数模混合集成电路实现一维小波变换
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摘要
小波变换不仅在电力系统行波保护中得到应用，而且目前在语音、图像、通信等很多方面得到应用，是多学科关注的热点，是信号处理的前言课题。遗憾的是绝大多数的小波变换是单纯基于离散时间系统的变换。离散时间系统有采用的方式灵活等特点，但由于离散时间系统需要A／D、D／A转换，处理信号的速度慢等缺点。因此综合离散时间域和连续时间域的优缺点，本文提出了一种用数模混合集成电路实现连续小波变换的设计。
首先，本文讨论了傅立叶变换、Gabor(加窗傅立叶变换)和小波变换在时间和频率域的分辨率问题上的优缺点，得出了选择小波变换的原因。
第二，本文从数学和多抽样率信号的角度上对小波变换进行了较深入的讨论，得到两者之间的联系和怎样对满足要求的小波母函数的选择。由于小波变换涉及到带通滤波器的设计，为了简化滤波器的设计本文采用频谱搬移技术，把带通滤波器转化为低通滤波器的设计；多种中心频率的产生我们采用了直接数字频率综合(DDS)的方式；与传统的用模拟电路采用压控振荡器(VCO)和锁相环(PLL)的方式简化了电路的设计，加速了系统的完成。
第三，在以往的小波变换中所采取的滤波器都是数字滤波器。数字滤波器的缺点在于要进行两次模数转换，处理信号的速度慢。模拟电路不需要模数转换，而且可以达到高频领域，因此用模拟小波有无可比拟的优势。因此本文提出了用模拟集成电路来实现一组所需要的模拟小波低通滤波器。在模拟集成电路中，电感的实现是很困难的，因此模拟滤波器的实现采用有源滤波器。在有源滤波器的设计中运算放大器的设计是很关键的一个部分就是运算放大器的设计，在本文中比较详细的讨论它的设计。对改进电路做了仿真。高斯滤波器有着良好的时频特性，因此我们选择的小波函数是高斯滤波函数，在此基础上设计了一组高斯滤波器，并进行了仿真。
第四，综合以上设计我们得到了一个完整的数模混合集成电路实现一维模拟小波变换设计。该电路包括了用DDS产生的中心频率发生器、5对低通滤波器、20个乘法器和一个加法器。这样我们就完成了信号从分解到重构的过程。实现了本文预期的目标。
The wavelet transform is no only used in the protection of traveling wave in the power system, but also having many applications in the acoustics . graph and communication. It is also the focus of many subject. It is regretted that most of wavelet transform is based on discrete-time system. The working pattern of discrete-time system is flexible, but it need A/D and D/A, which make that system work slowly. Analysis the virtue and shortcoming of these two system, this paper put forward a way to achieve wavelet transform through hybrid of analog and digital circuit.
First ,this paper discuss the virtue and shortcoming of the Fourie transform Gabor transform and wavelet transform .Get out the result why we choose the wavelet transform.
Second, we discuss the wavelet transform deeply from math and multi-rate sampling, getting the relations of them and how to get mother wavelet correctly. In order to simplify the designation of circuit, we use complex demodulation technique, it can let us design low pass filter instead of bandpass filter. We make use of DDS to get different central frequency, comparing to use VCO and PLL through analog IC, it simplified the designation of circuits, improved the speed of design.
Third, the digital filter is commonly used in the wavelet transform in the past. Its shortcoming is that the speed of signal process is slow because of A/D. Analog circuit don't need A/D, so its speed can get very high., having great advantage. The paper bring out a way using analog filter to achieve a group of low pass filter which are needed by the wavelet transform. In the analog IC the achievement is difficult, though we use active filter to achieve the goal. In the designation of active filter, the operational amplifier is very important; we will particularly discuss the designation of the op amp. At last we get the circuit, and simulating the circuit. The Gaussian filter has a good time-frequency rate, we choose Gaussian filter as mother wavelet. We design the circuit and get the simulation result.
At last, we get a completely designation of the implementation of an analog
wavelet transform through hybrid of analog and digital circuit. This circuit include DDS which generate central frequency, five pair of low pass filter, 20 multipliers, and an adder. We finish the process from decompose to reconstruct, achieving the goal that we want.
首先，本文讨论了傅立叶变换、Gabor(加窗傅立叶变换)和小波变换在时间和频率域的分辨率问题上的优缺点，得出了选择小波变换的原因。
第二，本文从数学和多抽样率信号的角度上对小波变换进行了较深入的讨论，得到两者之间的联系和怎样对满足要求的小波母函数的选择。由于小波变换涉及到带通滤波器的设计，为了简化滤波器的设计本文采用频谱搬移技术，把带通滤波器转化为低通滤波器的设计；多种中心频率的产生我们采用了直接数字频率综合(DDS)的方式；与传统的用模拟电路采用压控振荡器(VCO)和锁相环(PLL)的方式简化了电路的设计，加速了系统的完成。
第三，在以往的小波变换中所采取的滤波器都是数字滤波器。数字滤波器的缺点在于要进行两次模数转换，处理信号的速度慢。模拟电路不需要模数转换，而且可以达到高频领域，因此用模拟小波有无可比拟的优势。因此本文提出了用模拟集成电路来实现一组所需要的模拟小波低通滤波器。在模拟集成电路中，电感的实现是很困难的，因此模拟滤波器的实现采用有源滤波器。在有源滤波器的设计中运算放大器的设计是很关键的一个部分就是运算放大器的设计，在本文中比较详细的讨论它的设计。对改进电路做了仿真。高斯滤波器有着良好的时频特性，因此我们选择的小波函数是高斯滤波函数，在此基础上设计了一组高斯滤波器，并进行了仿真。
第四，综合以上设计我们得到了一个完整的数模混合集成电路实现一维模拟小波变换设计。该电路包括了用DDS产生的中心频率发生器、5对低通滤波器、20个乘法器和一个加法器。这样我们就完成了信号从分解到重构的过程。实现了本文预期的目标。
The wavelet transform is no only used in the protection of traveling wave in the power system, but also having many applications in the acoustics . graph and communication. It is also the focus of many subject. It is regretted that most of wavelet transform is based on discrete-time system. The working pattern of discrete-time system is flexible, but it need A/D and D/A, which make that system work slowly. Analysis the virtue and shortcoming of these two system, this paper put forward a way to achieve wavelet transform through hybrid of analog and digital circuit.
First ,this paper discuss the virtue and shortcoming of the Fourie transform Gabor transform and wavelet transform .Get out the result why we choose the wavelet transform.
Second, we discuss the wavelet transform deeply from math and multi-rate sampling, getting the relations of them and how to get mother wavelet correctly. In order to simplify the designation of circuit, we use complex demodulation technique, it can let us design low pass filter instead of bandpass filter. We make use of DDS to get different central frequency, comparing to use VCO and PLL through analog IC, it simplified the designation of circuits, improved the speed of design.
Third, the digital filter is commonly used in the wavelet transform in the past. Its shortcoming is that the speed of signal process is slow because of A/D. Analog circuit don't need A/D, so its speed can get very high., having great advantage. The paper bring out a way using analog filter to achieve a group of low pass filter which are needed by the wavelet transform. In the analog IC the achievement is difficult, though we use active filter to achieve the goal. In the designation of active filter, the operational amplifier is very important; we will particularly discuss the designation of the op amp. At last we get the circuit, and simulating the circuit. The Gaussian filter has a good time-frequency rate, we choose Gaussian filter as mother wavelet. We design the circuit and get the simulation result.
At last, we get a completely designation of the implementation of an analog
wavelet transform through hybrid of analog and digital circuit. This circuit include DDS which generate central frequency, five pair of low pass filter, 20 multipliers, and an adder. We finish the process from decompose to reconstruct, achieving the goal that we want.
引文
[1] I.Daubechies, Where do wavelets come from? — A personal point of view, Proc.IEEE84(5),510——513, 1996。
[2] 董新洲，耿中行等，小波变换应用于电力系统故障信号分析初探，中国电机工程学报，1999年06期。
[3] 董新洲，葛耀中等输电线路行波保护的现状与展望，电力系统自动化，2000年10期。
[4] 崔锦泰著，程正兴译，小波分析导论，西安交通大学出版社，1995年。
[5] Mallat著，杨力华等译，信号处理的小波导引，机械工业出版社，2002年。
[6] Stephane G.Mallat, Multifrequency Channel Decomposition of Images and Wavelet Models,IEEE Transactions on acoustics, speech, and signal processing VOL.37, NO. 12.December 1989:2091-2110.
[7] 王世一著，数字信号处理，北京理工大学出版社，1997。
[8] 郑君里著，信号与系统，高等教育出版社，2001。
[9] 宗孔德，多抽样率信号处理，清华大学出版社，1995
[10] H. Weyl. The Theory of Groups and Quantum Mechanics, Dutton, New York,1931
[11] Moreira-Yamayo O, Pineda De Gyvez J. Time-domain analog wavelet transform in real time [A] . Proc Of IEEE Int Symp Cir & Sys[C] , 1995,3: 1640-1643.
[12] Lin J, Kim-H, Edwards T, et al.Analog VLSI implementations of auditory wavelet transform using switched-capacitor circuits[J] .IEEE Trans Cir & Sys, 1994-Ⅰ, 41(9): 572-583.
[13] Goodman D J, Carey M J. Nine digital filters for decimation and interpolation. IEEE Trans Acoustics, speech and signal proc,1977,ASSP-25(NO.2):121-126.
[14] Eugene B. Hogenauer, An economical clss of digital filters for decimation
and interpolation,IEEE Trans on acoustic,speech, and signal proc, vol.ASSP-29,NO.2,Aprol 1981:155-162.
[15] 杨福生，小波变换的工程分析与应用，科学出版社，1999年
[16] Smith M J T, Bamwell Ⅲ T P. A procedure for designing Extract construction filter banks for tree structured subband coders. Proc IEEE Int Conf Acoustics, speech and signal processing (San Diego), 1984, Mar:27·1· 1-27·1·4
[17] Edwards R T, Godfrey M D. An analog wavelet transform chip [A] . Proc of IEEE Int Conf Neural Networks [c] . 1993, 3:1247-1251.
[18] Edwards R T, Cauwenberghs G. A VLSI implementation of the continuous wavelet transform[a] . Proc of IEEE Int Symp Cir & Sys [c] .1996,4:368-371.
[19] C.Mead, Analog VLSI and Neural Systems. Readings, MA: Addison-Wesley, 1989.
[20] 陈立新，Shannon定理在数字锁相环中的应用。微电子技术，2000年2期：pp23-27；
[21] 毕查德·拉扎维著，陈贵灿等译，模拟CMOS集成电路设计 西安交通大学出版社，2002年
[22] N. M. Nguyen and R. G. Meyer. Start-up and Frequency stability in high-frequency oscillators. IEEE Journal of Solid-state Circuit, vol. 27, pp. 810-820, May 1992.
[23] R. E. Best. Phase-locked Loops. Second Ed., New York: McGraw-Hill, 1993.
[24] R.S. Muller and T.I. Kamins, Device Electronics for integrated Circuits. Second Ed., New York: Wiley, 1986.
[25] Y. Taur and T.H. Ning.fundamentals of Moderu VLSI Devices, New York: Cambridge University Press, 1998..
[26] Y. Tsividis. Operatiom and Modeling of the MOS Transistor. Second Ed., Boston:McGraw—Hill.
[27] 陈贵灿，邵志标等，CMOS集成电路设计，西安交通大学出版社，2000
年第二版．
[28] P. Larsson. Parasitic Resistance in an MOS Transistor Used as On-Chip Decoupling Capacitor. IEEE J. Solid-State Circuits, vol.32, pp. 574-576, April. 1997.
[29] P.R.Gray and R.G. Meyer. Analysis and Design of Analog Integrated Circuits. Third Ed., New York: Wiley, 1993.
[30] A．巴尔纳著，朱维麟译，运算放大器，国防工业出版社，1979年
[31] 康华光，电子技术基础—模拟部分(第四版)，高等教育出版社，1998年
[32] B.K Ahuja. An improved frequency compensation technique for CMOS operational amplifiers. IEEE J. of solid—state circuits, vol.18,pp 629-633, Dec. 1983.
[33] P.R. Gray and R. G. Meyer. MOS operational Amplifier Design-A tutorial Overview. IEEE J. of solid—state circuits, vol. 17,pp 969-982, Dec. 1983.
[34] 贾新山，武岳山著，Or CAD／Capture CIS 9使用教程，西安电子科技大学出版社，2000年
[35] 贾新山，Or CAD／Pspice 9使用教程，西安电子科技大学出版社，1999年．
[36] 高文焕等著，模拟电路的计算机分析与设计—Pspice程序应用，清华大学出版社，1999年。
[37] M，S高西，K．R莱克著，刘根全等译，现代滤波器设计—有源RC和开关电容，科学出版社，1989年
[38] 哈里．Y-F拉姆著，冯儒云、应启珩等译，模拟和数字滤波器的设计和实现，人民邮电出版社，1985年
[39] 黄席椿、高顺泉著，滤波器综合法设计原理，人民邮电出版社，1978年
[40] D．E．约翰逊、J．R．约翰逊、H．P．穆尔著，李国荣译，有源滤波器精确设计手册，电子工业出版社，1984年
[41] J．L 希尔本、D．E．约翰逊，有源滤波器设计手册，地质出版社，1980年
[42] W. McC. Siebert, Circuits signals and systems. Cambridge,MA: The MIT Press,1986, pp.496-497.
[43] 程佩青著，数字信号处理，清华大学出版社，1995年
[44] C．Toumazon等编，姚玉洁译，模拟集成电路设计：电流模法，高等教育出版社，1996年
[45] 周汀等，离散小波的VLSI设计，半导体学报，1997年3期，pp：180-183．
[46] 乔世杰等，离散小波变换VLSI实现，微电子学，2001年02期，Pp：143-145．
[2] 董新洲，耿中行等，小波变换应用于电力系统故障信号分析初探，中国电机工程学报，1999年06期。
[3] 董新洲，葛耀中等输电线路行波保护的现状与展望，电力系统自动化，2000年10期。
[4] 崔锦泰著，程正兴译，小波分析导论，西安交通大学出版社，1995年。
[5] Mallat著，杨力华等译，信号处理的小波导引，机械工业出版社，2002年。
[6] Stephane G.Mallat, Multifrequency Channel Decomposition of Images and Wavelet Models,IEEE Transactions on acoustics, speech, and signal processing VOL.37, NO. 12.December 1989:2091-2110.
[7] 王世一著，数字信号处理，北京理工大学出版社，1997。
[8] 郑君里著，信号与系统，高等教育出版社，2001。
[9] 宗孔德，多抽样率信号处理，清华大学出版社，1995
[10] H. Weyl. The Theory of Groups and Quantum Mechanics, Dutton, New York,1931
[11] Moreira-Yamayo O, Pineda De Gyvez J. Time-domain analog wavelet transform in real time [A] . Proc Of IEEE Int Symp Cir & Sys[C] , 1995,3: 1640-1643.
[12] Lin J, Kim-H, Edwards T, et al.Analog VLSI implementations of auditory wavelet transform using switched-capacitor circuits[J] .IEEE Trans Cir & Sys, 1994-Ⅰ, 41(9): 572-583.
[13] Goodman D J, Carey M J. Nine digital filters for decimation and interpolation. IEEE Trans Acoustics, speech and signal proc,1977,ASSP-25(NO.2):121-126.
[14] Eugene B. Hogenauer, An economical clss of digital filters for decimation
and interpolation,IEEE Trans on acoustic,speech, and signal proc, vol.ASSP-29,NO.2,Aprol 1981:155-162.
[15] 杨福生，小波变换的工程分析与应用，科学出版社，1999年
[16] Smith M J T, Bamwell Ⅲ T P. A procedure for designing Extract construction filter banks for tree structured subband coders. Proc IEEE Int Conf Acoustics, speech and signal processing (San Diego), 1984, Mar:27·1· 1-27·1·4
[17] Edwards R T, Godfrey M D. An analog wavelet transform chip [A] . Proc of IEEE Int Conf Neural Networks [c] . 1993, 3:1247-1251.
[18] Edwards R T, Cauwenberghs G. A VLSI implementation of the continuous wavelet transform[a] . Proc of IEEE Int Symp Cir & Sys [c] .1996,4:368-371.
[19] C.Mead, Analog VLSI and Neural Systems. Readings, MA: Addison-Wesley, 1989.
[20] 陈立新，Shannon定理在数字锁相环中的应用。微电子技术，2000年2期：pp23-27；
[21] 毕查德·拉扎维著，陈贵灿等译，模拟CMOS集成电路设计 西安交通大学出版社，2002年
[22] N. M. Nguyen and R. G. Meyer. Start-up and Frequency stability in high-frequency oscillators. IEEE Journal of Solid-state Circuit, vol. 27, pp. 810-820, May 1992.
[23] R. E. Best. Phase-locked Loops. Second Ed., New York: McGraw-Hill, 1993.
[24] R.S. Muller and T.I. Kamins, Device Electronics for integrated Circuits. Second Ed., New York: Wiley, 1986.
[25] Y. Taur and T.H. Ning.fundamentals of Moderu VLSI Devices, New York: Cambridge University Press, 1998..
[26] Y. Tsividis. Operatiom and Modeling of the MOS Transistor. Second Ed., Boston:McGraw—Hill.
[27] 陈贵灿，邵志标等，CMOS集成电路设计，西安交通大学出版社，2000
年第二版．
[28] P. Larsson. Parasitic Resistance in an MOS Transistor Used as On-Chip Decoupling Capacitor. IEEE J. Solid-State Circuits, vol.32, pp. 574-576, April. 1997.
[29] P.R.Gray and R.G. Meyer. Analysis and Design of Analog Integrated Circuits. Third Ed., New York: Wiley, 1993.
[30] A．巴尔纳著，朱维麟译，运算放大器，国防工业出版社，1979年
[31] 康华光，电子技术基础—模拟部分(第四版)，高等教育出版社，1998年
[32] B.K Ahuja. An improved frequency compensation technique for CMOS operational amplifiers. IEEE J. of solid—state circuits, vol.18,pp 629-633, Dec. 1983.
[33] P.R. Gray and R. G. Meyer. MOS operational Amplifier Design-A tutorial Overview. IEEE J. of solid—state circuits, vol. 17,pp 969-982, Dec. 1983.
[34] 贾新山，武岳山著，Or CAD／Capture CIS 9使用教程，西安电子科技大学出版社，2000年
[35] 贾新山，Or CAD／Pspice 9使用教程，西安电子科技大学出版社，1999年．
[36] 高文焕等著，模拟电路的计算机分析与设计—Pspice程序应用，清华大学出版社，1999年。
[37] M，S高西，K．R莱克著，刘根全等译，现代滤波器设计—有源RC和开关电容，科学出版社，1989年
[38] 哈里．Y-F拉姆著，冯儒云、应启珩等译，模拟和数字滤波器的设计和实现，人民邮电出版社，1985年
[39] 黄席椿、高顺泉著，滤波器综合法设计原理，人民邮电出版社，1978年
[40] D．E．约翰逊、J．R．约翰逊、H．P．穆尔著，李国荣译，有源滤波器精确设计手册，电子工业出版社，1984年
[41] J．L 希尔本、D．E．约翰逊，有源滤波器设计手册，地质出版社，1980年
[42] W. McC. Siebert, Circuits signals and systems. Cambridge,MA: The MIT Press,1986, pp.496-497.
[43] 程佩青著，数字信号处理，清华大学出版社，1995年
[44] C．Toumazon等编，姚玉洁译，模拟集成电路设计：电流模法，高等教育出版社，1996年
[45] 周汀等，离散小波的VLSI设计，半导体学报，1997年3期，pp：180-183．
[46] 乔世杰等，离散小波变换VLSI实现，微电子学，2001年02期，Pp：143-145．
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