基于信号相干统计理论的周期性信号检测
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摘要
周期性信号检测是信号检测的一个重要研究方面,其应用十分广泛。
本文针对实际信号中不存在纯粹的周期信号,应用确定的谐波信号表示周期信号只是数学上的一种方便,并不准确这一问题,建立了新的周期性信号模型,用变化的周期信号来模拟在各个不同的科学领域中观测到的信号。这种随机调制周期信号模型与能产生零带宽谐波的标准的理论周期模型相比,这种信号模型更加真实,这种调制的假设更加合适。
分析研究信号的频域相干的相关理论,确定了适用于周期性信号检测的信号相干函数。对信号相干函数的原理进行了公式推导及理论分析,并进行了一系列统计分析。
提出了一种基于相干统计理论的周期性信号检测的具体方法,该方法易于计算机实现,且易于自动化。应用该方法与目前实际应用的原有方法进行仿真比较,证明无论在有无外加噪声情况下,该检测方法都优于标准瀑布谱方法。分析了该方法的虚警率、检测率以及模型参数对检测的影响。给出了信号存在,已知信号的频率范围的情况下,信号基本周期的确定方法。
Nature does not produce perfect periodic signals. There is always some variation in the waveform which is labeled as periodic signal. All periodic signals have some sort of variability from period to period regardless of how stable they appear to be. For example, a true sinusoidal time series is a deterministic function of time, so it has zero bandwidth around the sinusoid’s frequency. As all known, a zero bandwidth is impossible in nature. Deterministic sinusoids are used to model cycles as a mathematical convenience, and not accurate. It is time to break away from this simplification in order to model various periodic signals that observed in different sciences fields, so we need set up a new periodic signals model.
The traditional signal detection is often assumed that the probability characteristics of the observing sample is known or have some prior knowledge. Because of signal detection in most cases are in strong noise background, traditional time-domain detection have poor performance. And in strong noise environment, when signal is non-stationary, especially when has unknown parameters, the conventional detection method does not applicable. We know that sinusoidal signal in noise when the signal’s frequency is known, but amplitude and phase is unknown, if lack of the priori knowledge of unknown parameters, then we use the generalized likelihood ratio test method. However, this method does not take full advantage of the signal priori knowledge, at the actual periodic signal detection circumstances, we probably know the frequency of the signal, even if do not know, we know it random distribution in a limited band. At this point, we put it as completely unknown signal to detect, obviously is wrong. In order to improve signal to noise ratio and adapt the complicated signal, it is essential to carry out such periodic signal detection research. Therefore, we should further research the detection theory, develop new detection theory, introduct new detection methods, and improve detector’s detection performance in a complex environment and low SNR environment.
This paper set up a new periodic signal model, with changed periodic signal to simulate observed signal in the different science fields. Such random modulation periodic signal model comparing with original periodic signal model which can produce zero-bandwidth harmonic. This signal model more realistic, and this modulation assumption more appropriate.
By analysis of the theory of signals in frequency domain coherent, I determine the signal coherence function applied to the periodic signal detection. The principle of signal coherence function is derived and theoretical analysis, and then it conducts a series of statistical analysis.
This paper presents a specific signal detection method which is based on the statistical theory of signal coherence, and this method is easy computer implementation, and easy automation. Application of the method and current practical application methods to simulate and to compare, proved that additional noise whether or not, this detection method is superior to the standard spectral waterfall method. Analysis of the false alarm probability, detection probability, as well as the detection influence of parameters, and it draw the additional noise only required to satisfy stationarity and finite dependence, do not need the assumption noise is Gaussian noise. It gives a situation of the signal’s existence, we known the signal frequency range, the method of determine the signal basic cycle.
The following gives the main work of this paper in detail.
1. I comprehensively collect, organize, read and studied a variety of domestic and foreign literature related to the signal detection, sum up the background and application of the signal detection and periodic signal detection. Aiming at the problems that the nature does not produce perfect periodic signals and deterministic sinusoids are used to model cycles as a mathematical convenience, not accurate, we need to set up a new model. Aiming at the problems of the traditional methods did not take full advantage of the prior knowledge of the signals, so we need to study new detection methods.
2. It introduces the coherent signal theory, gives the proof of traditional frequency-domain coherence function equal one. It gives detailed description on the relevant signal statistical theory, including the evaluation criteria and some formula. It gives the periodic signal express in time domain and frequency domain and the classification of the periodic signal.
3. It introduces the detection classification, points out that according to the noise type of detection this paper belongs to non-parametric testing, according to the type of signal types this paper belongs to unknown parameters detection, according to the type of observing sample values to deal with this paper belongs to non-fixed observation sample value. A detailed analysis of the signal detection rules, we derived calculating likelihood ratio of maximum posteriori probability criterion, Bayesian criterion and the minimum error probability criterion need to know a priori probability. For this paper, obtain a priori probability is very difficult, in order to guarantee a low probability of false alarm, only to restrict the probability of false alarm and to make the probability of detection greatest, so we should use Neyman-Pearson criteria. It introduces the periodic signal detection methods, infers the periodic signal detection problem in strong noise background, an intuitive way is to improve the signal to noise ratio. Under this paper, gives detailed description on time-domain average processing, signal correlation and periodogram at periodic signal detection applications, and gives the simulation results and analysis.
4. Aiming at the fact that the nature does not produce perfect periodic signals, I find a random modulated periodic signal model which can descript the changes in the periodic signal, analysis the model and formula for deformation, study the elimination of the linear and nonlinear trend of the signal, and use matlab to simulate them.
5. The principle of the signal coherence function is analyzed and formula derivation, it gives the statistical analysis of the signal coherence function, according to the traditional amplitude squared coherence function’s conclusions, it draws the signal coherence function’s messages, and simulates the coherent function and studies it performance.
6. It presents a specific signal detection method which based on a statistical theory of signal coherence, using this method simulation comparing with the periodogram. Analysis of the false alarm probability, detection probability, as well as the detection influence of parameters. It gives a situation of the existence of signal, we known the signal frequency range, the method of determine the basic cycle.
本文针对实际信号中不存在纯粹的周期信号,应用确定的谐波信号表示周期信号只是数学上的一种方便,并不准确这一问题,建立了新的周期性信号模型,用变化的周期信号来模拟在各个不同的科学领域中观测到的信号。这种随机调制周期信号模型与能产生零带宽谐波的标准的理论周期模型相比,这种信号模型更加真实,这种调制的假设更加合适。
分析研究信号的频域相干的相关理论,确定了适用于周期性信号检测的信号相干函数。对信号相干函数的原理进行了公式推导及理论分析,并进行了一系列统计分析。
提出了一种基于相干统计理论的周期性信号检测的具体方法,该方法易于计算机实现,且易于自动化。应用该方法与目前实际应用的原有方法进行仿真比较,证明无论在有无外加噪声情况下,该检测方法都优于标准瀑布谱方法。分析了该方法的虚警率、检测率以及模型参数对检测的影响。给出了信号存在,已知信号的频率范围的情况下,信号基本周期的确定方法。
Nature does not produce perfect periodic signals. There is always some variation in the waveform which is labeled as periodic signal. All periodic signals have some sort of variability from period to period regardless of how stable they appear to be. For example, a true sinusoidal time series is a deterministic function of time, so it has zero bandwidth around the sinusoid’s frequency. As all known, a zero bandwidth is impossible in nature. Deterministic sinusoids are used to model cycles as a mathematical convenience, and not accurate. It is time to break away from this simplification in order to model various periodic signals that observed in different sciences fields, so we need set up a new periodic signals model.
The traditional signal detection is often assumed that the probability characteristics of the observing sample is known or have some prior knowledge. Because of signal detection in most cases are in strong noise background, traditional time-domain detection have poor performance. And in strong noise environment, when signal is non-stationary, especially when has unknown parameters, the conventional detection method does not applicable. We know that sinusoidal signal in noise when the signal’s frequency is known, but amplitude and phase is unknown, if lack of the priori knowledge of unknown parameters, then we use the generalized likelihood ratio test method. However, this method does not take full advantage of the signal priori knowledge, at the actual periodic signal detection circumstances, we probably know the frequency of the signal, even if do not know, we know it random distribution in a limited band. At this point, we put it as completely unknown signal to detect, obviously is wrong. In order to improve signal to noise ratio and adapt the complicated signal, it is essential to carry out such periodic signal detection research. Therefore, we should further research the detection theory, develop new detection theory, introduct new detection methods, and improve detector’s detection performance in a complex environment and low SNR environment.
This paper set up a new periodic signal model, with changed periodic signal to simulate observed signal in the different science fields. Such random modulation periodic signal model comparing with original periodic signal model which can produce zero-bandwidth harmonic. This signal model more realistic, and this modulation assumption more appropriate.
By analysis of the theory of signals in frequency domain coherent, I determine the signal coherence function applied to the periodic signal detection. The principle of signal coherence function is derived and theoretical analysis, and then it conducts a series of statistical analysis.
This paper presents a specific signal detection method which is based on the statistical theory of signal coherence, and this method is easy computer implementation, and easy automation. Application of the method and current practical application methods to simulate and to compare, proved that additional noise whether or not, this detection method is superior to the standard spectral waterfall method. Analysis of the false alarm probability, detection probability, as well as the detection influence of parameters, and it draw the additional noise only required to satisfy stationarity and finite dependence, do not need the assumption noise is Gaussian noise. It gives a situation of the signal’s existence, we known the signal frequency range, the method of determine the signal basic cycle.
The following gives the main work of this paper in detail.
1. I comprehensively collect, organize, read and studied a variety of domestic and foreign literature related to the signal detection, sum up the background and application of the signal detection and periodic signal detection. Aiming at the problems that the nature does not produce perfect periodic signals and deterministic sinusoids are used to model cycles as a mathematical convenience, not accurate, we need to set up a new model. Aiming at the problems of the traditional methods did not take full advantage of the prior knowledge of the signals, so we need to study new detection methods.
2. It introduces the coherent signal theory, gives the proof of traditional frequency-domain coherence function equal one. It gives detailed description on the relevant signal statistical theory, including the evaluation criteria and some formula. It gives the periodic signal express in time domain and frequency domain and the classification of the periodic signal.
3. It introduces the detection classification, points out that according to the noise type of detection this paper belongs to non-parametric testing, according to the type of signal types this paper belongs to unknown parameters detection, according to the type of observing sample values to deal with this paper belongs to non-fixed observation sample value. A detailed analysis of the signal detection rules, we derived calculating likelihood ratio of maximum posteriori probability criterion, Bayesian criterion and the minimum error probability criterion need to know a priori probability. For this paper, obtain a priori probability is very difficult, in order to guarantee a low probability of false alarm, only to restrict the probability of false alarm and to make the probability of detection greatest, so we should use Neyman-Pearson criteria. It introduces the periodic signal detection methods, infers the periodic signal detection problem in strong noise background, an intuitive way is to improve the signal to noise ratio. Under this paper, gives detailed description on time-domain average processing, signal correlation and periodogram at periodic signal detection applications, and gives the simulation results and analysis.
4. Aiming at the fact that the nature does not produce perfect periodic signals, I find a random modulated periodic signal model which can descript the changes in the periodic signal, analysis the model and formula for deformation, study the elimination of the linear and nonlinear trend of the signal, and use matlab to simulate them.
5. The principle of the signal coherence function is analyzed and formula derivation, it gives the statistical analysis of the signal coherence function, according to the traditional amplitude squared coherence function’s conclusions, it draws the signal coherence function’s messages, and simulates the coherent function and studies it performance.
6. It presents a specific signal detection method which based on a statistical theory of signal coherence, using this method simulation comparing with the periodogram. Analysis of the false alarm probability, detection probability, as well as the detection influence of parameters. It gives a situation of the existence of signal, we known the signal frequency range, the method of determine the basic cycle.
引文
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[2]沈允春,田园主.信号检测与估计[M].哈尔滨工程大学出版社,2007.
[3]丁鹭飞,耿富录.雷达原理[M].西安电子科技大学出版社,2004.
[4]赵国庆.雷达对抗原理[M].西安电子科技大学出版社,1999.
[5]隆克平,聂能,竺南直编.第九届全国青年通信学术会议论文集[C].北京:电子工业出版社,2004.
[6] Proakis,J.G. .Digital Communications[M].2nd Ed.,McGraw-Hill,New York, 1989.
[7] Rabiner,L.,B-H Juang.Fundamentals of Speech Recognition[M]. Prentice-Hall, Englewood Cliffs,N.J., 1993.
[8] Knight,W.S,R.G.Pridham,S.M.Kay. Digital Signal Processing for Sonar[J]. Proc. IEEE, 1981,69:1451-1506.
[9] Chan,D.S.K,D.A.Staver.Spatial Processing Techniques for the Detection of Small Targets in IR Clutter[J].SPIE,Signal and Data Processing of Small Targets, 1990,1305:53-62.
[10] Gustafson,D.E. .ECG/VCG Rhythm Diagnosis Using Statistical Signal Analysis[J]. IEEE Trans.Biomed.Eng., 1978,BME25:353-361.
[11] Willsky,A.S,H.L.Jones.A Generalized Likelihood Ratio Approach to Detection and Estimation of Jumps in Linear Systems[J].IEEE Trans,Automat. Contr, 1976, AC-21: 108-112.
[12] Justice,J.H..Array Processing in Exploration Seismology[M].in Array Signal Processing, S.Haykin, Ed.,Prentice-Hall,EnglewoodCliffs, 1985.
[13]李文华.正弦加噪的语音信号模型的研究[D].北京:华北电力大学,2005.
[14] X.Serra. Musical Sound Modeling with Sinusoids plus Noise[J]. Roads C. & Pope S.& Picialli G. & De Poli G.(eds). Musical signa1 Proeessing.Swets & Zeitlinger Publishers, 1997.
[15]马徐棍.浅析水下高速航行体对转螺旋桨辐射噪声线谱建模[J].声学学报,2002,27(6):502-506.
[16]胡凯衡,李泳.阵性泥石流的周期性分析[J].山地学报,2001,19(2):104-208.
[17]赵利红.水文时间序列周期分析方法的研究[D].南京:海河大学,2007.
[18]谢正祥,钟雪飞,谢丹玫.关于幅值平方相干函数[J].中国医学物理学杂志,2005,22(3):539-547.
[19]沈凤麟,叶中付,钱玉美.信号统计分析与处理[M].合肥:中国科技大学出版社,2001.
[20]谢式千,潘承毅.概率论与数理统计[M].北京:高等教育出版社,2001.
[21]何凤霞,张翠莲.蒙特卡罗方法的应用及算例[M].华北电力大学学报,2005.
[22]张谨,赫慈辉.信号与系统[M].北京:人民邮电出版社,1990.
[23]刘树索译.信号与系统[M].西安交通大学出版社,1998.
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