多分量信号的信号分量分离技术研究
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摘要
本文研究了在通信、雷达、声纳、语音、生物医药工程等领域中有着广泛及重要应用的多分量信号的多个重叠信号分量的分离技术。文中基于不同的分析方法，建立了不同形式的信号模型，并用不同方法对各个模型的参数进行估计，从而进行信号分量的分离。文中提出或推导了一系列具有理论和实际价值的新方法，并通过计算机仿真试验验证了所提方法的优良性能。归纳起来，本文的贡献主要包括以下几个方面：
(1) 对于多分量信号从信号定义，到信号分量可分离性分析，再到已有的分离方法，进行了概括和总结。对多分量信号的分离性以及已有的分离方法进行归类分析。
(2) 基于Weierstrass理论和PSP(Per-Survivor Processing)方法，提出了一种基于模型拟合的多分量信号的重叠信号分量分离方法。该方法将重叠信号分量分离问题转化为输入序列和时变信道参数的估计问题，从而便于处理。该方法的优良性能表现为：即使信号分量的频谱完全重叠，该方法也能很好地进行信号分量的分离。
(3) 利用能量算子和信号分量的短时单频假设，提出了一种多分量信号的重叠信号分量分离方法。该方法将能量算子扩展到多信号分量情况的应用中，充分利用了能量算子的计算简单和高时域分辨率特性，使得分离方法具有快速准确的特性。
(4) 通过对非平稳多分量信号建立时变AR(AutoRegressive)模型，利用时变功率谱进行信号分量的瞬时频率、幅度估计这一思路，讨论了一种基于时变AR模型的多分量信号的重叠信号分量分离方法。该方法通过对时变AR系数进行长椭球基函数的分解，将时变AR系数的估计转化为时不变系数的估计问题，并推导了—利用位移秩的阶数递归方法，使得能够对模型参数进行递归求解，计算量大大减少，同时利用时变AR模型的高时频分辨率可以获得很好的信号分量分离效果。
(5) 基于贝叶斯分析，提出了一种利用贝叶斯估计的多分量信号的重叠信号分量分离方法。通过基函数分解，建立了—便于进行贝叶斯分析的信号模型，以及其相应的贝叶斯模型。基于该贝叶斯模型，利用可逆跳跃MCMC(Markov
This dissertation focuses on the separation of overlapped signal components of the multicomponent signal which has various and important applications in the fields of communications, radar, sonar, speech, biomedical engineering and so on. Based on different analysis methods, various signal models are developed. Several theoretically and practically valued methods are proposed or derived to estimate the parameters of those models, and to perform the signal components separation. Computer simulations and their results are given to verify the efficiency of those proposed methods. The main contributions of this dissertation can be concluded as follows:
(1) The definition, the separability, and existed separation approaches of the multicomponent signal are summarized. Based on this, the various separability analysis and separation approaches are carefully classified.
(2) Based on the Weierstrass theory and PSP (Per-Survivor Processing), a model fitting based methods, which can separate the overlapped signal components of the multicomponent signal, is proposed. This method turns the problem of multi-signal components separation to that of the sequence and channel parameters estimation, which is much more convenient to process. Even in the situation that the spectra of the signal components are totally overlapped, they can be separated successfully by using this method.
(3) A new method to separate the overlapped signal components of the multicomponent signal is proposed, which uses the short time and sinusoidal assumptions of the signal component, and extends the application of energy operator to the multi-signal components. The computational simplicity and high resolution properties of the energy operator are folly utilized, which leads to fast and accurate signal component separation.
(4) Based on the idea of developing a time varying AR model for the multicomponent nonstationary signal, and using the time varying spectrum to estimate instantaneous frequency and amplitude for each signal component, a new
(1) 对于多分量信号从信号定义，到信号分量可分离性分析，再到已有的分离方法，进行了概括和总结。对多分量信号的分离性以及已有的分离方法进行归类分析。
(2) 基于Weierstrass理论和PSP(Per-Survivor Processing)方法，提出了一种基于模型拟合的多分量信号的重叠信号分量分离方法。该方法将重叠信号分量分离问题转化为输入序列和时变信道参数的估计问题，从而便于处理。该方法的优良性能表现为：即使信号分量的频谱完全重叠，该方法也能很好地进行信号分量的分离。
(3) 利用能量算子和信号分量的短时单频假设，提出了一种多分量信号的重叠信号分量分离方法。该方法将能量算子扩展到多信号分量情况的应用中，充分利用了能量算子的计算简单和高时域分辨率特性，使得分离方法具有快速准确的特性。
(4) 通过对非平稳多分量信号建立时变AR(AutoRegressive)模型，利用时变功率谱进行信号分量的瞬时频率、幅度估计这一思路，讨论了一种基于时变AR模型的多分量信号的重叠信号分量分离方法。该方法通过对时变AR系数进行长椭球基函数的分解，将时变AR系数的估计转化为时不变系数的估计问题，并推导了—利用位移秩的阶数递归方法，使得能够对模型参数进行递归求解，计算量大大减少，同时利用时变AR模型的高时频分辨率可以获得很好的信号分量分离效果。
(5) 基于贝叶斯分析，提出了一种利用贝叶斯估计的多分量信号的重叠信号分量分离方法。通过基函数分解，建立了—便于进行贝叶斯分析的信号模型，以及其相应的贝叶斯模型。基于该贝叶斯模型，利用可逆跳跃MCMC(Markov
This dissertation focuses on the separation of overlapped signal components of the multicomponent signal which has various and important applications in the fields of communications, radar, sonar, speech, biomedical engineering and so on. Based on different analysis methods, various signal models are developed. Several theoretically and practically valued methods are proposed or derived to estimate the parameters of those models, and to perform the signal components separation. Computer simulations and their results are given to verify the efficiency of those proposed methods. The main contributions of this dissertation can be concluded as follows:
(1) The definition, the separability, and existed separation approaches of the multicomponent signal are summarized. Based on this, the various separability analysis and separation approaches are carefully classified.
(2) Based on the Weierstrass theory and PSP (Per-Survivor Processing), a model fitting based methods, which can separate the overlapped signal components of the multicomponent signal, is proposed. This method turns the problem of multi-signal components separation to that of the sequence and channel parameters estimation, which is much more convenient to process. Even in the situation that the spectra of the signal components are totally overlapped, they can be separated successfully by using this method.
(3) A new method to separate the overlapped signal components of the multicomponent signal is proposed, which uses the short time and sinusoidal assumptions of the signal component, and extends the application of energy operator to the multi-signal components. The computational simplicity and high resolution properties of the energy operator are folly utilized, which leads to fast and accurate signal component separation.
(4) Based on the idea of developing a time varying AR model for the multicomponent nonstationary signal, and using the time varying spectrum to estimate instantaneous frequency and amplitude for each signal component, a new
引文
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