基于信号相位差的海水声速测量方法研究
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摘要
海水声速是进行水下超声波测距与定位、探伤及海洋环境监测等测量过程中的重要参数之一,它随海水温度、压力及盐度等的差异而变化。精确地测量海水声速具有重要意义,可以有效地为测深仪、声纳等水声设备校正测量误差提供准确的声速数据。
本文对基于信号相位差的海水声速测量方法进行了深入研究。主要研究了利用单频信号相位差进行声速测量的方法,针对单频信号相位差估计存在的相位模糊,提出了利用双频信号相位差进行声速测量的方法。论文的主要工作包括以下四个方面:
(1)归纳了海水声速的分布规律及特点,分析并对比了目前国内外进行海水声速测量的方法及特点。在此基础上,本文提出了利用信号相位差进行海水声速测量方法。
(2)提出了利用单频信号相位差进行声速测量的方法。根据时差法进行声速测量的原理,通过将时间的测量转换为相位的估计,在距离测量精度足够高的条件下,信号频率越高,要求的相位差估计精度就越低,则声速测量精度就越高。在信号频率确定的条件下,相位差估计的精度是声速测量精度的关键。因此,本文着重研究了各种相位估计方法,包括过零比较法、数字相关法及FFT谱分析法。通过分析及对比,提出了利用FFT谱分析进行信号相位差估计的方法。此外,为了分析换能器及水声信道特性对信号相位差估计的影响,本文建立了声速测量系统的数学模型,并利用此模型进行了基于单频信号相位差的声速测量仿真分析。
(3)提出了利用双频信号相位差进行声速测量的方法。为了消除采用单频信号存在的相位模糊,进一步提高声速测量精度,本文提出采用频差很小的双频信号进行声速测量的方法。分析了测量原理及利用FFT谱分析时频谱泄漏对信号相位差估计的影响,利用声速测量系统模型进行了基于双频信号相位差的声速测量仿真分析。
(4)设计了声速测量实验系统,包括信号发射及采集的硬件电路,搭建了声速测量的实验平台,分析了实验平台的反射回波及各种环境因素对相位差估计结果的影响,距离测量精度对声速测量精度的影响。利用搭建的实验平台进行了基于信号相位差的声速测量实验,对采集的数据进行了分析和处理,验证了利用信号相位差进行声速测量的结论。
The speed of sound in seawater is one of the important parameters during the measurement of the underwater ultrasonic ranging and positioning, testing and monitoring the marine environment and so on. The propagation speed with the water temperature, pressure and salinity varies. Accurately measure the speed of sound in seawater is important, can be effective for the depth sounder, sonar and other acoustic equipment to provide accurate speed of sound data measurement to correct measurement error.
This paper mainly studies the speed of sound measurement in seawater based on phase difference. Critical study of the use of single-frequency signal phase difference estimation method for speed of sound measurement. For phase ambiguity problem of the single-frequency signal, proposed the use of dual-frequency signal phase difference estimation for speed of sound measurement method. The main paper work includes the following aspects:
(1) This paper summarizes the distribution of speed of sound in seawater and characteristics, analysis and comparison the current international approach to speed of sound measurement of seawater and characteristics, on the basis of these, using the phase difference estimation for speed of sound measurement method in seawater is proposed in this paper.
(2)Proposed a seawater velocity measurement method based on single-frequency signal phase difference estimation. Based on the principle of speed of sound measurement of time difference method, if the time measurement transformed to the phase difference estimate, in the conditions the distance measurement accuracy is high enough, the higher the frequency, the phase difference estimation accuracy requirements lower, the greater the speed of sound measurement accuracy high. In the conditions the signal frequency to determine, the key factor of the speed of sound measurement accuracy is the phase difference estimation accuracy. Therefore, the paper focuses on a variety of phase estimation methods, including zero comparison, digital correlation method and the FFT spectrum analysis. Through analysis and comparison, proposed the use of FFT spectrum analysis as the phase difference estimation method. Established a simplified model of speed of sound measurement system and using the model to analyze their impact on the estimated phase difference. We carried out simulation analysis of speed of sound measurements using single-frequency signal phase difference estimation.
(3) Proposed a seawater speed of sound measurement method based on dual-frequency signal phase difference estimation. To solve the phase ambiguity problem for single-frequency signal, getting the higher speed of sound measurement accuracy, this paper proposes the speed of sound measurement methods using a small dual-frequency difference signal, analysis of the measuring principle and the impact of spectral leakage of FFT spectral analysis to the dual-frequency signal phase difference estimation. We carried out simulation analysis of speed of sound measurements using dual-frequency signals phase difference estimation.
(4)Building a sound speed of sound measurement experimental system based on the estimated phase difference estimation, the design of signal transmission and signals acquisition hardware circuits, analysis of the impact the experimental platform for distance measurement accuracy to speed of sound measurement accuracy, echo and a variety of environmental factors on the phase difference estimation results. Using the experimental platform to carry out the speed of sound measurement experiment based on the single-frequency signal and the dual-frequency signal phase difference estimation. The experiment data were analyzed and processed to verify the speed of sound measured conclusions for use of signal phase difference estimation.
本文对基于信号相位差的海水声速测量方法进行了深入研究。主要研究了利用单频信号相位差进行声速测量的方法,针对单频信号相位差估计存在的相位模糊,提出了利用双频信号相位差进行声速测量的方法。论文的主要工作包括以下四个方面:
(1)归纳了海水声速的分布规律及特点,分析并对比了目前国内外进行海水声速测量的方法及特点。在此基础上,本文提出了利用信号相位差进行海水声速测量方法。
(2)提出了利用单频信号相位差进行声速测量的方法。根据时差法进行声速测量的原理,通过将时间的测量转换为相位的估计,在距离测量精度足够高的条件下,信号频率越高,要求的相位差估计精度就越低,则声速测量精度就越高。在信号频率确定的条件下,相位差估计的精度是声速测量精度的关键。因此,本文着重研究了各种相位估计方法,包括过零比较法、数字相关法及FFT谱分析法。通过分析及对比,提出了利用FFT谱分析进行信号相位差估计的方法。此外,为了分析换能器及水声信道特性对信号相位差估计的影响,本文建立了声速测量系统的数学模型,并利用此模型进行了基于单频信号相位差的声速测量仿真分析。
(3)提出了利用双频信号相位差进行声速测量的方法。为了消除采用单频信号存在的相位模糊,进一步提高声速测量精度,本文提出采用频差很小的双频信号进行声速测量的方法。分析了测量原理及利用FFT谱分析时频谱泄漏对信号相位差估计的影响,利用声速测量系统模型进行了基于双频信号相位差的声速测量仿真分析。
(4)设计了声速测量实验系统,包括信号发射及采集的硬件电路,搭建了声速测量的实验平台,分析了实验平台的反射回波及各种环境因素对相位差估计结果的影响,距离测量精度对声速测量精度的影响。利用搭建的实验平台进行了基于信号相位差的声速测量实验,对采集的数据进行了分析和处理,验证了利用信号相位差进行声速测量的结论。
The speed of sound in seawater is one of the important parameters during the measurement of the underwater ultrasonic ranging and positioning, testing and monitoring the marine environment and so on. The propagation speed with the water temperature, pressure and salinity varies. Accurately measure the speed of sound in seawater is important, can be effective for the depth sounder, sonar and other acoustic equipment to provide accurate speed of sound data measurement to correct measurement error.
This paper mainly studies the speed of sound measurement in seawater based on phase difference. Critical study of the use of single-frequency signal phase difference estimation method for speed of sound measurement. For phase ambiguity problem of the single-frequency signal, proposed the use of dual-frequency signal phase difference estimation for speed of sound measurement method. The main paper work includes the following aspects:
(1) This paper summarizes the distribution of speed of sound in seawater and characteristics, analysis and comparison the current international approach to speed of sound measurement of seawater and characteristics, on the basis of these, using the phase difference estimation for speed of sound measurement method in seawater is proposed in this paper.
(2)Proposed a seawater velocity measurement method based on single-frequency signal phase difference estimation. Based on the principle of speed of sound measurement of time difference method, if the time measurement transformed to the phase difference estimate, in the conditions the distance measurement accuracy is high enough, the higher the frequency, the phase difference estimation accuracy requirements lower, the greater the speed of sound measurement accuracy high. In the conditions the signal frequency to determine, the key factor of the speed of sound measurement accuracy is the phase difference estimation accuracy. Therefore, the paper focuses on a variety of phase estimation methods, including zero comparison, digital correlation method and the FFT spectrum analysis. Through analysis and comparison, proposed the use of FFT spectrum analysis as the phase difference estimation method. Established a simplified model of speed of sound measurement system and using the model to analyze their impact on the estimated phase difference. We carried out simulation analysis of speed of sound measurements using single-frequency signal phase difference estimation.
(3) Proposed a seawater speed of sound measurement method based on dual-frequency signal phase difference estimation. To solve the phase ambiguity problem for single-frequency signal, getting the higher speed of sound measurement accuracy, this paper proposes the speed of sound measurement methods using a small dual-frequency difference signal, analysis of the measuring principle and the impact of spectral leakage of FFT spectral analysis to the dual-frequency signal phase difference estimation. We carried out simulation analysis of speed of sound measurements using dual-frequency signals phase difference estimation.
(4)Building a sound speed of sound measurement experimental system based on the estimated phase difference estimation, the design of signal transmission and signals acquisition hardware circuits, analysis of the impact the experimental platform for distance measurement accuracy to speed of sound measurement accuracy, echo and a variety of environmental factors on the phase difference estimation results. Using the experimental platform to carry out the speed of sound measurement experiment based on the single-frequency signal and the dual-frequency signal phase difference estimation. The experiment data were analyzed and processed to verify the speed of sound measured conclusions for use of signal phase difference estimation.
引文
[1]汪德昭,尚尔昌.水声学[M].北京:科学出版社,1981.
[2] JI.M.布列霍夫斯基.海洋声学[M].科学出版社,1983:1-6页.
[3]R.J.乌立克.工程水声原理[M],北京:国防工业出版社,1972:108-112.
[4]刘伯胜,雷加煜.水声学原理[M],哈尔滨:哈尔滨工程大学出版社,2010:67-68.
[5]顾今海,叶学千.水声学基础[M],国防工业出版社,1981.
[6]Brian D. Dushaw, Peter F. Worcester, Bruce D.Cornuelle.On equations for the Speed of sound in seawater[J].The Journal of the Acoustical Society of America, 1993, 93(1):255-275.
[7]王琦.脉冲多次回波法声速、衰减测量的研究及应用[D].上海:同济大学研究生院,2007.
[8]Chen-Tung Chen, Frank J. Millero.Speed of sound in seawater at high pressures [J].The Journal of the Acoustical Society of America, 1977, 65(5), 1129-1135.
[9]V. A. Del Grosso. New equation for the speed of sound in natural waters (with comparisons to other equations)[J]. The Journal of the Acoustical Society of America, 1974, 56(4),1084-1091.
[10]Wilson. Speed of Sound in Sea Water as a Function of Temperature, Pressure, and Salonity[J]. The Journal of the Acoustical Society of America, 1960, 32(6),641-644.
[11]陈红霞,吕连港,华锋等.三种常用声速算法的比较.2005, 23(3):359-362.
[12]SBE.91l plus CTD System Operating and Repair Manual[M].Bellevue,USA:Sea- Bird ElectronicsInc,2002.
[13]于连生等.声光悬浮沙粒径谱测量仪[J].海洋技术,2000,20(1):1041.
[14]杨雪.基于共振声谱法的海水声速测量技术研究[D].长沙:国防科技大学研究生院,2008:2-3.
[15]于连生.毫米级高精度海水声速测量技术研究[J].海洋技术,2003, 22(3):63-64.
[16]赵卫东.相位法测声速[J].物理通报,2001 (4):35-36.
[17]关致和,赵先龙,王莉娜等.声速仪标定系统.第十四届海洋测绘综合性学术研讨会论文集.天津,2002:336-340.
[18]周丰年,赵建虎,周才扬.多波束测深系统最优声速公式的确定[J].台湾海峡,2001, 20(4):411-419.
[19]刘贞文,杨燕明,许德伟等.海水声速直接测量和间接测量结果分析[J].海洋技术,2007, 26(4):44-46.
[20]Alfred Weissler V. A. Del Grosso. The Velocity of Sound in Sea Water[J]. The Journal of the Acoustical Society of America, 1951, 23(2),219-223.
[21]V. A. Del Grosso C.W.Mader. Speed of Sound in Sea-water Samples[J]. The Journal of the Acoustical Society of America, 1972, 52(3),961-974.
[22]V. A. Del Grosso. Tables of the Speed of Sound in open ocean water(with Mediterranean Sea and Red Sea applicability) [J]. The Journal of the Acoustical Society of America, 1973, 53(5),1384-1401.
[23]管铮.在我国使用声速改正公式的精度分析[J].海洋测绘,1990(3):32-37.
[24]朱昌平,韩庆邦,李建等.水声通信基本原理与应用[M],北京:电子工业出版社出版社,2009.
[25]童建平,隋成华,魏高尧.时差法声速测量仪的研制[J].传感器技术,2004,23 (1):28-29.
[26]E. P. Papadakis. Ultrasonic Properities of Glasses at low Temperatures[J]. Physical Acoustics, 1976, 10(2):277-282.
[27]吴贵玉,陆玲珍,钟德元等.PEO型精密超声声速仪[J].应用声学,1982:45-47.
[28]H.J.Mcskimin. Pulse Superposition Method for Measuring Ultrasonic Wave Velocities in solids[J]. The Journal of the Acoustical Society of America, 1961, 33(1):12-16.
[29]关致和,赵先龙,于政等.HY1200声速剖面仪计算测深声速改正数方法[J].海洋测绘,2006,26(1):66-68.
[30]查济漩.在PEO法声速测量中确定反射相移时延修正值与判别正确重合的方法[J].声学学报,1986, 11(5):267-275.
[31]万锟.新型精密声速仪的研制[D].合肥:中国科学技术大学研究生院,2003.
[32]赵先龙.声速仪的设计[J].海洋测绘,2002, 22(1):54-56.
[33]梁济仁,黄开连.驻波法测量声速[J].广西民族大学学报(自然科学版),2009,15(3):68-72.
[34]冯晓娟,林鸿,刘强等.圆柱定程干涉法声速测量原理与实验系统研制[J].工程热物理学报,2011,32(5):726-728.
[35]沈绍宾.测量声时的均匀延迟平均法[D].上海:同济大学声学研究所,2003.
[36]于连生.利用超声共振法测量声速和声衰减系数[J].海洋技术,1999,18(3):381.
[37]马水龙,余钦范.共振声谱法测量液体声速实验[J].石油仪器,2004.
[38]曹建庆,江兴方.相位比较法在声速测量中的应用[J].江苏石油化工学院学报,2001,13(4):62-64.
[39]邹红玉,江影.采用相位法与极大值法测量超声波声速的准确度的研究[J].大学物理,2007,26(5):32-34.
[40]潘雯,马青玉.流体声速高精度相位法测量研究[J].南京师范大学学报(工程技术版),2009,9(3):79-82.
[41] Chen Jian, Zhao Shen, Qiao Chunjie.Acoustic Velocity Measurement in Seawater Based on Phase Difference of Signal.Proceedings of 10th International conference on Electronic Measurement & Instruments[C], Beijing, China: IEEE Press,2011,3: 181-184.
[42]葛宪生.用于相位测量的多通道信号采集和处理系统的设计[D].哈尔滨:哈尔滨工程大学研究生院,2009.
[43]张志刚,秦树人,邱建伟.基于虚拟仪器技术的数字相位计设计[J].中国测试技术.2006(1):38-41.
[44]王兆华,黄翔东.基于全相位谱分析的相位测量原理及其应用[J].数据采集与处理.2009,24(6):777-782.
[45]杨新华,陈玉松,金兴文.基于FFT谱分析算法的高精度相位差测量方法[J].自动化与仪器仪表.2006(6):75-77.
[46]朱士明等.提高测量声时精度的“过零检测数字平均法”[J].声学技术, 1993,12(3): 21-26.
[47]邓祖朴.同频信号相位差的高精度检测[J].计算机应用与研究.2009,26(7): 2661-2663.
[48]翁丽靖,张熙昀.基于DSP和信号相关分析的相位差求取方法[J].信息化研究. 2010,36(6): 22-25.
[49]陆招兰,施文康.相位差检测分析与仿真计算[J].武汉工业学院学报.2009,28(1): 45-48.
[50]雷雨,陶永红.数字化相位差测量算法的研究[J].四川工业学院学报.2004(23):110 -112.
[51]刘艳平.数字实时脉冲回波谱分析法薄材料声速测量系统的研制与应用[D].上海:同济大学声学研究所,2009.
[52]林俊武,林金阳. FFT分析中一种减少频谱泄漏的方法[J].三明学院学报.2007,24(2):166 -169.
[53]路艳洁,席志红,王姜铂. FFT法与数字相关法在相位测量上的比较[J].信息技术.2007(12):105 -108.
[54]江亚群,何怡刚.基于加窗DFT的相位差高精度测量算法[J].电路与系统学报.2005,10(2):112-116.
[55]张海涛,涂亚庆.基于FFT的一种计及负频率影响的相位差测量新方法[J].计量学报.2008,29(2):168-171.
[56]费业泰.误差理论与数据处理[M],北京:机械工业出版社,2000.
[57]冯士筰,李凤岐,李少箐.海洋科学导论[M],北京:高等教育出版社,1998.
[58]W.S.Burdic. Underwater Acoustic System Analysis[M].2nd edition. EnglewoodCliffs,NJ: Prentice-Hall.1991.
[59]Michael.J.Buckingham, Michael D Richardson.On Tone-Burst Measurements of Sound Speed and Attenuation in Sandy Marine Sediments[J]. IEEE journal of oceanic engineering, 2002,27(2):429-439.
[60]吴京.信号与系统分析[M].长沙:国防科技大学出版社,2002.
[61]于达仁,鲍文,徐敏强.基于FFT的一种计及负频率影响的相位差测量新方法[J].哈尔滨工业大学学报.1995,27(3):84-87.
[62]杜振辉,蒋诚志,桂垣等.激光干涉仪测量长度[J].河北建筑工程学院学报.2003,21(2):35-37.
[2] JI.M.布列霍夫斯基.海洋声学[M].科学出版社,1983:1-6页.
[3]R.J.乌立克.工程水声原理[M],北京:国防工业出版社,1972:108-112.
[4]刘伯胜,雷加煜.水声学原理[M],哈尔滨:哈尔滨工程大学出版社,2010:67-68.
[5]顾今海,叶学千.水声学基础[M],国防工业出版社,1981.
[6]Brian D. Dushaw, Peter F. Worcester, Bruce D.Cornuelle.On equations for the Speed of sound in seawater[J].The Journal of the Acoustical Society of America, 1993, 93(1):255-275.
[7]王琦.脉冲多次回波法声速、衰减测量的研究及应用[D].上海:同济大学研究生院,2007.
[8]Chen-Tung Chen, Frank J. Millero.Speed of sound in seawater at high pressures [J].The Journal of the Acoustical Society of America, 1977, 65(5), 1129-1135.
[9]V. A. Del Grosso. New equation for the speed of sound in natural waters (with comparisons to other equations)[J]. The Journal of the Acoustical Society of America, 1974, 56(4),1084-1091.
[10]Wilson. Speed of Sound in Sea Water as a Function of Temperature, Pressure, and Salonity[J]. The Journal of the Acoustical Society of America, 1960, 32(6),641-644.
[11]陈红霞,吕连港,华锋等.三种常用声速算法的比较.2005, 23(3):359-362.
[12]SBE.91l plus CTD System Operating and Repair Manual[M].Bellevue,USA:Sea- Bird ElectronicsInc,2002.
[13]于连生等.声光悬浮沙粒径谱测量仪[J].海洋技术,2000,20(1):1041.
[14]杨雪.基于共振声谱法的海水声速测量技术研究[D].长沙:国防科技大学研究生院,2008:2-3.
[15]于连生.毫米级高精度海水声速测量技术研究[J].海洋技术,2003, 22(3):63-64.
[16]赵卫东.相位法测声速[J].物理通报,2001 (4):35-36.
[17]关致和,赵先龙,王莉娜等.声速仪标定系统.第十四届海洋测绘综合性学术研讨会论文集.天津,2002:336-340.
[18]周丰年,赵建虎,周才扬.多波束测深系统最优声速公式的确定[J].台湾海峡,2001, 20(4):411-419.
[19]刘贞文,杨燕明,许德伟等.海水声速直接测量和间接测量结果分析[J].海洋技术,2007, 26(4):44-46.
[20]Alfred Weissler V. A. Del Grosso. The Velocity of Sound in Sea Water[J]. The Journal of the Acoustical Society of America, 1951, 23(2),219-223.
[21]V. A. Del Grosso C.W.Mader. Speed of Sound in Sea-water Samples[J]. The Journal of the Acoustical Society of America, 1972, 52(3),961-974.
[22]V. A. Del Grosso. Tables of the Speed of Sound in open ocean water(with Mediterranean Sea and Red Sea applicability) [J]. The Journal of the Acoustical Society of America, 1973, 53(5),1384-1401.
[23]管铮.在我国使用声速改正公式的精度分析[J].海洋测绘,1990(3):32-37.
[24]朱昌平,韩庆邦,李建等.水声通信基本原理与应用[M],北京:电子工业出版社出版社,2009.
[25]童建平,隋成华,魏高尧.时差法声速测量仪的研制[J].传感器技术,2004,23 (1):28-29.
[26]E. P. Papadakis. Ultrasonic Properities of Glasses at low Temperatures[J]. Physical Acoustics, 1976, 10(2):277-282.
[27]吴贵玉,陆玲珍,钟德元等.PEO型精密超声声速仪[J].应用声学,1982:45-47.
[28]H.J.Mcskimin. Pulse Superposition Method for Measuring Ultrasonic Wave Velocities in solids[J]. The Journal of the Acoustical Society of America, 1961, 33(1):12-16.
[29]关致和,赵先龙,于政等.HY1200声速剖面仪计算测深声速改正数方法[J].海洋测绘,2006,26(1):66-68.
[30]查济漩.在PEO法声速测量中确定反射相移时延修正值与判别正确重合的方法[J].声学学报,1986, 11(5):267-275.
[31]万锟.新型精密声速仪的研制[D].合肥:中国科学技术大学研究生院,2003.
[32]赵先龙.声速仪的设计[J].海洋测绘,2002, 22(1):54-56.
[33]梁济仁,黄开连.驻波法测量声速[J].广西民族大学学报(自然科学版),2009,15(3):68-72.
[34]冯晓娟,林鸿,刘强等.圆柱定程干涉法声速测量原理与实验系统研制[J].工程热物理学报,2011,32(5):726-728.
[35]沈绍宾.测量声时的均匀延迟平均法[D].上海:同济大学声学研究所,2003.
[36]于连生.利用超声共振法测量声速和声衰减系数[J].海洋技术,1999,18(3):381.
[37]马水龙,余钦范.共振声谱法测量液体声速实验[J].石油仪器,2004.
[38]曹建庆,江兴方.相位比较法在声速测量中的应用[J].江苏石油化工学院学报,2001,13(4):62-64.
[39]邹红玉,江影.采用相位法与极大值法测量超声波声速的准确度的研究[J].大学物理,2007,26(5):32-34.
[40]潘雯,马青玉.流体声速高精度相位法测量研究[J].南京师范大学学报(工程技术版),2009,9(3):79-82.
[41] Chen Jian, Zhao Shen, Qiao Chunjie.Acoustic Velocity Measurement in Seawater Based on Phase Difference of Signal.Proceedings of 10th International conference on Electronic Measurement & Instruments[C], Beijing, China: IEEE Press,2011,3: 181-184.
[42]葛宪生.用于相位测量的多通道信号采集和处理系统的设计[D].哈尔滨:哈尔滨工程大学研究生院,2009.
[43]张志刚,秦树人,邱建伟.基于虚拟仪器技术的数字相位计设计[J].中国测试技术.2006(1):38-41.
[44]王兆华,黄翔东.基于全相位谱分析的相位测量原理及其应用[J].数据采集与处理.2009,24(6):777-782.
[45]杨新华,陈玉松,金兴文.基于FFT谱分析算法的高精度相位差测量方法[J].自动化与仪器仪表.2006(6):75-77.
[46]朱士明等.提高测量声时精度的“过零检测数字平均法”[J].声学技术, 1993,12(3): 21-26.
[47]邓祖朴.同频信号相位差的高精度检测[J].计算机应用与研究.2009,26(7): 2661-2663.
[48]翁丽靖,张熙昀.基于DSP和信号相关分析的相位差求取方法[J].信息化研究. 2010,36(6): 22-25.
[49]陆招兰,施文康.相位差检测分析与仿真计算[J].武汉工业学院学报.2009,28(1): 45-48.
[50]雷雨,陶永红.数字化相位差测量算法的研究[J].四川工业学院学报.2004(23):110 -112.
[51]刘艳平.数字实时脉冲回波谱分析法薄材料声速测量系统的研制与应用[D].上海:同济大学声学研究所,2009.
[52]林俊武,林金阳. FFT分析中一种减少频谱泄漏的方法[J].三明学院学报.2007,24(2):166 -169.
[53]路艳洁,席志红,王姜铂. FFT法与数字相关法在相位测量上的比较[J].信息技术.2007(12):105 -108.
[54]江亚群,何怡刚.基于加窗DFT的相位差高精度测量算法[J].电路与系统学报.2005,10(2):112-116.
[55]张海涛,涂亚庆.基于FFT的一种计及负频率影响的相位差测量新方法[J].计量学报.2008,29(2):168-171.
[56]费业泰.误差理论与数据处理[M],北京:机械工业出版社,2000.
[57]冯士筰,李凤岐,李少箐.海洋科学导论[M],北京:高等教育出版社,1998.
[58]W.S.Burdic. Underwater Acoustic System Analysis[M].2nd edition. EnglewoodCliffs,NJ: Prentice-Hall.1991.
[59]Michael.J.Buckingham, Michael D Richardson.On Tone-Burst Measurements of Sound Speed and Attenuation in Sandy Marine Sediments[J]. IEEE journal of oceanic engineering, 2002,27(2):429-439.
[60]吴京.信号与系统分析[M].长沙:国防科技大学出版社,2002.
[61]于达仁,鲍文,徐敏强.基于FFT的一种计及负频率影响的相位差测量新方法[J].哈尔滨工业大学学报.1995,27(3):84-87.
[62]杜振辉,蒋诚志,桂垣等.激光干涉仪测量长度[J].河北建筑工程学院学报.2003,21(2):35-37.