核磁共振波谱法无创血糖测量的信号处理与算法优化
|
摘要
糖尿病是由于遗传因素、免疫功能紊乱、微生物感染、自由基毒素、精神因素等各种致病因子作用于机体导致胰岛素分泌缺陷或胰岛素抵抗而产生的一种激素分泌障碍性疾病。糖尿病患者的一个主要治疗手段就是实时的对病患自身血糖水平进行监测。目前大多数糖尿病人都是利用有创的血糖检测手段来检测自身的血糖,这种方法有很多不利之处,如容易使病患因为痛感产生抵触情绪,容易造成伤口的感染等。因此,许多科研机构提出自己的无创血糖检测方法,就目前的研究状况来看,利用红外光谱进行无创血糖检测是一个使用比较成熟的技术。
本文提出了一种无创血糖检测的新方法即基于质子系统核磁共振的无创血糖检测,文章首先概括介绍了磁共振的原理及利用磁共振技术对物质定量测量的方法。之后对核磁共振的磁场、射频收发线圈、控制电路等做了详细的介绍并给出了实际设计的磁共振仪器装置的图片。最后对核磁共振信号的实时采集及信号的处理和频谱分析做了详细的说明和重要的推导并得出了频谱分析的结果。
文章中的实时采集系统是基于MATLAB将示波器与计算机连接通讯而实现的,在此系统中利用示波器的高采样率将其作为信号的采集与模数转换模块并直接与计算机连接。因为本研究项目尚处在可行性研究阶段,所以本文利用MATLAB对磁共振自由衰减信号进行了仿真分析,并添加了实际试验中出现的噪声,设计了相应的滤波程序对其进行处理。信号频谱分析的显示结果表明核磁共振方法能够比较清晰地显示出不同比例葡萄糖与水溶液的谱线区别,也就证明了利用核磁共振方法对人体血糖进行无创检测的方法是可行的。在文章的最后,本文详细说明了目前研究成果的不足之处和未来研究的方向,并提出了对于该项目继续深入发展的建议。
Diabetes is due to kinds of pathogenic factors such as genetic factors, immune disorders, microbial infections, free radical toxins, mental factors that act on the body leading to insulin secretion or insulin resistance caused by a hormone disorders.One of the major treatment techniques for diabetics is to monitor their blood glucose levels in real time. Presently, most diabetics are using invasive glucose detection equipment to monitor their own blood sugar level, this method has many disadvantages, such as patients likely tend to generate resistance because of pain and the cuts for extracting blood are easily causing infections. Therefore, many research institutions propose their own non-invasive blood glucose detection methods. Views of the present research are that using infrared spectroscopy for noninvasive blood glucose monitoring is a relatively mature technology.
This paper presents a new non-invasive method for blood glucose monitoring systems based on proton nuclear magnetic resonance of non-invasive blood glucose monitoring; the paper first outlined the principle of magnetic resonance and magnetic resonance techniques using quantitative measurement methods for material. After that, the article makes a detail on the NMR magnetic field, RF transceiver coil, the control circuit and gives practical introduction to the design of magnetic resonance equipment device as well as the picture. Finally, the paper makes a specific description on the acquisition and processing of the real-time magnetic resonance signal as well as spectrum analysis.
The real time acquisition system in the article is based on the MATLAB which connect the oscilloscope and the computer, in this system, the high sample rate oscilloscope is working as a signal acquisition and analog-digital conversion module connecting directly with the computer. Because of this research project is still in the feasibility study stage, so this paper uses MATLAB to simulate the free induction decay signals from the magnetic resonance equipment, adds the actual noise based on actual situation and design the corresponding filter to process the signal. Signal spectrum analysis results show that the NMR method can clearly show the different of the spectrum based on the different ratio between glucose and water solution, also it proves that noninvasive blood glucose detection system which uses the nuclear magnetic resonance method is feasible. At the end, this article details the current research shortcomings and future research directions, and proposes the suggestion to continue for the further development of this project.
本文提出了一种无创血糖检测的新方法即基于质子系统核磁共振的无创血糖检测,文章首先概括介绍了磁共振的原理及利用磁共振技术对物质定量测量的方法。之后对核磁共振的磁场、射频收发线圈、控制电路等做了详细的介绍并给出了实际设计的磁共振仪器装置的图片。最后对核磁共振信号的实时采集及信号的处理和频谱分析做了详细的说明和重要的推导并得出了频谱分析的结果。
文章中的实时采集系统是基于MATLAB将示波器与计算机连接通讯而实现的,在此系统中利用示波器的高采样率将其作为信号的采集与模数转换模块并直接与计算机连接。因为本研究项目尚处在可行性研究阶段,所以本文利用MATLAB对磁共振自由衰减信号进行了仿真分析,并添加了实际试验中出现的噪声,设计了相应的滤波程序对其进行处理。信号频谱分析的显示结果表明核磁共振方法能够比较清晰地显示出不同比例葡萄糖与水溶液的谱线区别,也就证明了利用核磁共振方法对人体血糖进行无创检测的方法是可行的。在文章的最后,本文详细说明了目前研究成果的不足之处和未来研究的方向,并提出了对于该项目继续深入发展的建议。
Diabetes is due to kinds of pathogenic factors such as genetic factors, immune disorders, microbial infections, free radical toxins, mental factors that act on the body leading to insulin secretion or insulin resistance caused by a hormone disorders.One of the major treatment techniques for diabetics is to monitor their blood glucose levels in real time. Presently, most diabetics are using invasive glucose detection equipment to monitor their own blood sugar level, this method has many disadvantages, such as patients likely tend to generate resistance because of pain and the cuts for extracting blood are easily causing infections. Therefore, many research institutions propose their own non-invasive blood glucose detection methods. Views of the present research are that using infrared spectroscopy for noninvasive blood glucose monitoring is a relatively mature technology.
This paper presents a new non-invasive method for blood glucose monitoring systems based on proton nuclear magnetic resonance of non-invasive blood glucose monitoring; the paper first outlined the principle of magnetic resonance and magnetic resonance techniques using quantitative measurement methods for material. After that, the article makes a detail on the NMR magnetic field, RF transceiver coil, the control circuit and gives practical introduction to the design of magnetic resonance equipment device as well as the picture. Finally, the paper makes a specific description on the acquisition and processing of the real-time magnetic resonance signal as well as spectrum analysis.
The real time acquisition system in the article is based on the MATLAB which connect the oscilloscope and the computer, in this system, the high sample rate oscilloscope is working as a signal acquisition and analog-digital conversion module connecting directly with the computer. Because of this research project is still in the feasibility study stage, so this paper uses MATLAB to simulate the free induction decay signals from the magnetic resonance equipment, adds the actual noise based on actual situation and design the corresponding filter to process the signal. Signal spectrum analysis results show that the NMR method can clearly show the different of the spectrum based on the different ratio between glucose and water solution, also it proves that noninvasive blood glucose detection system which uses the nuclear magnetic resonance method is feasible. At the end, this article details the current research shortcomings and future research directions, and proposes the suggestion to continue for the further development of this project.
引文
[1] PIRO MICHAEL(US).Apparatus for displaying self monitoring blood glucose equipment and supplies[P].美国专利:US2004197237,2004.02.11
[2] D.Someya,Y. Nikawa M. Yamamoto. Measurement of Blood Sugar Level Using Millimeter Waves[J]. Korea-Japan Microwave Workshop(KJMW2000). Proceeding,Korea, 2000:32-35
[3] Y.Nikawa, D.Someya. Application of Millimeter Wave to Measure Blood Sugar Level[J]. Proceeding of APMC2001, Taibei, Taiwan,2001:1303-1306
[4]李东升.血糖检测装置最新发展动态[J].上海生物医学工程,2005,26(1):33-36.
[5] Chang Youngchung, Winarta Handani. Method of using enzyme electrode[J]. Biotechnology Advances,1997,13(4):739
[6] HOME DIAGNOSTICS INC(US). Systems and methods for blood glucose sensing[P].美国专利: US2004182703,2004.01.26
[7] Bantle J. P.,Thomas W. Glucose Measurement in Patients with Diabetes Mellitus with Dermal Interstitial Fluid [J]. Journal of Clinical Medicine,1997,130:436-441
[8] Tierney M J, Tamada J A, Potts R O. Clinical Evaluation of the GlucoWatch Biographer: a Continual, Non-Invasive Glucose Monitor for Patients with Diabetes[J].Biosensors and Bioelectronics,2001,16(9-12):621-629
[9] Cho Ok Kyung, Kim Yoon Ok, Hiroshi Mitsumaki, et al. Noninvasive Measurement of Glucose by Metabolic Heat Conformation Method[J].Clinical Chemistry.2004, 50(10):1894-1898
[10]陈真诚,金星亮,徐效文等.一种无创血糖检测仪的初步研究[J].传感技术学报,2008,21(7)
[11]马显光,蒲晓允,陈仕国.无创血糖仪的研制[J].生物医学工程学杂志,2004,21(3)
[12]陈文亮,徐可欣,杜振辉,等.人体无创血糖检测技术[J].仪器仪表学报,2003,24(4):258-262
[13] Cameron B D, Gorde H, Cote G L. Development of an optical polarimeter for in vivo glucose monitoring[J]. Proceedings of SPIE, 1999, 3599:43-49
[14] Cameron B D, Cote G L. Polarimetric detection of chiralchemicals in biological fluids[J]. Proceedings of SPIE, 1997, 2982:308-313
[15] Duncan Arlene, Hannigan John, Freeborn Scott S, et al. Portable non-invasive blood glucose monitor[J]. International Conference on Solid-State Sensors and Actuators, and Euro sensors IX, 1995, Proceedings 2:455-458
[16] Zhao Z M, Myllyla R. Photo acoustic determination of glucose concentration in whole blood by a near-infrared laser diode[J]. Proceedings of SPIE, 2001, 4256:77-83
[17] Zhao Z M, Myllyla.R. The effect of optical scattering on pulsed photo acoustic measurement in weakly absorbing liquid[J]. Measurement Science and Technology,2001, 12:2172-2177
[18] Chaiken J., Finney W.F., Knudson P.E. Noninvasive blood analysis by tissue modulated NIR Raman spectroscopy[J]. Proceedings of SPIE-The International Society for Optical Engineering, Apr. 2001, Sponsored by:SPIE, 134-145
[19] Shaw Adrian D., Kaderbhai Naheed, et al.. Biotransformation by yeast of glucose to ethanol using dispersive Raman spectroscopy and chemometrics[J]. Applied Spectroscopy, 1999 53(11):1419-1428
[20] D. C. Klonoff, J. Braig, B. Sterling. Mid-Infrared Spectroscopy for Noninvasive Blood Glucose Monitoring[EB/OL]. http: //www. ieee. org/ organizations/ pubs/ newsletters/ leos/ apr98/ nearinfrared. htm
[21]陈文亮,徐可欣,杜振辉,等.人体无创血糖检测技术[J].仪器仪表学报.2003, 24(4):258-262
[22] Mark A A,Gary W S. Determination of physiological levels of glucose in an aqueous matrix with digitally filtered Fourier transforms near-infrared. Spectra. Anal.Chem. 1990,62(14):1457-1464
[23] Qing Ding,Gary W.Small,Mark A. Arnold. Evaluation of nonlinear model building strategies for the determination of glucose in biological matrices by near-infrared spectroscopy, Analytica Chimica Acta, 1999, 384:333-343
[24] Pan S T,Chung H, Mark A A. Near-infrared spectroscopic measurement of physiological glucose levels invariable metrics of protein and triglycerides. Analytical Chemistry, 1996,68(7):1124-1134
[25]李刚,李晓霞,林凌,等.消除个体条件测量差异的动态光谱及其频域提取法的研究.光谱学与光谱分析,2006,2
[26] Xiaoxia LI,Gang LI,Ling LIN,et al. Application of a Wavelet Adaptive Filter Based on Neural Networkto Minimize Distortion of the Pulsatile Spectrum. LECTURE NOTES IN COMPUTER SCIENCE,2004,3174:362-368
[27]张洪艳,丁东,赵振武等.人体血清中葡萄糖浓度的近红外光谱的测量和分析.光谱实验室,2004,21(6):1128-1130
[28]丁东,张洪艳,王丽等.用近红外光谱法测量分析全血的血糖浓度.激光与红外,2003,33(5):328-330
[29]顾华.小波分析对核磁共振信号的研究[M].中国科学技术大学,1998
[30]熊国欣,李立本.核磁共振成像原理[M].北京:科学出版社,2007
[31]黄永仁.核磁共振理论原理[M].上海:华东师范大学出版,1992
[32]卢希庭.原子核物理学[M].北京:原子能出版社,2001
[33]俎栋林.核磁共振成像学[M].北京:高等教育出版社,2004
[34]王鹤,李鲠颖.低场核磁共振系统中若干技术问题的研究[D].上海:华东师范大学,2007
[35]郑传行,张一鸣.低场脉冲核磁共振仪探头的研制[J].北京:核电子学与探测技术,2008
[36]夏平铸.永磁机构[M].北京:北京工业大学出版社,2000:13-95
[37]黄玉兰.射频电路理论与设计[M].北京:人民邮电出版社,2008:26-181
[38]飞思科技产品研发中心. MATLAB7基础与提高[M].北京:电子工业出版社,2005.4
[39]董长虹,余啸海.MATLAB接口技术与应用[M].北京:国防工业出版社,2004
[40]苏金明,张莲花,刘波.MATLAB工具箱应用[M].北京:电子工业出版社,2004
[41] D.I.Hoult. The Signal-to-Noise Ratio of the Nuclear Magnetic Resonance Experiment[J]. Magn.Reson,1976,24:71-85
[42] D.D.Griffin. Spin Dynamies of Carr-Pureell-Meiboom-Gill-like Sequenees in Grossly Inhomogeneous B0 and B1 Field and Application to NMR Well Logging[J]. Magn,Reson, 2000,voll43:120-135
[43] Gadi.Goeman,G.Pramer. The CPMG Pulse Sequence in Strong Magnetic Field Gradients with Application to oil-well Logging[J]. Magn,Reson, 1995,vol113:11-18
[44]王晶,王广德,常利民等.应用核磁共振氢谱测试人体的血清[J].光谱实验室. 2002.3
[45]邓亲恺.现代医学仪器设计原理[M].北京:科学出版社,2004.5
[46]高汉宾,张振芳.核磁共振原理与实验方法[M].武汉:武汉大学出版社,2008.4
[47] T.Yamaji,T.Saito,K.Hayamizu,et. al. Welcome to Spectral Database for Organic Compounds, SDBS[EB/OL]. http://riodb01. ibase. aist.go.jp/sdbs/cgi-bin/direct_frame_top.cgi
[48]毛希安.现代核磁共振实用技术及应用[M].北京:科学技术文献出版社,2000
[49]陈怀琛,吴大正,高西全.MATLAB及在电子信息课程中的应用[M].北京:电子工业出版社,2006.3
[50] Alan V.Oppenheim, Alan S.Willsky.刘树棠(译).信号与系统[M].西安:西安交通大学出版社,2004.3
[51]丁玉美,高西全.数字信号处理[M].西安:西安电子科技大学出版社,2004
[52] G.U.Yule. On a method of investigating periodicities in disturbed series, with special reference to wolfer’s sunspot numbers[J]. Phil. Trans. Roy. Soc.,1927,226-A:267–298.
[53] J. Makhoul. Linear prediction: A tutorial review[A]. Proceedings of the IEEE,1975, April 63(5):561–580
[54]张贤达.现代信号处理[M].北京:清华大学出版社,2001
[55] M. H. Hayes. Statistical Digital Signal Processing and Modeling[M]. Wiley & Sons, Inc., New York, 1996
[56]胡广书.数字信号处理[M].北京:清华大学出版社,1997
[57]崔景泰.小波分析导论[M].西安交通大学出版社,1995
[58]徐长发,李国宽.实用小波方法[M].武汉:华中科技大学出版社,2001
[59]岑冀刚,孙德宝,任毅.利用小波对信号进行去噪及参数估计[J].北京:现代雷达,2003
[60] Ulrich L.Gunther,Christian Ludwing,Heinz Ruterjans. WAVEWAT-Improved Solvent Suppression in NMR Spectra Employing Wavelet Transforms[J]. JOURNAL OF MAGNETIC RESONANCE,2002
[61]张贤达.现代数字信号处理[M].北京:清华大学出版社,2001
[62]李杰.低场脉冲核磁共振中噪声削弱方法的研究[D].中科院电工所.2004
[63]曹毅,张榆锋,毛选珍.小波分析及其在信号处理中的应用[J].现代电子技术,2003
[64]刘广臣,张惠安,贾爱宾.数字信号处理中的加窗问题研究[J].长沙大学学报,2003
[65] A.V.奥本海姆,R.W.谢弗.刘树棠,黄建国(译).离散时间信号处理[M].西安:西安交通大学出版社,2001.9
[2] D.Someya,Y. Nikawa M. Yamamoto. Measurement of Blood Sugar Level Using Millimeter Waves[J]. Korea-Japan Microwave Workshop(KJMW2000). Proceeding,Korea, 2000:32-35
[3] Y.Nikawa, D.Someya. Application of Millimeter Wave to Measure Blood Sugar Level[J]. Proceeding of APMC2001, Taibei, Taiwan,2001:1303-1306
[4]李东升.血糖检测装置最新发展动态[J].上海生物医学工程,2005,26(1):33-36.
[5] Chang Youngchung, Winarta Handani. Method of using enzyme electrode[J]. Biotechnology Advances,1997,13(4):739
[6] HOME DIAGNOSTICS INC(US). Systems and methods for blood glucose sensing[P].美国专利: US2004182703,2004.01.26
[7] Bantle J. P.,Thomas W. Glucose Measurement in Patients with Diabetes Mellitus with Dermal Interstitial Fluid [J]. Journal of Clinical Medicine,1997,130:436-441
[8] Tierney M J, Tamada J A, Potts R O. Clinical Evaluation of the GlucoWatch Biographer: a Continual, Non-Invasive Glucose Monitor for Patients with Diabetes[J].Biosensors and Bioelectronics,2001,16(9-12):621-629
[9] Cho Ok Kyung, Kim Yoon Ok, Hiroshi Mitsumaki, et al. Noninvasive Measurement of Glucose by Metabolic Heat Conformation Method[J].Clinical Chemistry.2004, 50(10):1894-1898
[10]陈真诚,金星亮,徐效文等.一种无创血糖检测仪的初步研究[J].传感技术学报,2008,21(7)
[11]马显光,蒲晓允,陈仕国.无创血糖仪的研制[J].生物医学工程学杂志,2004,21(3)
[12]陈文亮,徐可欣,杜振辉,等.人体无创血糖检测技术[J].仪器仪表学报,2003,24(4):258-262
[13] Cameron B D, Gorde H, Cote G L. Development of an optical polarimeter for in vivo glucose monitoring[J]. Proceedings of SPIE, 1999, 3599:43-49
[14] Cameron B D, Cote G L. Polarimetric detection of chiralchemicals in biological fluids[J]. Proceedings of SPIE, 1997, 2982:308-313
[15] Duncan Arlene, Hannigan John, Freeborn Scott S, et al. Portable non-invasive blood glucose monitor[J]. International Conference on Solid-State Sensors and Actuators, and Euro sensors IX, 1995, Proceedings 2:455-458
[16] Zhao Z M, Myllyla R. Photo acoustic determination of glucose concentration in whole blood by a near-infrared laser diode[J]. Proceedings of SPIE, 2001, 4256:77-83
[17] Zhao Z M, Myllyla.R. The effect of optical scattering on pulsed photo acoustic measurement in weakly absorbing liquid[J]. Measurement Science and Technology,2001, 12:2172-2177
[18] Chaiken J., Finney W.F., Knudson P.E. Noninvasive blood analysis by tissue modulated NIR Raman spectroscopy[J]. Proceedings of SPIE-The International Society for Optical Engineering, Apr. 2001, Sponsored by:SPIE, 134-145
[19] Shaw Adrian D., Kaderbhai Naheed, et al.. Biotransformation by yeast of glucose to ethanol using dispersive Raman spectroscopy and chemometrics[J]. Applied Spectroscopy, 1999 53(11):1419-1428
[20] D. C. Klonoff, J. Braig, B. Sterling. Mid-Infrared Spectroscopy for Noninvasive Blood Glucose Monitoring[EB/OL]. http: //www. ieee. org/ organizations/ pubs/ newsletters/ leos/ apr98/ nearinfrared. htm
[21]陈文亮,徐可欣,杜振辉,等.人体无创血糖检测技术[J].仪器仪表学报.2003, 24(4):258-262
[22] Mark A A,Gary W S. Determination of physiological levels of glucose in an aqueous matrix with digitally filtered Fourier transforms near-infrared. Spectra. Anal.Chem. 1990,62(14):1457-1464
[23] Qing Ding,Gary W.Small,Mark A. Arnold. Evaluation of nonlinear model building strategies for the determination of glucose in biological matrices by near-infrared spectroscopy, Analytica Chimica Acta, 1999, 384:333-343
[24] Pan S T,Chung H, Mark A A. Near-infrared spectroscopic measurement of physiological glucose levels invariable metrics of protein and triglycerides. Analytical Chemistry, 1996,68(7):1124-1134
[25]李刚,李晓霞,林凌,等.消除个体条件测量差异的动态光谱及其频域提取法的研究.光谱学与光谱分析,2006,2
[26] Xiaoxia LI,Gang LI,Ling LIN,et al. Application of a Wavelet Adaptive Filter Based on Neural Networkto Minimize Distortion of the Pulsatile Spectrum. LECTURE NOTES IN COMPUTER SCIENCE,2004,3174:362-368
[27]张洪艳,丁东,赵振武等.人体血清中葡萄糖浓度的近红外光谱的测量和分析.光谱实验室,2004,21(6):1128-1130
[28]丁东,张洪艳,王丽等.用近红外光谱法测量分析全血的血糖浓度.激光与红外,2003,33(5):328-330
[29]顾华.小波分析对核磁共振信号的研究[M].中国科学技术大学,1998
[30]熊国欣,李立本.核磁共振成像原理[M].北京:科学出版社,2007
[31]黄永仁.核磁共振理论原理[M].上海:华东师范大学出版,1992
[32]卢希庭.原子核物理学[M].北京:原子能出版社,2001
[33]俎栋林.核磁共振成像学[M].北京:高等教育出版社,2004
[34]王鹤,李鲠颖.低场核磁共振系统中若干技术问题的研究[D].上海:华东师范大学,2007
[35]郑传行,张一鸣.低场脉冲核磁共振仪探头的研制[J].北京:核电子学与探测技术,2008
[36]夏平铸.永磁机构[M].北京:北京工业大学出版社,2000:13-95
[37]黄玉兰.射频电路理论与设计[M].北京:人民邮电出版社,2008:26-181
[38]飞思科技产品研发中心. MATLAB7基础与提高[M].北京:电子工业出版社,2005.4
[39]董长虹,余啸海.MATLAB接口技术与应用[M].北京:国防工业出版社,2004
[40]苏金明,张莲花,刘波.MATLAB工具箱应用[M].北京:电子工业出版社,2004
[41] D.I.Hoult. The Signal-to-Noise Ratio of the Nuclear Magnetic Resonance Experiment[J]. Magn.Reson,1976,24:71-85
[42] D.D.Griffin. Spin Dynamies of Carr-Pureell-Meiboom-Gill-like Sequenees in Grossly Inhomogeneous B0 and B1 Field and Application to NMR Well Logging[J]. Magn,Reson, 2000,voll43:120-135
[43] Gadi.Goeman,G.Pramer. The CPMG Pulse Sequence in Strong Magnetic Field Gradients with Application to oil-well Logging[J]. Magn,Reson, 1995,vol113:11-18
[44]王晶,王广德,常利民等.应用核磁共振氢谱测试人体的血清[J].光谱实验室. 2002.3
[45]邓亲恺.现代医学仪器设计原理[M].北京:科学出版社,2004.5
[46]高汉宾,张振芳.核磁共振原理与实验方法[M].武汉:武汉大学出版社,2008.4
[47] T.Yamaji,T.Saito,K.Hayamizu,et. al. Welcome to Spectral Database for Organic Compounds, SDBS[EB/OL]. http://riodb01. ibase. aist.go.jp/sdbs/cgi-bin/direct_frame_top.cgi
[48]毛希安.现代核磁共振实用技术及应用[M].北京:科学技术文献出版社,2000
[49]陈怀琛,吴大正,高西全.MATLAB及在电子信息课程中的应用[M].北京:电子工业出版社,2006.3
[50] Alan V.Oppenheim, Alan S.Willsky.刘树棠(译).信号与系统[M].西安:西安交通大学出版社,2004.3
[51]丁玉美,高西全.数字信号处理[M].西安:西安电子科技大学出版社,2004
[52] G.U.Yule. On a method of investigating periodicities in disturbed series, with special reference to wolfer’s sunspot numbers[J]. Phil. Trans. Roy. Soc.,1927,226-A:267–298.
[53] J. Makhoul. Linear prediction: A tutorial review[A]. Proceedings of the IEEE,1975, April 63(5):561–580
[54]张贤达.现代信号处理[M].北京:清华大学出版社,2001
[55] M. H. Hayes. Statistical Digital Signal Processing and Modeling[M]. Wiley & Sons, Inc., New York, 1996
[56]胡广书.数字信号处理[M].北京:清华大学出版社,1997
[57]崔景泰.小波分析导论[M].西安交通大学出版社,1995
[58]徐长发,李国宽.实用小波方法[M].武汉:华中科技大学出版社,2001
[59]岑冀刚,孙德宝,任毅.利用小波对信号进行去噪及参数估计[J].北京:现代雷达,2003
[60] Ulrich L.Gunther,Christian Ludwing,Heinz Ruterjans. WAVEWAT-Improved Solvent Suppression in NMR Spectra Employing Wavelet Transforms[J]. JOURNAL OF MAGNETIC RESONANCE,2002
[61]张贤达.现代数字信号处理[M].北京:清华大学出版社,2001
[62]李杰.低场脉冲核磁共振中噪声削弱方法的研究[D].中科院电工所.2004
[63]曹毅,张榆锋,毛选珍.小波分析及其在信号处理中的应用[J].现代电子技术,2003
[64]刘广臣,张惠安,贾爱宾.数字信号处理中的加窗问题研究[J].长沙大学学报,2003
[65] A.V.奥本海姆,R.W.谢弗.刘树棠,黄建国(译).离散时间信号处理[M].西安:西安交通大学出版社,2001.9