随机脉冲测量中数字滤波性能与采样参数关系的研究
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摘要
近年来,基于数字信号处理的辐射探测技术在高能物理、辐射成像等领域中应用的越来越广泛。相对于模拟电路,数字滤波电路具有灵活、稳定、自适应等优点,但其性能受到模数转换器采样参数的影响。对于辐射探测中随机脉冲测量,由于采样引起的误差分析,目前还没有系统的理论分析。因此,有必要研究ADC采样参数对随机脉冲测量中数字滤波性能的影响,为用于辐射探测的数字滤波器设计提供指导。比如,随着探测通道数目的增加,功耗成为信号处理电路的关键问题,需要定量研究数字滤波性能与采样参数的关系,尽可能降低ADC的功耗。
本文针对目前比较通用的辐射探测数字信号处理电路结构,分析了随机脉冲幅度测量的数字滤波性能与ADC采样频率的关系,主要包括以下几个内容:1)推导了采样后的信号频谱和噪声功率谱,在此基础上分析了数字滤波幅度测量性能与采样频率的定量关系,给出了在一定采样频率下数字滤波所能获得的最佳信噪比和几种常用的数字滤波器噪声指数。2)研究了随机到达时刻造成数字滤波测量误差与采样频率的关系,包括幅度均值偏移和涨落。这两种误差都会随着采样频率的增加迅速下降,而当采样周期降低到脉冲上升时间的1/3到1/5时,这种误差基本可以忽略。此外,还提出采用定时估计算法来校正幅度测量,并进行了初步的分析。
本文还通过数值仿真和基于数字示波器采样的幅度测量系统,对幅度测量误差与采样频率的关系进行了验证。实验测得的ORTEC 142AH电荷灵敏前放的噪声和CdTe探测器的241Am能谱分辨率,随采样频率的变化规律与理论分析基本一致,较好的验证了理论分析。
Recently, radiation detection based on the digital signal processing has been widely applied in the fields as high energy physics, radiation imaging and so on. Compared with analog circuits, the digital filters have the advantages as flexibility stability and adaptivity, although its performance is limited by the Analog-to-Digital Converter (ADC). In random pulse measurement of radiation detection, there has been no systemic study in theory on the ADC sampling induced error analysis. The study on effect of ADC parameters to digital filtering performance is necessary for digital filter design. For example the power consumption becomes critical issue for signal processing circuit when the number of readout channels increases significantly. In such case, the quantitative study of the dependence of the filter performance on ADC parameters is necessary for reducing ADC power consumption.
This thesis analyzes the dependence of digital filtering performance on ADC sampling frequency in random pulse measurement based on commonly applied digital signal processing circuit. The thesis includes the following parts. 1) Derive the signal spectrum and the noise power spectral density after sampling, analyze quantitatively the amplitude measurement performance on the sampling frequency, and then obtain the optimum signal-to-noise ratio under certain sampling frequency as well as noise index for several commonly applied digital filters. 2) Analyze the random arriving time induced measurement errors on sampling frequency, including the expected amplitude shift and fluctuation, which decrease significantly with increasing sampling frequency. When the sampling interval is less than 1/3 to 1/5 of the signal rising time, the measurement errors can be ignored. The timing estimation algorithm is proposed to amplitude measurement correction and analyzed preliminary.
The dependence of amplitude measurement fluctuation on the sampling frequency is demonstrated by the numerical simulation and measurements with digital oscilloscope sampling. The dependence of experimental results on the sampling frequency is consistent with the theoretical results, which include the noise of ORTEC 142AH charge sensitive preamplifier and the ~(241)Am energy spectrum of CdTe detector. The theoretical analysis is demonstrated.
本文针对目前比较通用的辐射探测数字信号处理电路结构,分析了随机脉冲幅度测量的数字滤波性能与ADC采样频率的关系,主要包括以下几个内容:1)推导了采样后的信号频谱和噪声功率谱,在此基础上分析了数字滤波幅度测量性能与采样频率的定量关系,给出了在一定采样频率下数字滤波所能获得的最佳信噪比和几种常用的数字滤波器噪声指数。2)研究了随机到达时刻造成数字滤波测量误差与采样频率的关系,包括幅度均值偏移和涨落。这两种误差都会随着采样频率的增加迅速下降,而当采样周期降低到脉冲上升时间的1/3到1/5时,这种误差基本可以忽略。此外,还提出采用定时估计算法来校正幅度测量,并进行了初步的分析。
本文还通过数值仿真和基于数字示波器采样的幅度测量系统,对幅度测量误差与采样频率的关系进行了验证。实验测得的ORTEC 142AH电荷灵敏前放的噪声和CdTe探测器的241Am能谱分辨率,随采样频率的变化规律与理论分析基本一致,较好的验证了理论分析。
Recently, radiation detection based on the digital signal processing has been widely applied in the fields as high energy physics, radiation imaging and so on. Compared with analog circuits, the digital filters have the advantages as flexibility stability and adaptivity, although its performance is limited by the Analog-to-Digital Converter (ADC). In random pulse measurement of radiation detection, there has been no systemic study in theory on the ADC sampling induced error analysis. The study on effect of ADC parameters to digital filtering performance is necessary for digital filter design. For example the power consumption becomes critical issue for signal processing circuit when the number of readout channels increases significantly. In such case, the quantitative study of the dependence of the filter performance on ADC parameters is necessary for reducing ADC power consumption.
This thesis analyzes the dependence of digital filtering performance on ADC sampling frequency in random pulse measurement based on commonly applied digital signal processing circuit. The thesis includes the following parts. 1) Derive the signal spectrum and the noise power spectral density after sampling, analyze quantitatively the amplitude measurement performance on the sampling frequency, and then obtain the optimum signal-to-noise ratio under certain sampling frequency as well as noise index for several commonly applied digital filters. 2) Analyze the random arriving time induced measurement errors on sampling frequency, including the expected amplitude shift and fluctuation, which decrease significantly with increasing sampling frequency. When the sampling interval is less than 1/3 to 1/5 of the signal rising time, the measurement errors can be ignored. The timing estimation algorithm is proposed to amplitude measurement correction and analyzed preliminary.
The dependence of amplitude measurement fluctuation on the sampling frequency is demonstrated by the numerical simulation and measurements with digital oscilloscope sampling. The dependence of experimental results on the sampling frequency is consistent with the theoretical results, which include the noise of ORTEC 142AH charge sensitive preamplifier and the ~(241)Am energy spectrum of CdTe detector. The theoretical analysis is demonstrated.
引文
[1] Simoes J B, Correia C M B A. Pulse processing architectures. Nucl Instr and Meth, 1999, A422:405-410.
[2] Bardelli L. Development of sampling and digital signal processing techniques with applications to Nuclear Physics detectors [PhD Dissertation]. University of Firenze, 2005.
[3] Mota B, B?chler J, Bramm R, et al. Performance of the ALTRO chip on data acquired on an ALICE TPC prototype. Nucl Instr and Meth, 2004, A535:500-505.
[4] The LCTPC collaboration. http://www.lctpc.org.
[5] MAX109 Manuals. http://www.maxim-ic.com.cn.
[6] Drndarevic V, Ryge R, Gozani T. Digital signal processing for high rate gammay-ray spectroscopy. Nucl Instr and Meth, 1989, A277:532-536.
[7] Rost M, Weihs W. 30 MHz hardware digital filter for signals of the ZEUS forward tracking detector. Nucl Instr and Meth, 1994, A345:324-328.
[8] Kihm T, Bobrakov V F, Klapdor-Kleingrothaus H V. A digital multi-channel spectroscopy system with 100 MHz flash ADC module for the GENIUS-TF and GENIUS projects. Nucl Instr and Meth, 2003, A498:334-339
[9] Abbiati R, Geraci A, Ripamonti G. Self-configuring digital processor for on-line pulse analysis. IEEE Trans Nucl Sci, 2004, 51:826-830.
[10] Gatti E, Geraci A, Riboldi S, et al. Digital Penalized LMS method for filter synthesis with arbitrary constraints and noise. Nucl Instr and Meth, 2004, A523:167-185.
[11] Riboldi S, Abbiati R. Experimental comparison of state-of-the-art methods for digital optimum filter synthesis with arbitrary constraints and noise. IEEE Trans Nucl Sci, 2005, 52:954-958
[12] Lauer M. Digital Signal Processing for segmented HPGe Detectors Preprocessing Algorithms and Pulse Shape Analysis [PhD Dissertation]. University of Heidelberg, 2004
[13] Knoll GF. Radiation Detection and Measurement. 3th ed. New York: John Wiley & Sons, 2000.
[14] Riboldi S, Geraci A, Gatti E, et al. A new digital auto-tracking pole-zero compensation technique for high-resolution spectroscopy. Nucl Instr and Meth, 2002, A482:475-490.
[15] Abbiati R, Gatti E, Geraci A, et al. A new digital estimation technique for baseline restoration. Nucl Instr and Meth, 2005, A548:507-516.
[16] Lakatos T. Adaptive digital signal processing for x-ray spectrometry. Nucl Instr and Meth, 1990, B47:307-310.
[17] Georgiev A, Gast W. Digital pulse processing in high resolution, high throughput gamma-ray spectroscopy. IEEE Trans Nucl Sci, 1993, 40(4): 770-779.
[18] Jordanov V T, Knoll G F. Digital techniques for real-time pulse shaping in radiation measurements. Nucl Instr and Meth, 1994, A353:261-264.
[19] Imperiale C. On nuclear spectrometry pulses digital shaping and processing. Measurement, 2001, 30:49-73.
[20] Sampietro M, Bertuccio G, Geraci A. Digital system for 'optimum' resolution in x-ray spectroscopy. Rev Sci Instr, 1995, 66:975-981.
[21] Gatti E, Geraci A, Ripamonti G. Automatic synthesis of optimum filters with arbitrary constraints and noises: A new method. Nucl Instr and Meth, 1996, A381:117-127.
[22] Ripamonti G, Geraci A. Towards real-time digital pulse processing based on least-mean-squares algorithms. Nucl Instr and Meth, 1997, A400:447-455.
[23] Fazzi A, Varoli V. Digital spectrometer for 'optimum' pulse processing. IEEE Trans Nucl Sci, 1998, 45: 843-848
[24] Jordanov V T. Some Digital Techniques for Real Time Processing of Pulses from Radiation Detectors [PhD Dissertation]. University of Michigan, 1994.
[25] Gatti E, Geraci A. Timing of pulses of any shape with arbitrary constraints and noises: Optimum filters synthesis method. Nucl Instr and Meth, 2001, A457:347-355
[26] Petrick N, Hero A O III, Clinthorne, N H, et al. Fast least-squares arrival time estimator for scintillation pulses. IEEE Trans Nucl Sci, 1994, 41:758-761.
[27] Abbiati R, Bertossi L, Geraci A, et al. High-resolution digital online linear procedure for timing of detected events. IEEE Trans Nucl Sci, 2006, 53:1270-1274.
[28] XIA LIC. http://www.xia.com.
[29] CAEN Nuclear Physics. http://www.caen.it/nuclear/index.php.
[30] ORTEC Inc. http://www.ortec-online.com/spec-systems.htm.
[31] Codino A. Pulse digitization for measuring the time of flight of ionizing particles. Nucl Instr and Meth, 2000, A440:191-201.
[32] Bardelli L, Poggi G, Bini M, et al. Time measurements by means of digitalsampling techniques: A study case of 100 ps FWHM time resolution with a 100 MSample/s, 12 bit digitizer. Nucl Instr and Meth, 2004, A521:480-492.
[33] Bertuccio G, Gati E, Sampietro M. Sampling and optimum data processing of detector signals. Nucl Instr and Meth, 1992, A322:271-279.
[34] Bertuccio G., Fazzi A, Geraci A, et al. Optimum digital signal processing for radiation spectroscopy. Nucl Instr and Meth, 1994, A353:257-260.
[35] Cattaneo P W. Optimum FIR filter for sampled signals in presence of jitter. Nucl Instr and Meth, 1996, A373:93-96.
[36] Cattaneo P W. The anti-aliasing requirements for amplitude measurements in sampled systems. Nucl Instr and Meth, 2002, A481:632-636.
[37] Pullia A. Design-chart aided optimization of digital spectrometers. IEEE Trans Nucl Sci, 2002, 49:1791-1797.
[38] Abbiati R, Geraci A, Ripamonti G, et al. Analog shaping optimization for digital processing of radiation detector signals. IEEE Trans Nucl Sci, 2005, 52:1638-1642.
[39] Bardelli L, Poggi G. Digital-sampling systems in high-resolution and wide dynamic-range energy measurements: Comparison with peak sensing ADCs. Nucl Instr and Meth, 2006, A560:517-523.
[40] Bardelli L, Poggi G. Digital-sampling systems in high-resolution and wide dynamic-range energy measurements: Finite time window, baseline effects, and experimental tests. Nucl Instr and Meth, 2006, A560:524-538.
[41] Bousselham A, Bohm C. Sampling pulses for optimal timing. IEEE Trans Nucl Sci, 2007, 54:320-326.
[42] Fallu-Labruyere A, Tan H, Hennig W, et al. Time resolution studies using digital constant fraction discrimination. Nucl Instr and Meth, 2007, 579:247-251.
[43]肖无云,魏义祥,艾宪芸.数字化多道脉冲幅度分析中的梯形成形算法.清华大学学报:自然科学版, 2005, 45(6):810-812.
[44]肖无云,魏义祥,艾宪芸.多道脉冲幅度分析器中的数字基线估计方法.核电子学与探测技术, 2005, 25(6):601-604.
[45]张软玉,周清华,罗小兵,等.核信号数值仿真方法的研究及应用.核电子学与探测技术, 2006, 26(4):421-424.
[46]肖无云,魏义祥,艾宪芸,等.数字化多道脉冲幅度分析技术研究.核技术, 2005, 28(10):787-790.
[47]张软玉,陈世国,罗小兵,等.数字化核能谱获取中信号处理方法研究.原子能科学技术, 2004, 38(3):252-255.
[48]敖奇,魏义祥,文向阳.基于DSP的数字化多道脉冲幅度分析器设计.核技术,2007, 30(6):532-536.
[49]清华大学工程物理系.核辐射物理及探测学.北京:清华大学出版社, 2004.
[50]王经瑾,范天民,钱永庚.核电子学.北京:原子能出版社, 1985.
[51] Fernandes P, Simoes S, Dos Santos F. Digital rise-time discrimination of large-area avalanche photodiode signals in X-ray detection. IEEE Trans Nucl Sci, 2002, 49:1699-1703.
[52] Jastaniah S D, Sellin P J. Digital pulse-shape algorithms for scintillation-based neutron detectors. IEEE Trans Nucl Sci, 2002, 49:1824-1828.
[53] Kurokawa M, Shimoura S, Iwasaki H. Pulse shape simulation and analysis of segmented Ge detectors for position extraction. IEEE Trans Nucl Sci, 2003, 50:1309-1316.
[54]邓智.碲锌镉探测器低噪声电荷灵敏CMOS专用集成前放研究[博士学位论文].北京:清华大学工程物理系, 2005.
[55] Nicholson P W. Nuclear electronics. New York: Wiley, 1974.
[56] Spieler H. Semiconductor detector systems. New York: Oxford University Press, 2005.
[57] Subiela D E, Dugoujon S, Esteve-Bosch L, et al. A low–power 16–channel AD converter and digital processor ASIC. IEEE ESSCIRC, 2002:259-262.
[58]魏旭云.核电子信号离散化研究[硕士学位论文].北京:清华大学工程物理系, 2005.
[59] Kester W. Analog-digital conversation. Analog Device Inc, 2004.
[60] IEEE Instrumentation and Measurement Society. IEEE Std 1241-2000. IEEE standard for terminology and test methods for analog-to-digital converters. IEEE-SA Standards Board, 2000.
[61]胡广书.数字信号处理:理论,算法与实现. 2版.北京:清华大学出版社, 2003.
[62] Oppenhim A V, Schafer R W, Buck J R. Discrete-time signal processing. 2版.北京:清华大学出版社, 2005.
[63]吴崇试.数学物理方法. 2版.北京:北京大学出版社, 2003.
[64] Agilent products. http://www.home.agilent.com.
[65] ORTEC products. http://www.ortec-online.com.
[66] Tektronix products. http://www.tek.com.
[67] Kay S M著,罗鹏飞等译.统计信号处理基础:估计与检测理论.北京:电子工业出版社, 2003.
[2] Bardelli L. Development of sampling and digital signal processing techniques with applications to Nuclear Physics detectors [PhD Dissertation]. University of Firenze, 2005.
[3] Mota B, B?chler J, Bramm R, et al. Performance of the ALTRO chip on data acquired on an ALICE TPC prototype. Nucl Instr and Meth, 2004, A535:500-505.
[4] The LCTPC collaboration. http://www.lctpc.org.
[5] MAX109 Manuals. http://www.maxim-ic.com.cn.
[6] Drndarevic V, Ryge R, Gozani T. Digital signal processing for high rate gammay-ray spectroscopy. Nucl Instr and Meth, 1989, A277:532-536.
[7] Rost M, Weihs W. 30 MHz hardware digital filter for signals of the ZEUS forward tracking detector. Nucl Instr and Meth, 1994, A345:324-328.
[8] Kihm T, Bobrakov V F, Klapdor-Kleingrothaus H V. A digital multi-channel spectroscopy system with 100 MHz flash ADC module for the GENIUS-TF and GENIUS projects. Nucl Instr and Meth, 2003, A498:334-339
[9] Abbiati R, Geraci A, Ripamonti G. Self-configuring digital processor for on-line pulse analysis. IEEE Trans Nucl Sci, 2004, 51:826-830.
[10] Gatti E, Geraci A, Riboldi S, et al. Digital Penalized LMS method for filter synthesis with arbitrary constraints and noise. Nucl Instr and Meth, 2004, A523:167-185.
[11] Riboldi S, Abbiati R. Experimental comparison of state-of-the-art methods for digital optimum filter synthesis with arbitrary constraints and noise. IEEE Trans Nucl Sci, 2005, 52:954-958
[12] Lauer M. Digital Signal Processing for segmented HPGe Detectors Preprocessing Algorithms and Pulse Shape Analysis [PhD Dissertation]. University of Heidelberg, 2004
[13] Knoll GF. Radiation Detection and Measurement. 3th ed. New York: John Wiley & Sons, 2000.
[14] Riboldi S, Geraci A, Gatti E, et al. A new digital auto-tracking pole-zero compensation technique for high-resolution spectroscopy. Nucl Instr and Meth, 2002, A482:475-490.
[15] Abbiati R, Gatti E, Geraci A, et al. A new digital estimation technique for baseline restoration. Nucl Instr and Meth, 2005, A548:507-516.
[16] Lakatos T. Adaptive digital signal processing for x-ray spectrometry. Nucl Instr and Meth, 1990, B47:307-310.
[17] Georgiev A, Gast W. Digital pulse processing in high resolution, high throughput gamma-ray spectroscopy. IEEE Trans Nucl Sci, 1993, 40(4): 770-779.
[18] Jordanov V T, Knoll G F. Digital techniques for real-time pulse shaping in radiation measurements. Nucl Instr and Meth, 1994, A353:261-264.
[19] Imperiale C. On nuclear spectrometry pulses digital shaping and processing. Measurement, 2001, 30:49-73.
[20] Sampietro M, Bertuccio G, Geraci A. Digital system for 'optimum' resolution in x-ray spectroscopy. Rev Sci Instr, 1995, 66:975-981.
[21] Gatti E, Geraci A, Ripamonti G. Automatic synthesis of optimum filters with arbitrary constraints and noises: A new method. Nucl Instr and Meth, 1996, A381:117-127.
[22] Ripamonti G, Geraci A. Towards real-time digital pulse processing based on least-mean-squares algorithms. Nucl Instr and Meth, 1997, A400:447-455.
[23] Fazzi A, Varoli V. Digital spectrometer for 'optimum' pulse processing. IEEE Trans Nucl Sci, 1998, 45: 843-848
[24] Jordanov V T. Some Digital Techniques for Real Time Processing of Pulses from Radiation Detectors [PhD Dissertation]. University of Michigan, 1994.
[25] Gatti E, Geraci A. Timing of pulses of any shape with arbitrary constraints and noises: Optimum filters synthesis method. Nucl Instr and Meth, 2001, A457:347-355
[26] Petrick N, Hero A O III, Clinthorne, N H, et al. Fast least-squares arrival time estimator for scintillation pulses. IEEE Trans Nucl Sci, 1994, 41:758-761.
[27] Abbiati R, Bertossi L, Geraci A, et al. High-resolution digital online linear procedure for timing of detected events. IEEE Trans Nucl Sci, 2006, 53:1270-1274.
[28] XIA LIC. http://www.xia.com.
[29] CAEN Nuclear Physics. http://www.caen.it/nuclear/index.php.
[30] ORTEC Inc. http://www.ortec-online.com/spec-systems.htm.
[31] Codino A. Pulse digitization for measuring the time of flight of ionizing particles. Nucl Instr and Meth, 2000, A440:191-201.
[32] Bardelli L, Poggi G, Bini M, et al. Time measurements by means of digitalsampling techniques: A study case of 100 ps FWHM time resolution with a 100 MSample/s, 12 bit digitizer. Nucl Instr and Meth, 2004, A521:480-492.
[33] Bertuccio G, Gati E, Sampietro M. Sampling and optimum data processing of detector signals. Nucl Instr and Meth, 1992, A322:271-279.
[34] Bertuccio G., Fazzi A, Geraci A, et al. Optimum digital signal processing for radiation spectroscopy. Nucl Instr and Meth, 1994, A353:257-260.
[35] Cattaneo P W. Optimum FIR filter for sampled signals in presence of jitter. Nucl Instr and Meth, 1996, A373:93-96.
[36] Cattaneo P W. The anti-aliasing requirements for amplitude measurements in sampled systems. Nucl Instr and Meth, 2002, A481:632-636.
[37] Pullia A. Design-chart aided optimization of digital spectrometers. IEEE Trans Nucl Sci, 2002, 49:1791-1797.
[38] Abbiati R, Geraci A, Ripamonti G, et al. Analog shaping optimization for digital processing of radiation detector signals. IEEE Trans Nucl Sci, 2005, 52:1638-1642.
[39] Bardelli L, Poggi G. Digital-sampling systems in high-resolution and wide dynamic-range energy measurements: Comparison with peak sensing ADCs. Nucl Instr and Meth, 2006, A560:517-523.
[40] Bardelli L, Poggi G. Digital-sampling systems in high-resolution and wide dynamic-range energy measurements: Finite time window, baseline effects, and experimental tests. Nucl Instr and Meth, 2006, A560:524-538.
[41] Bousselham A, Bohm C. Sampling pulses for optimal timing. IEEE Trans Nucl Sci, 2007, 54:320-326.
[42] Fallu-Labruyere A, Tan H, Hennig W, et al. Time resolution studies using digital constant fraction discrimination. Nucl Instr and Meth, 2007, 579:247-251.
[43]肖无云,魏义祥,艾宪芸.数字化多道脉冲幅度分析中的梯形成形算法.清华大学学报:自然科学版, 2005, 45(6):810-812.
[44]肖无云,魏义祥,艾宪芸.多道脉冲幅度分析器中的数字基线估计方法.核电子学与探测技术, 2005, 25(6):601-604.
[45]张软玉,周清华,罗小兵,等.核信号数值仿真方法的研究及应用.核电子学与探测技术, 2006, 26(4):421-424.
[46]肖无云,魏义祥,艾宪芸,等.数字化多道脉冲幅度分析技术研究.核技术, 2005, 28(10):787-790.
[47]张软玉,陈世国,罗小兵,等.数字化核能谱获取中信号处理方法研究.原子能科学技术, 2004, 38(3):252-255.
[48]敖奇,魏义祥,文向阳.基于DSP的数字化多道脉冲幅度分析器设计.核技术,2007, 30(6):532-536.
[49]清华大学工程物理系.核辐射物理及探测学.北京:清华大学出版社, 2004.
[50]王经瑾,范天民,钱永庚.核电子学.北京:原子能出版社, 1985.
[51] Fernandes P, Simoes S, Dos Santos F. Digital rise-time discrimination of large-area avalanche photodiode signals in X-ray detection. IEEE Trans Nucl Sci, 2002, 49:1699-1703.
[52] Jastaniah S D, Sellin P J. Digital pulse-shape algorithms for scintillation-based neutron detectors. IEEE Trans Nucl Sci, 2002, 49:1824-1828.
[53] Kurokawa M, Shimoura S, Iwasaki H. Pulse shape simulation and analysis of segmented Ge detectors for position extraction. IEEE Trans Nucl Sci, 2003, 50:1309-1316.
[54]邓智.碲锌镉探测器低噪声电荷灵敏CMOS专用集成前放研究[博士学位论文].北京:清华大学工程物理系, 2005.
[55] Nicholson P W. Nuclear electronics. New York: Wiley, 1974.
[56] Spieler H. Semiconductor detector systems. New York: Oxford University Press, 2005.
[57] Subiela D E, Dugoujon S, Esteve-Bosch L, et al. A low–power 16–channel AD converter and digital processor ASIC. IEEE ESSCIRC, 2002:259-262.
[58]魏旭云.核电子信号离散化研究[硕士学位论文].北京:清华大学工程物理系, 2005.
[59] Kester W. Analog-digital conversation. Analog Device Inc, 2004.
[60] IEEE Instrumentation and Measurement Society. IEEE Std 1241-2000. IEEE standard for terminology and test methods for analog-to-digital converters. IEEE-SA Standards Board, 2000.
[61]胡广书.数字信号处理:理论,算法与实现. 2版.北京:清华大学出版社, 2003.
[62] Oppenhim A V, Schafer R W, Buck J R. Discrete-time signal processing. 2版.北京:清华大学出版社, 2005.
[63]吴崇试.数学物理方法. 2版.北京:北京大学出版社, 2003.
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