语音增强方法研究及应用
|
摘要
语音增强的目的是从带噪语音信号中提取尽可能纯净的原始语音信号,在语音识别与编码、语音通信等领域中有着广泛的应用,现已成为语音信号处理的一个重要分支。本文对受加性噪声污染的语音信号增强方法进行了研究,主要工作和创新点如下:
(1)对谱相减法、维纳滤波法、卡尔曼滤波法等语音增强方法的基本原理进行了分析,并比较了这些方法的优缺点。
(2)论述了小波变换的基本理论,介绍了常用的小波函数,分析了语音信号和噪声信号在小波分解后的不同特性,阐述了小波去噪的原理和方法,给出了一种改进阈值函数的小波去噪方法。实验仿真表明该方法与传统小波去噪方法相比,能获得较满意的去噪效果。
(3)论述了小波包变换以及小波包去噪的原理,通过实验与小波去噪比较验证了小波包去噪的有效性。由于用小波包对染噪语音信号进行分析时,能进一步细分信号的高频部分,对高频部分的信号进行更精细的处理,从而能提高语音去噪后的信噪比。论述了多小波变换的原理以及多小波的常用预处理方法,将常用于图像处理的多小波去噪方法引入到语音信号去噪中,实验证实了多小波语音去噪的有效性。
(4)论述了信号子空间法语音增强原理,并将其应用到端点检测中,给出了一种基于信号子空间和信息复杂度相结合的语音端点检测方法,给出了一种新的判断语音与非语音的信息复杂度的门限。实验仿真表明,该方法相对传统的语音端点检测方法,能提高语音端点检测准确率,特别在低信噪比条件下具有较高的端点检测准确率。
The purpose of speech enhancement is extracting speeeh information from noisy speeeh signal with might and main, which is extensively used in speeeh reeognition, speeeh coding, speeeh communication and other fields.speech enhancement is becoming an important branch of speech signal processing now.This paper mainly studied the enhancement methods of speeeh signal which is polluted by additive noise . The main works and innovations are as follows:
(1) The basic principles of several speech enhancement methods are discussed such as spectral subtraction method, Wiener filtering method,Kalman filtering method.The strongpoint and shortcoming of the above methods are also compared with each other in this paper.
(2)The basic principle of wavelet transform is discussed,and the common wavelet function is introduced.The different characters of wavelet analysis coefficients between speech signal and noise signal are analysed,and the principle of wavelet denoising is expatiated.A new method with an improved threshold function is proposed in this paper. Experimental results show that a satisfying de-noising result can be obtained by this method compared with traditional methods.
(3)The thoeries of wavelet packet transform and wavelet packet denoising are discussed,the experimnetal sumulations show the validity of this method compared with wavelet denoising,because wavelet packet ananlysis can decompose and process high-frequence signal,and a higher output SNR can be obtained.The thoeries of multi-wavelet transform and the common preprocessing methods are also introduced,which are usually used to denoise in image processing.We used the multi-wavelet thoery in speech denoising, the validity of this method can be proved by experimental sumulations.
(4)The principles of speech enhancement by signal subspace are discussed,which are used in speech endpoint detection.A new speech endpoint detection method based on signal subspace and the information complexity is proposed,and an improved threshold is given to compute the information complexity to decide which is speech or not. Experimental simulations show that this method can increase the endpoint detection accuracy ratio compared with the traditional speech endpoint detection method, especially it has high endpoint detection accuracy ratio under low signal-to-noise ratio.
(1)对谱相减法、维纳滤波法、卡尔曼滤波法等语音增强方法的基本原理进行了分析,并比较了这些方法的优缺点。
(2)论述了小波变换的基本理论,介绍了常用的小波函数,分析了语音信号和噪声信号在小波分解后的不同特性,阐述了小波去噪的原理和方法,给出了一种改进阈值函数的小波去噪方法。实验仿真表明该方法与传统小波去噪方法相比,能获得较满意的去噪效果。
(3)论述了小波包变换以及小波包去噪的原理,通过实验与小波去噪比较验证了小波包去噪的有效性。由于用小波包对染噪语音信号进行分析时,能进一步细分信号的高频部分,对高频部分的信号进行更精细的处理,从而能提高语音去噪后的信噪比。论述了多小波变换的原理以及多小波的常用预处理方法,将常用于图像处理的多小波去噪方法引入到语音信号去噪中,实验证实了多小波语音去噪的有效性。
(4)论述了信号子空间法语音增强原理,并将其应用到端点检测中,给出了一种基于信号子空间和信息复杂度相结合的语音端点检测方法,给出了一种新的判断语音与非语音的信息复杂度的门限。实验仿真表明,该方法相对传统的语音端点检测方法,能提高语音端点检测准确率,特别在低信噪比条件下具有较高的端点检测准确率。
The purpose of speech enhancement is extracting speeeh information from noisy speeeh signal with might and main, which is extensively used in speeeh reeognition, speeeh coding, speeeh communication and other fields.speech enhancement is becoming an important branch of speech signal processing now.This paper mainly studied the enhancement methods of speeeh signal which is polluted by additive noise . The main works and innovations are as follows:
(1) The basic principles of several speech enhancement methods are discussed such as spectral subtraction method, Wiener filtering method,Kalman filtering method.The strongpoint and shortcoming of the above methods are also compared with each other in this paper.
(2)The basic principle of wavelet transform is discussed,and the common wavelet function is introduced.The different characters of wavelet analysis coefficients between speech signal and noise signal are analysed,and the principle of wavelet denoising is expatiated.A new method with an improved threshold function is proposed in this paper. Experimental results show that a satisfying de-noising result can be obtained by this method compared with traditional methods.
(3)The thoeries of wavelet packet transform and wavelet packet denoising are discussed,the experimnetal sumulations show the validity of this method compared with wavelet denoising,because wavelet packet ananlysis can decompose and process high-frequence signal,and a higher output SNR can be obtained.The thoeries of multi-wavelet transform and the common preprocessing methods are also introduced,which are usually used to denoise in image processing.We used the multi-wavelet thoery in speech denoising, the validity of this method can be proved by experimental sumulations.
(4)The principles of speech enhancement by signal subspace are discussed,which are used in speech endpoint detection.A new speech endpoint detection method based on signal subspace and the information complexity is proposed,and an improved threshold is given to compute the information complexity to decide which is speech or not. Experimental simulations show that this method can increase the endpoint detection accuracy ratio compared with the traditional speech endpoint detection method, especially it has high endpoint detection accuracy ratio under low signal-to-noise ratio.
引文
[1]易克初,田斌,付强.语音信号处理[M].北京:国防工业出版社,2000:1-10.
[2]黄苏雨,梁声灼,黄苏园.语音增强方法综述[J].计算机与现代化,2007,3(1):16-20.
[3]胡航.语音信号处理[M].哈尔滨:哈尔滨工业大学出版社,2000:186-194.
[4]姚天任.数字语音信号处理[M].武汉:华中科技大学出版社,2003:14-24.
[5]丁沛.语音识别中的抗噪声技术[D].北京:清华大学,2003.
[6]J.S.Lim,A.V.Oppehneim.All-Pole Modeling of Degraded Speeeh[J].IEEE Transactions on Acoustics Speech and Signal Processing,1978,26(3):197-210.
[7]J Slim,Openheim A V.Enhancement and Bandwidth Compression of Noisy Speech[J].Proceeding of IEEE,1979,67(12):1586-1604.
[8]Boll S F.Suppression of Acoustic Noise in Speech Using Spectral Subtraction[J].IEEE Trans on Acoust Speech and Signal Processing,1979,27(2):113-120.
[9]R.J.Maulya,M.L.Malpass.Speeeh Enhancement Using a Soft-decision Noise Suppression Filter[J].IEEE Transactions on Acoustics Speech and Signal Processing, 1980, 28(2):137-145.
[10] Y. Ephraim, D. Malah. Speech Enhacement Using a Minimum Mean-square Error Short-time Spectral Amplitude estimator[J]. IEEE Transactions on Acoustics Speech and Signal Processing, 1984, 32(6): 1109-1121.
[11] Y. Ephraim. Speech Enhancement Using a Minimum Mean-square Error Speech Log-spectral Amplitude Estimator[J]. IEEE Transactions on Acoustics Speech and Signal Processing, 1985, 33 (2): 443-445.
[12] Y. Ephraim. A Bayesian Estimation Approach for Speech Enhancement Using Hidden Markov Models[J]. IEEE Transactions on Acoustics Speech and Signal Processing, 1993,40(4): 725-732.
[13] Hossein Sameti, Hamid Sheikhzadeh, Li Deng, Robert L. Brennan. HMM-based Strategies for Enhancement of Speech Signal Embedded in Nonstationary Noise[J]. IEEE Transactions on Acoustics Speech and Signal Processing, 1998, 6(5):445-455.
[14] David Y. Zhao, W. Bastiaan Kleijn.HMM-Based Gain Modeling for Enhancement of Speech in Noise[J].IEEE Transactions on Acoustics Speech and Signal Processing, 2007, 15(3):882 -892.
[15] Knecht, W. G. Schenkel, M. E. Moschytz, G. S. Neural Network Filters for Speech Enhancement[J]. IEEE Transactions on Acoustics Speech and Signal Processing,1995,3(6):433-438.
[16]Potamitis.I,Fakotakis.N.D,Kokkinakis.G.Impulsive Noise Suppression Using Neural Networks[J].IEEE Transactions on Acoustics Speech and Signal Processing,2000,3(3):1871-1874.
[17]David L.Donoho.De-Noising by Soft-Thresholding[J].IEEE Transactions on information theory,1995,41(3):613-627.
[18]Sungwook Chang,Y.Kwon,Sung-il Yang.Speech Enhancement for Non-stationary Noise Environment by Adaptive Wavelet Packet[J].ICASSP,2002,1(2):561-564.
[19]Yariv Ephraim,Hany L.Van Trees.A Signal Subspace Approach for Speech Enhancement[J].IEEE Transaction on Speech and Audio Processing,1995,3(4):251-266.
[20]Afshin Rezayee,Saeed Gazor.An Adaptive KLT Approach for Speech Enhancement[J].IEEE Transaction on Speech and Audio Processing,2001,9(2):87-95.
[21]Nathalie Virag.Single Channel Speech Enhancemnet Based on Masking properties of Human Auditory System[J].IEEE Transaction on Speech and Audio Processing,1999,7(2):126-137.
[22]陶智,赵鹤鸣,龚呈卉.基于听觉掩蔽效应和Bark子波变换的语音增强[J].声学学报,2005,30(4):367-372.
[23]王光艳,赵晓群,王霞.基于数学形态学的非线性语音增强方法[J].计算机工程与应用,42(34):53-56.
[24]赵晓群,王津.一种基于形态学的语音增强方法[J].同济大学学报(自然科学版),2006,34(10):1394-1397.
[25]彭煊,刘金福,王炳锡.基于独立分量分析的语音增强[J].信号处理,2002,18(5):477-479.
[26]周成,刘钊.基于独立分量分析的单通道语音降噪算法研究[J].激光与红外,2005,35(5):374-377.
[27]林秋华,郑永瑞,殷福亮.基于参考独立分量分析的语音增强方法[J].大连理工大学学报,46(6):915-919.
[28]陈砚圃,卜凡亮,戴启军等.语音中相位的听觉感知实验研究[J].声学学报,2003,28(1):9-13.
[29]R.D.Preuss.Evaluation of a correlation Subtraction Method for Enhancing Speech Degraded by Additive White Noise[J].IEEE Transactions on Acoustics Speech and Signal Processing,1978,26(3):471-472.
[30]M.Berouti,R.Schwartz,and J.Makhoul.Enhancement of Speech Corrupted by Acoustic Noise[J].Proceedings of the IEEE International Conference on Acoustics Speech and Signal Processing,1979,4(2),208-211.
[31]Ning Ma.Speech Enhancement Algorithms Using Kalman Filter and Masking Properties of Human Auditory Sysmtems[D].Ottawa:Ottawa University,2005.
[32]E.J.Nemer.Speech Analysis and Quality Enhancement Using Higher Order Cumulants[D].Carleton:Carleton University,1999.
[33]R.Paliwal,A.basu.A Speech Enhancement Method Based on Kalman Filtering[J].Proceedings of the IEEE International Conference on Acoustics Speech and Signal Processing,1987,12(1):297-300.
[34]Ning Ma,Martin Bouchard,Rafik.A.Goubran.Speech Enhancement Using a Masking Threshold Constrained Kalman Filter and its Heuristic Implementations[J].IEEE Transactions on Acoustics Speech and Signal Processing,2006,14(1):19-32.
[35]沈亚强,程仲文.建立在卡尔曼滤波基础上的语音增强方法.声学学报,1994,19(3):227-233.
[36]Marcel Gabrea.Adaptive Kalman Filtering-Based Speech Enhancement Alogorithm[J].Canadian Conference on Electrical and Computer Engineering,2001,1(2):521-526.
[37]管亮,冯新泸.基于小波变换的信号消噪效果影响因素研究及Matlab实践[J].自动化与仪器仪表,2004,6(3):43-46.
[38]飞思科技产品研发中心.小波分析理论与MATLAB7实现[M].北京:电子工业出版社,2005:30-80.
[39]冯象初,甘小冰,宋国乡.数值范函与小波理论[M].西安:西安电子科技大学出版社,2003:157-159.
[40]魏明果.实用小波分析[M].北京:北京理工大学出版社,2005:8-13.
[41]杨福生.小波变换的工程分析与应用[M].北京:科学出版社,1999:64-65.
[42]苏丽.远程心电监护诊断系统心电信号处理方法研究[D].哈尔滨:哈尔滨工程大学,2006.
[43]Cohen A,Daubechies I,Plonka G.Regularity of Refinable Function Vectors[J].Journal of Fourier Analysis and Application,1997,3(3):295-324.
[44]Daubechies I.Orthonomral Bases of Compactly Supported Wavelets[J].Communications on Pure and Applied Mathematics,1988,41(2):909-999.
[45]林文华.基于小波变换的去噪方法及其应用研究[D].广州:暨南大学,2000.
[46]胡昌华,张军波,夏军等.基于MATLAB的系统分析与设计-小波分析[M].西安:西安电子科技大学出版社,1999:6-12.
[47]王侠,顾明亮.一种基于小波变换的语音增强新方法[J].徐州师范大学学报(自然科学版),2005,23(3):57-60.
[48]沈亚强,金洪震,刘旭.基于子波变换的语音去噪方法[J].信号处理,2000,16(3):221-226.
[49]李倩,王让定,陈金儿.基于改进阈值的小波域语音增强算法[J].宁波大学学报(理工版),2005,18(3):344-348.
[50]D.L.Donoho,I.M.Johnstone.Ideal Spatial Adaptation by Wavelet shrinkage[J].Biometrika,1994,81(3):425-455.
[51]陈益,李书.改进的小波阈值消噪法应用于超声信号处理[J].北京航空航天大学学报,2006,32(14):466-470.
[52]周静,陈允平,周策,梁劲.小波系数软硬阈值折中方法在故障定位消噪中的应用[J].电力系统自动化,2005,29(1):65-68.
[53]王振力,张雄伟,郑翔等.一种新的子波域语音增强方法[J].信号处理,2006,22(3):325-328.
[54]Xiaojie Zou,Xueyao Li,Rubo Zhang.Speech Enhancement Based on Hilbert-Huang Transform Theory[J].Proceedings of the First international Multi-Symposiums on Computer and Computational Sciences,2006,1(3):208-213.
[55]秦前清,杨凯.实用小波分析[M].西安:西安电子科技大学出版社,1998:60-99.
[56]胡广书.现代信号处理教程[M].北京:清华大学出版社,2004:347-358.
[57]周凤岐,遣小光,周军.基于平稳多小波变换的红外图像噪声抑制方法[J].红外与毫米波学报,2005,24(2):151-155.
[58]董卫军,周明全,耿国华.一种新的基于多小波的图像去噪算法[J].计算机应用与软件,2006,23(4):6-136.
[59]陈香朋,曹思远.GHM类正交多小波变换及其在地震资料去噪中的应用[J].地震地质,2005,27(3):479-486.
[60]成礼智,王红霞,罗永等.小波的理论与应用[M].北京:科学出版社,2004:133-178.
[61]冯象初,甘小冰,宋国乡等.数值泛函与小波理论[M].西安:西安电子科技大学出版社,2003:141-147.
[62]吴爱弟,孙福芹,赵小山.用正交多小波压制信号的随机噪声[J].计算机应用与软件,2003,9(5):11-65.
[63]Strela V,Heller P,Strang G.The Application of Multiwavelet Filter-banks to Image processing[J].IEEE Trans on Signal Processing,1999,8(4):548-563.
[64]Xia X G,Hardin D,Geronimo J,Stuer B W.Design of Prefi lters for Discrete Multiwavelet Transform[J].IEEE Trans on Signal Processing,1996,44(1):25-35.
[65]Xia G.A New Prefilter Design for Discrete Multiwavelet Transform[J].IEEE Trans on Signal Processing,1998,46(6):1558-1570.
[66]刘志刚.多小波理论及其在电力系统故障信号处理中的应用研究[D].重庆:西南交通大学电气化自动化研究所,2003.
[67]邹海林,宁书年,邹华胜.采用不同预处理方法的GRP图像去噪效果分析[J].地球物理学进展,2005,20(2):469-475.
[68]侯周国,钱盛友,姚畅.短时域语音端点检测中谱熵算法的改进[J].计算机工程与应用,2006,42(21):55-56.
[69]张学文.组成论[M].合肥:中国科学技术大学出版社,2003:70-75.
[70]王让定,柴佩琪.一个基于谱熵的语音端点检测改进方法[J].信息与控制,2004,33(1):77-81.
[2]黄苏雨,梁声灼,黄苏园.语音增强方法综述[J].计算机与现代化,2007,3(1):16-20.
[3]胡航.语音信号处理[M].哈尔滨:哈尔滨工业大学出版社,2000:186-194.
[4]姚天任.数字语音信号处理[M].武汉:华中科技大学出版社,2003:14-24.
[5]丁沛.语音识别中的抗噪声技术[D].北京:清华大学,2003.
[6]J.S.Lim,A.V.Oppehneim.All-Pole Modeling of Degraded Speeeh[J].IEEE Transactions on Acoustics Speech and Signal Processing,1978,26(3):197-210.
[7]J Slim,Openheim A V.Enhancement and Bandwidth Compression of Noisy Speech[J].Proceeding of IEEE,1979,67(12):1586-1604.
[8]Boll S F.Suppression of Acoustic Noise in Speech Using Spectral Subtraction[J].IEEE Trans on Acoust Speech and Signal Processing,1979,27(2):113-120.
[9]R.J.Maulya,M.L.Malpass.Speeeh Enhancement Using a Soft-decision Noise Suppression Filter[J].IEEE Transactions on Acoustics Speech and Signal Processing, 1980, 28(2):137-145.
[10] Y. Ephraim, D. Malah. Speech Enhacement Using a Minimum Mean-square Error Short-time Spectral Amplitude estimator[J]. IEEE Transactions on Acoustics Speech and Signal Processing, 1984, 32(6): 1109-1121.
[11] Y. Ephraim. Speech Enhancement Using a Minimum Mean-square Error Speech Log-spectral Amplitude Estimator[J]. IEEE Transactions on Acoustics Speech and Signal Processing, 1985, 33 (2): 443-445.
[12] Y. Ephraim. A Bayesian Estimation Approach for Speech Enhancement Using Hidden Markov Models[J]. IEEE Transactions on Acoustics Speech and Signal Processing, 1993,40(4): 725-732.
[13] Hossein Sameti, Hamid Sheikhzadeh, Li Deng, Robert L. Brennan. HMM-based Strategies for Enhancement of Speech Signal Embedded in Nonstationary Noise[J]. IEEE Transactions on Acoustics Speech and Signal Processing, 1998, 6(5):445-455.
[14] David Y. Zhao, W. Bastiaan Kleijn.HMM-Based Gain Modeling for Enhancement of Speech in Noise[J].IEEE Transactions on Acoustics Speech and Signal Processing, 2007, 15(3):882 -892.
[15] Knecht, W. G. Schenkel, M. E. Moschytz, G. S. Neural Network Filters for Speech Enhancement[J]. IEEE Transactions on Acoustics Speech and Signal Processing,1995,3(6):433-438.
[16]Potamitis.I,Fakotakis.N.D,Kokkinakis.G.Impulsive Noise Suppression Using Neural Networks[J].IEEE Transactions on Acoustics Speech and Signal Processing,2000,3(3):1871-1874.
[17]David L.Donoho.De-Noising by Soft-Thresholding[J].IEEE Transactions on information theory,1995,41(3):613-627.
[18]Sungwook Chang,Y.Kwon,Sung-il Yang.Speech Enhancement for Non-stationary Noise Environment by Adaptive Wavelet Packet[J].ICASSP,2002,1(2):561-564.
[19]Yariv Ephraim,Hany L.Van Trees.A Signal Subspace Approach for Speech Enhancement[J].IEEE Transaction on Speech and Audio Processing,1995,3(4):251-266.
[20]Afshin Rezayee,Saeed Gazor.An Adaptive KLT Approach for Speech Enhancement[J].IEEE Transaction on Speech and Audio Processing,2001,9(2):87-95.
[21]Nathalie Virag.Single Channel Speech Enhancemnet Based on Masking properties of Human Auditory System[J].IEEE Transaction on Speech and Audio Processing,1999,7(2):126-137.
[22]陶智,赵鹤鸣,龚呈卉.基于听觉掩蔽效应和Bark子波变换的语音增强[J].声学学报,2005,30(4):367-372.
[23]王光艳,赵晓群,王霞.基于数学形态学的非线性语音增强方法[J].计算机工程与应用,42(34):53-56.
[24]赵晓群,王津.一种基于形态学的语音增强方法[J].同济大学学报(自然科学版),2006,34(10):1394-1397.
[25]彭煊,刘金福,王炳锡.基于独立分量分析的语音增强[J].信号处理,2002,18(5):477-479.
[26]周成,刘钊.基于独立分量分析的单通道语音降噪算法研究[J].激光与红外,2005,35(5):374-377.
[27]林秋华,郑永瑞,殷福亮.基于参考独立分量分析的语音增强方法[J].大连理工大学学报,46(6):915-919.
[28]陈砚圃,卜凡亮,戴启军等.语音中相位的听觉感知实验研究[J].声学学报,2003,28(1):9-13.
[29]R.D.Preuss.Evaluation of a correlation Subtraction Method for Enhancing Speech Degraded by Additive White Noise[J].IEEE Transactions on Acoustics Speech and Signal Processing,1978,26(3):471-472.
[30]M.Berouti,R.Schwartz,and J.Makhoul.Enhancement of Speech Corrupted by Acoustic Noise[J].Proceedings of the IEEE International Conference on Acoustics Speech and Signal Processing,1979,4(2),208-211.
[31]Ning Ma.Speech Enhancement Algorithms Using Kalman Filter and Masking Properties of Human Auditory Sysmtems[D].Ottawa:Ottawa University,2005.
[32]E.J.Nemer.Speech Analysis and Quality Enhancement Using Higher Order Cumulants[D].Carleton:Carleton University,1999.
[33]R.Paliwal,A.basu.A Speech Enhancement Method Based on Kalman Filtering[J].Proceedings of the IEEE International Conference on Acoustics Speech and Signal Processing,1987,12(1):297-300.
[34]Ning Ma,Martin Bouchard,Rafik.A.Goubran.Speech Enhancement Using a Masking Threshold Constrained Kalman Filter and its Heuristic Implementations[J].IEEE Transactions on Acoustics Speech and Signal Processing,2006,14(1):19-32.
[35]沈亚强,程仲文.建立在卡尔曼滤波基础上的语音增强方法.声学学报,1994,19(3):227-233.
[36]Marcel Gabrea.Adaptive Kalman Filtering-Based Speech Enhancement Alogorithm[J].Canadian Conference on Electrical and Computer Engineering,2001,1(2):521-526.
[37]管亮,冯新泸.基于小波变换的信号消噪效果影响因素研究及Matlab实践[J].自动化与仪器仪表,2004,6(3):43-46.
[38]飞思科技产品研发中心.小波分析理论与MATLAB7实现[M].北京:电子工业出版社,2005:30-80.
[39]冯象初,甘小冰,宋国乡.数值范函与小波理论[M].西安:西安电子科技大学出版社,2003:157-159.
[40]魏明果.实用小波分析[M].北京:北京理工大学出版社,2005:8-13.
[41]杨福生.小波变换的工程分析与应用[M].北京:科学出版社,1999:64-65.
[42]苏丽.远程心电监护诊断系统心电信号处理方法研究[D].哈尔滨:哈尔滨工程大学,2006.
[43]Cohen A,Daubechies I,Plonka G.Regularity of Refinable Function Vectors[J].Journal of Fourier Analysis and Application,1997,3(3):295-324.
[44]Daubechies I.Orthonomral Bases of Compactly Supported Wavelets[J].Communications on Pure and Applied Mathematics,1988,41(2):909-999.
[45]林文华.基于小波变换的去噪方法及其应用研究[D].广州:暨南大学,2000.
[46]胡昌华,张军波,夏军等.基于MATLAB的系统分析与设计-小波分析[M].西安:西安电子科技大学出版社,1999:6-12.
[47]王侠,顾明亮.一种基于小波变换的语音增强新方法[J].徐州师范大学学报(自然科学版),2005,23(3):57-60.
[48]沈亚强,金洪震,刘旭.基于子波变换的语音去噪方法[J].信号处理,2000,16(3):221-226.
[49]李倩,王让定,陈金儿.基于改进阈值的小波域语音增强算法[J].宁波大学学报(理工版),2005,18(3):344-348.
[50]D.L.Donoho,I.M.Johnstone.Ideal Spatial Adaptation by Wavelet shrinkage[J].Biometrika,1994,81(3):425-455.
[51]陈益,李书.改进的小波阈值消噪法应用于超声信号处理[J].北京航空航天大学学报,2006,32(14):466-470.
[52]周静,陈允平,周策,梁劲.小波系数软硬阈值折中方法在故障定位消噪中的应用[J].电力系统自动化,2005,29(1):65-68.
[53]王振力,张雄伟,郑翔等.一种新的子波域语音增强方法[J].信号处理,2006,22(3):325-328.
[54]Xiaojie Zou,Xueyao Li,Rubo Zhang.Speech Enhancement Based on Hilbert-Huang Transform Theory[J].Proceedings of the First international Multi-Symposiums on Computer and Computational Sciences,2006,1(3):208-213.
[55]秦前清,杨凯.实用小波分析[M].西安:西安电子科技大学出版社,1998:60-99.
[56]胡广书.现代信号处理教程[M].北京:清华大学出版社,2004:347-358.
[57]周凤岐,遣小光,周军.基于平稳多小波变换的红外图像噪声抑制方法[J].红外与毫米波学报,2005,24(2):151-155.
[58]董卫军,周明全,耿国华.一种新的基于多小波的图像去噪算法[J].计算机应用与软件,2006,23(4):6-136.
[59]陈香朋,曹思远.GHM类正交多小波变换及其在地震资料去噪中的应用[J].地震地质,2005,27(3):479-486.
[60]成礼智,王红霞,罗永等.小波的理论与应用[M].北京:科学出版社,2004:133-178.
[61]冯象初,甘小冰,宋国乡等.数值泛函与小波理论[M].西安:西安电子科技大学出版社,2003:141-147.
[62]吴爱弟,孙福芹,赵小山.用正交多小波压制信号的随机噪声[J].计算机应用与软件,2003,9(5):11-65.
[63]Strela V,Heller P,Strang G.The Application of Multiwavelet Filter-banks to Image processing[J].IEEE Trans on Signal Processing,1999,8(4):548-563.
[64]Xia X G,Hardin D,Geronimo J,Stuer B W.Design of Prefi lters for Discrete Multiwavelet Transform[J].IEEE Trans on Signal Processing,1996,44(1):25-35.
[65]Xia G.A New Prefilter Design for Discrete Multiwavelet Transform[J].IEEE Trans on Signal Processing,1998,46(6):1558-1570.
[66]刘志刚.多小波理论及其在电力系统故障信号处理中的应用研究[D].重庆:西南交通大学电气化自动化研究所,2003.
[67]邹海林,宁书年,邹华胜.采用不同预处理方法的GRP图像去噪效果分析[J].地球物理学进展,2005,20(2):469-475.
[68]侯周国,钱盛友,姚畅.短时域语音端点检测中谱熵算法的改进[J].计算机工程与应用,2006,42(21):55-56.
[69]张学文.组成论[M].合肥:中国科学技术大学出版社,2003:70-75.
[70]王让定,柴佩琪.一个基于谱熵的语音端点检测改进方法[J].信息与控制,2004,33(1):77-81.