非平稳信号联合时频分析方法的若干问题研究与应用
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摘要
严格说来,自然界的信号都是非平稳信号。如何对这些信号进行有效地分析,并给出其参数的估计,是测试领域的专家学者研究的热门话题之一。
传统的信号分析方法从单一的时域或频域对信号进行描述,然而对于非平稳信号,其参数随时间在不断变化。因此,单一的时域或频域的分析法不能对其进行有效的处理。
联合时频分析(Time-Frequency Joint Analysis,TFJA)是非平稳信号分析的有效方法。时频分析改变了传统的单一的从时域或频域(如:傅立叶变换)表征信号特征的思路,而同时从时频域联合分析的角度来对信号进行研究。从时频域同时分析非平稳信号得到的信息与非平稳信号一阶或高阶统计量随时间变化的基本特征相吻合,从而可以有效提取非平稳信号参数的时变特征。
本文在研究了典型的时频表示方法的基础上,针对不同非平稳信号的不同分析方法,从以下几个方面进行了研究和探讨:
(1)短时傅立叶变换分析有限带宽非平稳信号的混叠问题研究
首先讨论了短时傅立叶变换(Short Time Fourier Transform,STFT)分析非平稳信号的针对性,讨论了STFT分析有限带宽非平稳信号的有效性。
文中针对STFT分析有限带宽非平稳信号过程中产生的混叠现象,研究了优化抑制混叠干扰的算法。首先,深入研究了STFT分析非平稳信号时混叠产生的物理本质,从信号的有限和无限带宽角度对信号进行划分,并分别讨论了混叠产生的原因。其次,文中研究了不同窗函数的分析性能。然后,通过对以汉明窗为基础的STFT在频域内通过插值算法实现了混叠的有效抑制。最终利用迭代的方法实现了算法的快速求解,并用仿真实例对算法进行了验证。
(2)小波包变换的频带泄漏和振荡问题研究
首先分析了小波包变换分析非平稳信号的特点,指出了其在提取非平稳暂态信号特征时具有其他分析方法所不具有的优势。
文中针对小波包变换分析非平稳暂态信号过程中,由于其时频域基函数的非紧支性导致的频带泄漏问题,深入研究了基于时域优化的泄漏抑制算法。该方法在保留小波包函数频域紧支性的前提下,通过改写其表达式,提升其时域的紧支性能,可以有效抑制频带泄漏的发生。
(3)小波包变换中“有限数据长度效应”问题研究
由于小波包变换的“加窗”本质,使其在对信号分析过程中,必然要进行数据的截断。数据的截断会造成“有限数据长度效应”,导致变换结果的频带泄漏。
针对这一问题,根据Gibbs理论,本文研究了通过对小波包滤波器频域插值的算法,从而抑制“有限数据长度效应”。文中给出了插值算法的快速实现,讨论了插值点数的确定方法。
(4) Wigner-Hough变换(WHT)分析多分量线性调频信号的输出性能研究
首先从WHT的本质入手,深入分析了WHT在多份量线性调频信号分析过程中的优势和不足。
针对Wigner-Hough变换分析多分量线性调频信号(Multi-Components LinearFrequency Modulation Signal)过程中,由于信号输入信噪比和信号采样点数变化导致的变换输出信噪比的恶化问题,本文进行了深入研究。分析了输入数据点数(data number)、输入信号信噪比(Input SNR)和变换输出信噪比(Output SNR)之间的联系,得出了三者之间的数学关系。在此基础上,研究使用PWV提高WHT变换输入信噪比,建立了PWHT算法模型。同时,研究使用数据域插值提高PWHT变换可用数据点数的算法。
通过上述改进算法,有效改善了Wigner-Hough变换分析LFM信号输出性能。
(5)优化的时频分析方法在工程中的实际应用
结合工程项目实例,将本文的算法进行了有效应用,具体包括:
其一:工业电机控制系统中电网电流电压的非平稳特征分析
本小节中对于电机整流调速控制系统中由于整流系统和电机运行状态的变化引起的电网电压电流非平稳信号进行分析。
通过第三章所述的小波包算法及其优化过程,对电机整流调速控制系统中电网电压的暂降、电流的时变及其谐波成分进行了有效的分析。
其二:强噪声背景下LFM信号的分析
本小节对于工程实例中强噪声背景下的LFM信号进行分析。
利用第四章所述优化的Wigner-Hough变换,对于强噪声背景下LFM信号的特征提取和数值进行了有效分析,验证了算法的实用性。
Strictly speaking, the natural signals are all nonstationary signals. How to measure these kinds of signals and estimate their characteristics effectively is widely discussed by the researchers in measurement domain.
The classic signal procession methods describe the signals in the time or frequency domain separately. Since the characteristics of nonstationary signals are varying by time, the traditional approaches are less effective.
Time-Frequency Joint Analysis (TFJA) theory works more effectively in nonstationary signal analysis. It analyzes the signals in the time-frequency joint domain. The time-varying characteristics of nonstationary signals can be effectively extracted through the TFJA.
In this thesis, various nonstationary signals analyzing approaches in the measurement system are discussed:
(1) The aliasing restraining of the limited bandwidth nonsationary signals analysis based on the Short Time Fourier Transform
Firstly, the performance of nonstationary signal analyzed by STFT is discussed, and the result shows that STFT can extract the characteristics of limited bandwidth signals effectively.
And then, an optimized algorithm is proposed to restrain the aliasing. The physical essence of occurred aliasing is discussed. The filter window selected technical is described. Based on the interpolation method in the frequency domain, the STFT is optimized. Using the Newton iterative method, the fast computation of algorithm is implemented.
(2) The research of the frequency band leakage and oscillation of the transient signals processing based on the Wavelet Packet Transform (WPT)
In this section, aiming at the leakage occurred during the WPT, an optimized algorithm is proposed.
Firstly, the performance of the WPT analysis of the nonsationary transient signals is discussed, and the advantage is pointed out. The leakage caused by the incompactly support of the function is investigated.
And then a novel optimized algorithm in time domain is brought forward. By the algorithm, the compact support character in frequency domain of wavelet packet function is reserved, and the performance in time domain is improved. The simulation proved the effectiveness of the algorithm.
(3) The research of "limited data length effect" in the WPT
Because the essence of the WPT is a kind of "windowed" transform, during the course of analyzing the signal, the sampled data should be truncated inevitably. The truncation causes the "limited data length effect", and brings on the band leakage.
Aiming at this problem, based on the Gibbs theory, a kind of WPT frequency filter interpolation algorithm is bring forward to suppress those unwanted effect. The fast computation of interpolation is implemented, and the quantity of interpolating points is discussed.
(4) The research on the output Signal-to-Noise Ration (SNR) of the Wigner-Hough Transform (WHT) in the Linear Frequency Modulation (LFM) signal detection
The advantage and disadvantage of using WHT to detect the multi-component LFM signals are discussed.
Output SNR is deteriorated because the varying of the signal input SNR and the available data number. Aiming at these deteriorative factors, the thesis researches the relation of the factors in depth. The mathematic relation of them is deducted. A novel algorithm is brought forward based on the PWHT and interpolation. The simulation result proves the effectiveness of the algorithm.
(5) The application of the algorithms in engineering projects
The algorithms in this thesis are validated in engineering projects.
Firstly, the nonsatationary characteristics of voltage and current that are caused by industry electromotor control system in the power system are researched.
An engineering test model is set up to validate the algorithm in the 3~(rd) chapter.
The industry electromotor control system is used in this model. Because the trigger angle and the load of the motor are varying by time, the voltage and current in power system are changing too. Applied the optimized WPT in chapter 3, the characters of the varying voltage and current can be extracted effectively.
Secondly, a project is set up to validate the algorithm in the 4~(th) chapter.
Applied the optimized WHT algorithm, the parameters of multi-components LFM signals in strong noise background can be correctly extracted, and the time varying characters of signals are shown clearly.
传统的信号分析方法从单一的时域或频域对信号进行描述,然而对于非平稳信号,其参数随时间在不断变化。因此,单一的时域或频域的分析法不能对其进行有效的处理。
联合时频分析(Time-Frequency Joint Analysis,TFJA)是非平稳信号分析的有效方法。时频分析改变了传统的单一的从时域或频域(如:傅立叶变换)表征信号特征的思路,而同时从时频域联合分析的角度来对信号进行研究。从时频域同时分析非平稳信号得到的信息与非平稳信号一阶或高阶统计量随时间变化的基本特征相吻合,从而可以有效提取非平稳信号参数的时变特征。
本文在研究了典型的时频表示方法的基础上,针对不同非平稳信号的不同分析方法,从以下几个方面进行了研究和探讨:
(1)短时傅立叶变换分析有限带宽非平稳信号的混叠问题研究
首先讨论了短时傅立叶变换(Short Time Fourier Transform,STFT)分析非平稳信号的针对性,讨论了STFT分析有限带宽非平稳信号的有效性。
文中针对STFT分析有限带宽非平稳信号过程中产生的混叠现象,研究了优化抑制混叠干扰的算法。首先,深入研究了STFT分析非平稳信号时混叠产生的物理本质,从信号的有限和无限带宽角度对信号进行划分,并分别讨论了混叠产生的原因。其次,文中研究了不同窗函数的分析性能。然后,通过对以汉明窗为基础的STFT在频域内通过插值算法实现了混叠的有效抑制。最终利用迭代的方法实现了算法的快速求解,并用仿真实例对算法进行了验证。
(2)小波包变换的频带泄漏和振荡问题研究
首先分析了小波包变换分析非平稳信号的特点,指出了其在提取非平稳暂态信号特征时具有其他分析方法所不具有的优势。
文中针对小波包变换分析非平稳暂态信号过程中,由于其时频域基函数的非紧支性导致的频带泄漏问题,深入研究了基于时域优化的泄漏抑制算法。该方法在保留小波包函数频域紧支性的前提下,通过改写其表达式,提升其时域的紧支性能,可以有效抑制频带泄漏的发生。
(3)小波包变换中“有限数据长度效应”问题研究
由于小波包变换的“加窗”本质,使其在对信号分析过程中,必然要进行数据的截断。数据的截断会造成“有限数据长度效应”,导致变换结果的频带泄漏。
针对这一问题,根据Gibbs理论,本文研究了通过对小波包滤波器频域插值的算法,从而抑制“有限数据长度效应”。文中给出了插值算法的快速实现,讨论了插值点数的确定方法。
(4) Wigner-Hough变换(WHT)分析多分量线性调频信号的输出性能研究
首先从WHT的本质入手,深入分析了WHT在多份量线性调频信号分析过程中的优势和不足。
针对Wigner-Hough变换分析多分量线性调频信号(Multi-Components LinearFrequency Modulation Signal)过程中,由于信号输入信噪比和信号采样点数变化导致的变换输出信噪比的恶化问题,本文进行了深入研究。分析了输入数据点数(data number)、输入信号信噪比(Input SNR)和变换输出信噪比(Output SNR)之间的联系,得出了三者之间的数学关系。在此基础上,研究使用PWV提高WHT变换输入信噪比,建立了PWHT算法模型。同时,研究使用数据域插值提高PWHT变换可用数据点数的算法。
通过上述改进算法,有效改善了Wigner-Hough变换分析LFM信号输出性能。
(5)优化的时频分析方法在工程中的实际应用
结合工程项目实例,将本文的算法进行了有效应用,具体包括:
其一:工业电机控制系统中电网电流电压的非平稳特征分析
本小节中对于电机整流调速控制系统中由于整流系统和电机运行状态的变化引起的电网电压电流非平稳信号进行分析。
通过第三章所述的小波包算法及其优化过程,对电机整流调速控制系统中电网电压的暂降、电流的时变及其谐波成分进行了有效的分析。
其二:强噪声背景下LFM信号的分析
本小节对于工程实例中强噪声背景下的LFM信号进行分析。
利用第四章所述优化的Wigner-Hough变换,对于强噪声背景下LFM信号的特征提取和数值进行了有效分析,验证了算法的实用性。
Strictly speaking, the natural signals are all nonstationary signals. How to measure these kinds of signals and estimate their characteristics effectively is widely discussed by the researchers in measurement domain.
The classic signal procession methods describe the signals in the time or frequency domain separately. Since the characteristics of nonstationary signals are varying by time, the traditional approaches are less effective.
Time-Frequency Joint Analysis (TFJA) theory works more effectively in nonstationary signal analysis. It analyzes the signals in the time-frequency joint domain. The time-varying characteristics of nonstationary signals can be effectively extracted through the TFJA.
In this thesis, various nonstationary signals analyzing approaches in the measurement system are discussed:
(1) The aliasing restraining of the limited bandwidth nonsationary signals analysis based on the Short Time Fourier Transform
Firstly, the performance of nonstationary signal analyzed by STFT is discussed, and the result shows that STFT can extract the characteristics of limited bandwidth signals effectively.
And then, an optimized algorithm is proposed to restrain the aliasing. The physical essence of occurred aliasing is discussed. The filter window selected technical is described. Based on the interpolation method in the frequency domain, the STFT is optimized. Using the Newton iterative method, the fast computation of algorithm is implemented.
(2) The research of the frequency band leakage and oscillation of the transient signals processing based on the Wavelet Packet Transform (WPT)
In this section, aiming at the leakage occurred during the WPT, an optimized algorithm is proposed.
Firstly, the performance of the WPT analysis of the nonsationary transient signals is discussed, and the advantage is pointed out. The leakage caused by the incompactly support of the function is investigated.
And then a novel optimized algorithm in time domain is brought forward. By the algorithm, the compact support character in frequency domain of wavelet packet function is reserved, and the performance in time domain is improved. The simulation proved the effectiveness of the algorithm.
(3) The research of "limited data length effect" in the WPT
Because the essence of the WPT is a kind of "windowed" transform, during the course of analyzing the signal, the sampled data should be truncated inevitably. The truncation causes the "limited data length effect", and brings on the band leakage.
Aiming at this problem, based on the Gibbs theory, a kind of WPT frequency filter interpolation algorithm is bring forward to suppress those unwanted effect. The fast computation of interpolation is implemented, and the quantity of interpolating points is discussed.
(4) The research on the output Signal-to-Noise Ration (SNR) of the Wigner-Hough Transform (WHT) in the Linear Frequency Modulation (LFM) signal detection
The advantage and disadvantage of using WHT to detect the multi-component LFM signals are discussed.
Output SNR is deteriorated because the varying of the signal input SNR and the available data number. Aiming at these deteriorative factors, the thesis researches the relation of the factors in depth. The mathematic relation of them is deducted. A novel algorithm is brought forward based on the PWHT and interpolation. The simulation result proves the effectiveness of the algorithm.
(5) The application of the algorithms in engineering projects
The algorithms in this thesis are validated in engineering projects.
Firstly, the nonsatationary characteristics of voltage and current that are caused by industry electromotor control system in the power system are researched.
An engineering test model is set up to validate the algorithm in the 3~(rd) chapter.
The industry electromotor control system is used in this model. Because the trigger angle and the load of the motor are varying by time, the voltage and current in power system are changing too. Applied the optimized WPT in chapter 3, the characters of the varying voltage and current can be extracted effectively.
Secondly, a project is set up to validate the algorithm in the 4~(th) chapter.
Applied the optimized WHT algorithm, the parameters of multi-components LFM signals in strong noise background can be correctly extracted, and the time varying characters of signals are shown clearly.
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