin addicts and 22 healthy persons.Then through extracting the average frequency and frequency centre of specified frequency region to analyse,it is found that the minimal average frequency and maximal frequency centre of heroin addicts is generally lower than that of healthy persons.Thus, as to minimal average frequency, 21 healthy persons and 14 heroin addicts are identified, Only one heroin addict B13 and two healthy persons Z05 and Z06 are misjudged, to maximal frequency center, 21 healthy persons and 15 heroin addicts are identified, only one healthy persons Z17 is misjudged. Finally using these two characteristic parameters as a two-dimensional characteristic vector, the critical parameter equation is determined that is used to classify heroin addicts and healthy persons.According to the equation, all healthy persons and heroin addicts are identified.
Wavelet transform is a good analytical method both in the time and the frequency domains, especially applicable for non-stationary signal processing. Basing on customer wavelet transform, Lifting wavelet transform in this paper don’t rely on Fourier transform and don’t construct wavelet by expanding, contracting and using translation, but through a simple lifting method to construct wavelet. This paper also use db4 orthogonal wavelet conduct lifting wavelet transfom to analyses the 37 samples of pulse signals.By extract the eighth Component of the third layer of wavelet coefficients and the second Component of the third layer of scalar coefficients to construct two-dimensional, we found the significant difference between the heroin addicts and the healthy persons, a primary criterion for measuring off the heroin addicts and the healthy persons was obtained. Based on this criterion, Z01 were misjudged.
Finally, we organize the two characteristic parameters from above method as a two-dimensional characteristic vector,adopts the the probabilistic neural network to identify the pulse signals.The experiments show the apply of network on human pulse has quick trained rate and the good clustery behavior,the discrimination reachs 97% and 100% respectively.
短时傅里叶变换(Short-Time Fourier Transform, STFT)和小波变换是目前最常用的时频分析方法。本文对短时傅里叶变换和小波变换的基本概念和基本理论进行了详细的阐述,并探讨了其物理意义;
短时傅里叶变换的基本思想是:把信号划分成许多小的时间间隔,用傅里叶变换分析每个时间间隔内的信号,以便确定在该间隔内信号的频谱信息。本文应用全极点滑动窗递归算法,分析了15例吸毒者和22例正常人脉象信号的离散短时傅里叶变换,再通过提取出特定频率段的平均频率和频率中心进行分析,发现吸毒者的最小平均频率值和最大频率中心值均低于正常人,因此当选取最小平均频率值时,20例正常人和14例吸毒者被检测出来,而吸毒者B13,正常人Z05和Z06被误判;当选取最大频率中心值时,21例正常人和15吸毒者被检测出来,正常人Z17被误判。最后以这两个值作为二维特征向量,初步提出了用于划分吸毒者和正常人的临界参数方程,根据该方程,正常人和吸毒者全部被检测出来。
小波分析是一种在时域和频域均具有良好局域性的分析方法,尤其适用于非平稳信号的处理,而本文更是在传统小波的基础上,提出了不依赖傅立叶变换,不必通过对一个函数的伸缩和平移来构造小波的小波提升算法。本文利用db4正交小波进行提升小波变换分析了37例样本的脉象信号,通过提取第三层小波系数的第8个分量和第三层尺度系数的第2个分量,构成二维特征向量,找出了吸毒者与正常人脉象信号之间的显著差异,初步提出了用于划分吸毒者和正常人的判据,根据该判据,Z01发生了错判。
最后针对这两种方法提取出的二维特征向量,应用概率神经网络算法进行了脉象信号的分类识别,发现网络的训练速度快,聚类效应好,对吸毒者和正常人的脉象信号的网络识别率也分别达到了97%和100%。
Traditional Chinese medicine all along receives publicity for its unique diagnostic method and particularly curative effects. With the development of sensor and computer technology, people hope to apply modern technology to human pulse diagnosis to reveal the essence and features of pulse phenomena scientifically, which is the main research aspect in this paper.
Short-time Fourier transform (STFT) and Wavelet transform are most commonly used in the time-frequency representation of signals. This paper deduced the theorems and formulas of the Short-time Fourier transform and wavelet transform, and discussed the physics meaning of them.
The basic idea of short-time Fourier transfom is to divide signal into many small time interval, using Fourier transform to analyse the each time interval in order to determine the spectrum information of the interval. In this paper,an efficient recursive algorithm with all-pole moving-windows is used to analyze the discrete short-time power spectra of pulse signals for 15 heroin addicts and 22 healthy persons.Then through extracting the average frequency and frequency centre of specified frequency region to analyse,it is found that the minimal average frequency and maximal frequency centre of heroin addicts is generally lower than that of healthy persons.Thus, as to minimal average frequency, 21 healthy persons and 14 heroin addicts are identified, Only one heroin addict B13 and two healthy persons Z05 and Z06 are misjudged, to maximal frequency center, 21 healthy persons and 15 heroin addicts are identified, only one healthy persons Z17 is misjudged. Finally using these two characteristic parameters as a two-dimensional characteristic vector, the critical parameter equation is determined that is used to classify heroin addicts and healthy persons.According to the equation, all healthy persons and heroin addicts are identified.
Wavelet transform is a good analytical method both in the time and the frequency domains, especially applicable for non-stationary signal processing. Basing on customer wavelet transform, Lifting wavelet transform in this paper don’t rely on Fourier transform and don’t construct wavelet by expanding, contracting and using translation, but through a simple lifting method to construct wavelet. This paper also use db4 orthogonal wavelet conduct lifting wavelet transfom to analyses the 37 samples of pulse signals.By extract the eighth Component of the third layer of wavelet coefficients and the second Component of the third layer of scalar coefficients to construct two-dimensional, we found the significant difference between the heroin addicts and the healthy persons, a primary criterion for measuring off the heroin addicts and the healthy persons was obtained. Based on this criterion, Z01 were misjudged.
Finally, we organize the two characteristic parameters from above method as a two-dimensional characteristic vector,adopts the the probabilistic neural network to identify the pulse signals.The experiments show the apply of network on human pulse has quick trained rate and the good clustery behavior,the discrimination reachs 97% and 100% respectively.
引文
[1]黄世林,孙明异.中医脉象研究[M].人民卫生出版社,1986:73-86.
[2]成都中医学院.中医诊断学[M].四川科学技术出版社,1988:85-102.
[3]王宏禹.非平稳随机信号分析与处理[M].国防工业出版社,1999:88-120.
[4]张贤达,保铮.非平稳信号分析与处理[M].国防工业出版社,2001:82-110.
[5]姚天任,孙洪.现代数字信号处理[M].华中科技大学出版社,1999:74-123.
[6]丁玉美.数字信号处理[M].西安:西安电子科技大学出版社,2002:45-68.
[7]胡广书.数字信号处理-理论、算法与实现[M].北京:清华大学出版社,1997:52-65.
[8]费兆馥,张志枫.中医脉诊的图像化和定量化[J].自然杂志,1995,(17):269-274.
[9]王丽勤.中医诊寸口脉的历史和体会[J].北京医科大学学报,1994,(26):55-57.
[10]杨福生,高上凯.生物医学信号处理[M].高等教育出版社,1989:46-78.
[11]黄世林,孙明异.中医脉象研究[M].人民卫生出版社,1986:56-75.
[12]朱翠玲等.现代生物医学信号[M].中国科学技术出版社,1992:47-85.
[13]朱英华.阵列式脉搏传感器的研制及小波变换在脉搏信息分析中的应用[D].重庆大学硕士学位论文,2000.
[14]张贤达,现代信号处理[M].清华大学出版社,2002.
[15] Jones,D.L,and Park,T.W,A resolution comparison of several time-frequency representations. SP,1992,(l.40):413-420.
[16] Amin,M.G.A new approach to recursive Fourier transform .Proc.IEEE,1987,(75):1537-1538.
[17] Chen,W,Kehtarnavaz,N.and Spencer,T.W. An efficient recursive algorithm for time-varying Fourier transform[J].IEEE Trans.SP,1993,(41),:2488-2450.
[18] Henry,K.Kwok,and Douglas L.Jones.Improved instantaneous frequency estimation using an adaptive short-time Fourier transform[J].IEEE Tran.SP,2000,(48):2964-2972.
[19]刘军.基于短时傅里叶变换和连续小波变换的先天性心脏病心音比较分析研究[J].云南大学学报.2006,(28):89-93.
[20]张榆锋.基于小波变换与基于短时傅里叶变换的超声多普勒血流信号时频分布比较研究[J].中国生物医学工程学报,2005,(24):107-109.
[21]蔡立羽.基于短时傅里叶变换的肌电信号识别方法[J].中国医疗器械杂志. 2000,(24)133-136.
[22]魏松.基于短时傅里叶变换语言信号分析算法[J].电子测量技术. 2006,(29)16-17.
[23]许瑜昀.基于短时傅里叶变换的高频地波雷达射频干扰抑制[J].武汉大学学报. 2004,(20)645-648.
[24]吴子英.短时傅里叶变换在大型水轮发电机组振动分析中的应用[J].水力发电学报.2005,(24)115-120.
[25]赵淑红.短时傅里叶变换在研究沉积旋回地质体中的应用[J].长安大学学报. 2003,(25)549-642.
[26]周霞.中医脉象信号的短时傅里叶分析.重庆大学学报[J].2003,(26)47-51.
[27]朱冰莲.杨磊.心音信号的短时傅里叶变换分析[J].重庆大学学报(自然科学版).2004,83-85.
[28]吴太阳.吸毒者脉象信号的小波与神经网络分析[J].重庆大学学报2007:50-54.
[29]张大波.基于第二代小波变换的心电信号分析算法[J].数据采集与处理.2006:450-453.
[30]姜印平.基于提升方法的脉搏波信号处理.计算机仿真[J].2006:98-100.
[31]段晨东.一种基于提升小波变换的故障特征提取方法及其应用[J].振动与冲击.2007:10-13.
[32]欧瑞清.基于快速提升小波变换的语音特征提取方法.计算机辅助工程[J].2006:102-105.
[33]王忠民.基于提升小波和神经网络的超高压电网故障类型识别[J].华东电力.2006:29-33.
[34]银涛.基于概率神经网络的变压器故障诊断的研究.电气应用[J].2006:15-17.
[35]周长锋.概率神经网络在文本无关说话人识别中的应用.北京工商大学学报[J].2007:49-51.
[36]孙延奎.小波分析及其应用[M].机械工业出版社,2005.
[37] Portnoff,MR.Time-frequency representation of digital signal and systems on short-time Fourier analysis[J].IEEE Trans.ASSP,1980,(28),:55-68.
[38]梁学章等.小波分析[M].国防工业出版社2005.
[39]秦前清.实用小波分析[M].西安电子科技大学出版社. 1998 .
[40]唐晓初.小波分析及其应用[M].重庆大学光电工程学院,2003.
[41] Umberto Amato, Claudia Angelini, Carmine Serio. Compression of AVHRR images by wavelet packets[J]. Environmental Modelling & Software 15,2000:127–138.
[42] M Maslen, P Abbott. Automation of the lifting factorisation of wavelet transforms[J]. Computer Physics Communications 127,2000:309–326.
[43] L-K.Shark and D.Qi, Approach to Wavelet Transform Implementation: Wavelet-like filter banks[J], ELECTRONICS LETTERS 20th November 1997,(33):2011-2012.
[44] Donald B.Percival Wavelet Methods for Time Series Analysis China Machine Press 2004.
[45]阎刚.基于自适应提升小波的图像压缩[D].西安电子科技大学硕士学位论文.2006.
[46] Sweldens. W. The lifting scheme: a new philosophy in biorthogonal wavelet constructions[J]. Proc. SPIE-Int. Soc. Opt. Eng., 1995, (2569),:68-79.
[47] Sweldens. W. The lifting scheme: a custom-design construction of biorthogonal wavelets[J].Appl. Comput. Harmon. Anal., 1996, (2),:186-200.
[48] Sweldens. W. The lifting scheme: a construction of second generation wavelets[J].SIAM J. Math. Anal., 1997,(2),:511-546.
[49] Daubechies. I. and Sweldens. W. Factoring wavelet transforms into lifting step[J]. J.Fourier Anal. Appl., 1998, (3):247-269.
[50]许东.基于MATLAB6.X的系统分析与设计—神经网络[M].西安:西安电子科技大学出版社,2002.
[51] Simmon Haykin .Neural networks[M].China Machine Press 2004.
[52] Fabio Ancona, Anna Marai Colla, Implementing Probabilistic Neural Networks[J], Neural Computing&Applic,1997,(5):152-159.
[53] Donald F.specht Probabilistic Neural Network for Classification[J], Mapping, or Associative Memory, Digital Object Identifier 10.1109ACNN.1988,.525-532.
[54]徐旺林.概率神经网络及其在地球物理勘探中的应用[D]。兰州大学硕士论文,2003.
[55]杨晓楠.基于概率神经网络与小波变换的结构检测方法研究[D]。沈阳建筑大学硕士论文,2004.
[56] Anthony Zaknich,The Modified Probabilistic Neural Network as a Nonlinear CorrelatorDetector[J]. IEEE,1995,309-313.
[57] L.Anagnostopoulos, Classifying Web pages employing a probabilistic neural network[J]。IEEE, 2004:139-150.
[2]成都中医学院.中医诊断学[M].四川科学技术出版社,1988:85-102.
[3]王宏禹.非平稳随机信号分析与处理[M].国防工业出版社,1999:88-120.
[4]张贤达,保铮.非平稳信号分析与处理[M].国防工业出版社,2001:82-110.
[5]姚天任,孙洪.现代数字信号处理[M].华中科技大学出版社,1999:74-123.
[6]丁玉美.数字信号处理[M].西安:西安电子科技大学出版社,2002:45-68.
[7]胡广书.数字信号处理-理论、算法与实现[M].北京:清华大学出版社,1997:52-65.
[8]费兆馥,张志枫.中医脉诊的图像化和定量化[J].自然杂志,1995,(17):269-274.
[9]王丽勤.中医诊寸口脉的历史和体会[J].北京医科大学学报,1994,(26):55-57.
[10]杨福生,高上凯.生物医学信号处理[M].高等教育出版社,1989:46-78.
[11]黄世林,孙明异.中医脉象研究[M].人民卫生出版社,1986:56-75.
[12]朱翠玲等.现代生物医学信号[M].中国科学技术出版社,1992:47-85.
[13]朱英华.阵列式脉搏传感器的研制及小波变换在脉搏信息分析中的应用[D].重庆大学硕士学位论文,2000.
[14]张贤达,现代信号处理[M].清华大学出版社,2002.
[15] Jones,D.L,and Park,T.W,A resolution comparison of several time-frequency representations. SP,1992,(l.40):413-420.
[16] Amin,M.G.A new approach to recursive Fourier transform .Proc.IEEE,1987,(75):1537-1538.
[17] Chen,W,Kehtarnavaz,N.and Spencer,T.W. An efficient recursive algorithm for time-varying Fourier transform[J].IEEE Trans.SP,1993,(41),:2488-2450.
[18] Henry,K.Kwok,and Douglas L.Jones.Improved instantaneous frequency estimation using an adaptive short-time Fourier transform[J].IEEE Tran.SP,2000,(48):2964-2972.
[19]刘军.基于短时傅里叶变换和连续小波变换的先天性心脏病心音比较分析研究[J].云南大学学报.2006,(28):89-93.
[20]张榆锋.基于小波变换与基于短时傅里叶变换的超声多普勒血流信号时频分布比较研究[J].中国生物医学工程学报,2005,(24):107-109.
[21]蔡立羽.基于短时傅里叶变换的肌电信号识别方法[J].中国医疗器械杂志. 2000,(24)133-136.
[22]魏松.基于短时傅里叶变换语言信号分析算法[J].电子测量技术. 2006,(29)16-17.
[23]许瑜昀.基于短时傅里叶变换的高频地波雷达射频干扰抑制[J].武汉大学学报. 2004,(20)645-648.
[24]吴子英.短时傅里叶变换在大型水轮发电机组振动分析中的应用[J].水力发电学报.2005,(24)115-120.
[25]赵淑红.短时傅里叶变换在研究沉积旋回地质体中的应用[J].长安大学学报. 2003,(25)549-642.
[26]周霞.中医脉象信号的短时傅里叶分析.重庆大学学报[J].2003,(26)47-51.
[27]朱冰莲.杨磊.心音信号的短时傅里叶变换分析[J].重庆大学学报(自然科学版).2004,83-85.
[28]吴太阳.吸毒者脉象信号的小波与神经网络分析[J].重庆大学学报2007:50-54.
[29]张大波.基于第二代小波变换的心电信号分析算法[J].数据采集与处理.2006:450-453.
[30]姜印平.基于提升方法的脉搏波信号处理.计算机仿真[J].2006:98-100.
[31]段晨东.一种基于提升小波变换的故障特征提取方法及其应用[J].振动与冲击.2007:10-13.
[32]欧瑞清.基于快速提升小波变换的语音特征提取方法.计算机辅助工程[J].2006:102-105.
[33]王忠民.基于提升小波和神经网络的超高压电网故障类型识别[J].华东电力.2006:29-33.
[34]银涛.基于概率神经网络的变压器故障诊断的研究.电气应用[J].2006:15-17.
[35]周长锋.概率神经网络在文本无关说话人识别中的应用.北京工商大学学报[J].2007:49-51.
[36]孙延奎.小波分析及其应用[M].机械工业出版社,2005.
[37] Portnoff,MR.Time-frequency representation of digital signal and systems on short-time Fourier analysis[J].IEEE Trans.ASSP,1980,(28),:55-68.
[38]梁学章等.小波分析[M].国防工业出版社2005.
[39]秦前清.实用小波分析[M].西安电子科技大学出版社. 1998 .
[40]唐晓初.小波分析及其应用[M].重庆大学光电工程学院,2003.
[41] Umberto Amato, Claudia Angelini, Carmine Serio. Compression of AVHRR images by wavelet packets[J]. Environmental Modelling & Software 15,2000:127–138.
[42] M Maslen, P Abbott. Automation of the lifting factorisation of wavelet transforms[J]. Computer Physics Communications 127,2000:309–326.
[43] L-K.Shark and D.Qi, Approach to Wavelet Transform Implementation: Wavelet-like filter banks[J], ELECTRONICS LETTERS 20th November 1997,(33):2011-2012.
[44] Donald B.Percival Wavelet Methods for Time Series Analysis China Machine Press 2004.
[45]阎刚.基于自适应提升小波的图像压缩[D].西安电子科技大学硕士学位论文.2006.
[46] Sweldens. W. The lifting scheme: a new philosophy in biorthogonal wavelet constructions[J]. Proc. SPIE-Int. Soc. Opt. Eng., 1995, (2569),:68-79.
[47] Sweldens. W. The lifting scheme: a custom-design construction of biorthogonal wavelets[J].Appl. Comput. Harmon. Anal., 1996, (2),:186-200.
[48] Sweldens. W. The lifting scheme: a construction of second generation wavelets[J].SIAM J. Math. Anal., 1997,(2),:511-546.
[49] Daubechies. I. and Sweldens. W. Factoring wavelet transforms into lifting step[J]. J.Fourier Anal. Appl., 1998, (3):247-269.
[50]许东.基于MATLAB6.X的系统分析与设计—神经网络[M].西安:西安电子科技大学出版社,2002.
[51] Simmon Haykin .Neural networks[M].China Machine Press 2004.
[52] Fabio Ancona, Anna Marai Colla, Implementing Probabilistic Neural Networks[J], Neural Computing&Applic,1997,(5):152-159.
[53] Donald F.specht Probabilistic Neural Network for Classification[J], Mapping, or Associative Memory, Digital Object Identifier 10.1109ACNN.1988,.525-532.
[54]徐旺林.概率神经网络及其在地球物理勘探中的应用[D]。兰州大学硕士论文,2003.
[55]杨晓楠.基于概率神经网络与小波变换的结构检测方法研究[D]。沈阳建筑大学硕士论文,2004.
[56] Anthony Zaknich,The Modified Probabilistic Neural Network as a Nonlinear CorrelatorDetector[J]. IEEE,1995,309-313.
[57] L.Anagnostopoulos, Classifying Web pages employing a probabilistic neural network[J]。IEEE, 2004:139-150.