多分量线性调频信号的时频分析
|
摘要
在对大量实测ISAR飞机成像数据的研究中，我们发现，由于飞机的飞行速
度及姿态的变化，目标各散射点回波是非平稳的，许多情况下，可近似为多分量
线性调频信号。因此，对于机动飞行的飞机，传统的傅立叶交换成像法已不适用，
而是要设法获得各散射点正确的时频结构，进行目标的瞬时成像。
线性调频信号这种大时宽带宽积信号，不仅常出现在，也广泛应用于雷达、
声纳、通信、医学、地震探测等等众多信号处理领域中，因而，对线性调频信号
展开讨论，具有理论意义和实用价值。
对于非平稳信号，时频分布提供了一种更为直接且有效的手段，以获得其时
频结构。然而，在有多分量信号存在时，时频分布中交叉项的出现，却严重影响
了信号时变谱规律的可分辨性和可解释性。抑制交叉项，一直是时频分布研究领
域中一个棘手的问题，也是时频分布得以更广泛应用于各信号处理领域所要克服
的困难。
本文针对多分量线性调频信号，着重探讨如何抑制多分量线性调频信号时频
分布中交叉项的问题，以期获得具有高时频分辨力的时频结构图。全文主要从两
个角度出发来抑制交叉项的影响。一是基于模糊域自适应信号来设计核函数，获
得自适应核的时频分布；二是将多分量信号分解，并分别对被分解后的各子分量
进行时频分析。主要工作概述如下：
◇ 针对多分量线性调频信号，提出了一种新的自适应核时频分布—自适应高斯
核分布（AGD），采用高斯型核函数，并基于信号模糊域的特点，自适应设
计核函数，给出了简单而有效的核函数估计准则。仿真数据及实测ISAR飞
机成像数据的实验结果表明，采用自适应高斯核分布，能够较好地抑制多分
量线性调频信号时频分布中的交叉项，同时，保持了较高的信号时频聚集度。
利用AGD的时频分析结果对实测数据进行瞬时成像，能够较清晰地反映目
标的飞行姿态。
◇ 以自适应高斯核分布为例，分析了基于模糊域自适应设计核函数的时频分布
以及核参数的估计对信号自身项及交叉项的影响，从而说明自适应核相对于
固定核的优势所在。总结了基于模糊域自适应设计多分量线性调频信号核函
－11 多分量线性调频信号的时频分析
一
数的一般方法，分析了不同类型核函数的选取对时频分布的影响，进而说明
己有的一些基于模糊域自适应设计核函数的方法所存在的缺陷。
4 借鉴“ CLEAN”快速谱估计算法的思想。针对各分量具有不同持续长度、包
络缓变的多分量线性调频信号，提出了一种基于频域“CLEAN”分离多分量
信号，从而抑制其Wgner分布中交叉项的方法，简称其为FC－WVD。详细介
绍了该方法的原理及实现过程，并讨论了基于信号频域采用滤波技术提取信
号分量对信号中各分量及其WgnCr分布的作用和影响。仿真及实测ISAR成
像数据的实验结果表明，FC－WVD在提高信号时频分辨力、抑制交叉项的干
扰方面，有着令人较为满意的表现。该方法也适用于处理近似的正弦或线性
调频信号，这一点在实际应用中更有意义。
个 分析了频域“ CLEAN”与分数阶傅立叶变换和 Radon－Wgner变换（RWT）
的关系，并讨论了FC－WVD与RWT－滤波反投影的相似与不同。这些分析，
使得FC－WVD更具有理论意义。
个 依照自适应投影分解法的思想，针对多分量线性调频信号，以高斯型线性调
频小波作为基函数，提出一种简单而有效的自适应线调频小波基估计算法。
分析了算法的适用范围，实验结果证明了算法的有效性和准确性。采用该算
法可更好地恢复信号中各分量的时频信息，因而对各基函数分别进行时频分
析，可得到原信号具有高时频分辨力的时频分布。
The studies of real-world ISAR imaging data of airplanes indicate that, because of
the time-varying speeds and poses of the targets, the scatters?signals are nonstationary,
which in many cases can be approximated as multicomponent Linear Frequency-
Modulated signals( LFM, Chirp). Therefore, for the maneuvering targets, it is necessary
to obtain the correct time-frequency structure of each scatter for instantaneous imaging.
LFM signal not only appears but also is widely used in multitudinous signal
processing areas, such as Radar. Communications, Sonar, Medicine, and so on, which
makes its studies meaningful in both theories and applications.
Time-frequency Distribution (TFD) provides a direct and effective way to analyze
the time-frequency structures of nonstationary signals. The crossterms, however, which
arise in the TFD of multicomponents, make it difficult to identify and explain the tine-
varying spectrum of each component. Suppression of the crossterms is always -a hot
potato in time-frequency analysis.
With respect to multicomponent LFM signals, the dissertation is mainly concerned
with looking for ways to suppress the crossterms appearing in the TFD of
multicomponent signals, in order to obtain a TFD with high time-frequency resolution.
The following is the summarization of the main work:
<~- With respect to multicomponent LFM signals, a new kind of TFD-ada~ve
Gaussian kernel distribution (AGD), is proposed. in which the Gaussian kem~l is
designed adaptively based on the signals ambiguity function. A simple and
effective algorithm to estimate the kernel is given, and the experiments with
simulated and real-world data confirm the effects of the AGD in suppressing
crossterms and keeping high time-frequency concentration.
~- With the AGD as an example. the influence of the adaptive-kernel distribution
based on ambiguity domain and the kernel estimation on the crossterms and
signalterms is analyzed, which consequently explains the advantages of adaptive
kernels over fixed kernels. The method to adaptively design kernel based on the
-Iv-
ambiguity function of muliticomponent LFM signals is generalized and the effect
of different kind of kernels on TFD is also discussed.
~ Based on the 揅LEANZ~ algorithm, with respect to muliticomponent LFM signals.
in which each component has slowly-varying envelope and different time duration,
a new method called FC-WVD to suppress crossterrns in Wigner distribution is
presented. The basic idea of FC-WVIY is to first decompose the multicomponents
into separate subcomponents by use of band-pass filters with the 揅LEAN?
algorithm in frequency domain, and then each subcomponent is analyzed using
TFD. The influence of the band-pass filter on different component and its Wigner
distribution is discussed in detail, and the experiment with simulated and real-
world cl~a show satisfactory results of the FC-WVD in improving the time-
frequency resolution of multieomponent signals. FC-WVD is also suitable for the
time-frequency analysis of signals close to LFMs?or sinusoids.
~ The relationship between the decomposition algorithm based on the 揅LEAN?in
the frequency domain and the Fractional Fourier Trax~form (FRFT), the Radon-
Wigner Transform (RWT) is analyzed. Furthermore, the comparison between FC-
WVD and RWI?Filtered Back-projection algorithm is n~mde. These work makes the
FC-WVD method more meaningful
度及姿态的变化，目标各散射点回波是非平稳的，许多情况下，可近似为多分量
线性调频信号。因此，对于机动飞行的飞机，传统的傅立叶交换成像法已不适用，
而是要设法获得各散射点正确的时频结构，进行目标的瞬时成像。
线性调频信号这种大时宽带宽积信号，不仅常出现在，也广泛应用于雷达、
声纳、通信、医学、地震探测等等众多信号处理领域中，因而，对线性调频信号
展开讨论，具有理论意义和实用价值。
对于非平稳信号，时频分布提供了一种更为直接且有效的手段，以获得其时
频结构。然而，在有多分量信号存在时，时频分布中交叉项的出现，却严重影响
了信号时变谱规律的可分辨性和可解释性。抑制交叉项，一直是时频分布研究领
域中一个棘手的问题，也是时频分布得以更广泛应用于各信号处理领域所要克服
的困难。
本文针对多分量线性调频信号，着重探讨如何抑制多分量线性调频信号时频
分布中交叉项的问题，以期获得具有高时频分辨力的时频结构图。全文主要从两
个角度出发来抑制交叉项的影响。一是基于模糊域自适应信号来设计核函数，获
得自适应核的时频分布；二是将多分量信号分解，并分别对被分解后的各子分量
进行时频分析。主要工作概述如下：
◇ 针对多分量线性调频信号，提出了一种新的自适应核时频分布—自适应高斯
核分布（AGD），采用高斯型核函数，并基于信号模糊域的特点，自适应设
计核函数，给出了简单而有效的核函数估计准则。仿真数据及实测ISAR飞
机成像数据的实验结果表明，采用自适应高斯核分布，能够较好地抑制多分
量线性调频信号时频分布中的交叉项，同时，保持了较高的信号时频聚集度。
利用AGD的时频分析结果对实测数据进行瞬时成像，能够较清晰地反映目
标的飞行姿态。
◇ 以自适应高斯核分布为例，分析了基于模糊域自适应设计核函数的时频分布
以及核参数的估计对信号自身项及交叉项的影响，从而说明自适应核相对于
固定核的优势所在。总结了基于模糊域自适应设计多分量线性调频信号核函
－11 多分量线性调频信号的时频分析
一
数的一般方法，分析了不同类型核函数的选取对时频分布的影响，进而说明
己有的一些基于模糊域自适应设计核函数的方法所存在的缺陷。
4 借鉴“ CLEAN”快速谱估计算法的思想。针对各分量具有不同持续长度、包
络缓变的多分量线性调频信号，提出了一种基于频域“CLEAN”分离多分量
信号，从而抑制其Wgner分布中交叉项的方法，简称其为FC－WVD。详细介
绍了该方法的原理及实现过程，并讨论了基于信号频域采用滤波技术提取信
号分量对信号中各分量及其WgnCr分布的作用和影响。仿真及实测ISAR成
像数据的实验结果表明，FC－WVD在提高信号时频分辨力、抑制交叉项的干
扰方面，有着令人较为满意的表现。该方法也适用于处理近似的正弦或线性
调频信号，这一点在实际应用中更有意义。
个 分析了频域“ CLEAN”与分数阶傅立叶变换和 Radon－Wgner变换（RWT）
的关系，并讨论了FC－WVD与RWT－滤波反投影的相似与不同。这些分析，
使得FC－WVD更具有理论意义。
个 依照自适应投影分解法的思想，针对多分量线性调频信号，以高斯型线性调
频小波作为基函数，提出一种简单而有效的自适应线调频小波基估计算法。
分析了算法的适用范围，实验结果证明了算法的有效性和准确性。采用该算
法可更好地恢复信号中各分量的时频信息，因而对各基函数分别进行时频分
析，可得到原信号具有高时频分辨力的时频分布。
The studies of real-world ISAR imaging data of airplanes indicate that, because of
the time-varying speeds and poses of the targets, the scatters?signals are nonstationary,
which in many cases can be approximated as multicomponent Linear Frequency-
Modulated signals( LFM, Chirp). Therefore, for the maneuvering targets, it is necessary
to obtain the correct time-frequency structure of each scatter for instantaneous imaging.
LFM signal not only appears but also is widely used in multitudinous signal
processing areas, such as Radar. Communications, Sonar, Medicine, and so on, which
makes its studies meaningful in both theories and applications.
Time-frequency Distribution (TFD) provides a direct and effective way to analyze
the time-frequency structures of nonstationary signals. The crossterms, however, which
arise in the TFD of multicomponents, make it difficult to identify and explain the tine-
varying spectrum of each component. Suppression of the crossterms is always -a hot
potato in time-frequency analysis.
With respect to multicomponent LFM signals, the dissertation is mainly concerned
with looking for ways to suppress the crossterms appearing in the TFD of
multicomponent signals, in order to obtain a TFD with high time-frequency resolution.
The following is the summarization of the main work:
<~- With respect to multicomponent LFM signals, a new kind of TFD-ada~ve
Gaussian kernel distribution (AGD), is proposed. in which the Gaussian kem~l is
designed adaptively based on the signals ambiguity function. A simple and
effective algorithm to estimate the kernel is given, and the experiments with
simulated and real-world data confirm the effects of the AGD in suppressing
crossterms and keeping high time-frequency concentration.
~- With the AGD as an example. the influence of the adaptive-kernel distribution
based on ambiguity domain and the kernel estimation on the crossterms and
signalterms is analyzed, which consequently explains the advantages of adaptive
kernels over fixed kernels. The method to adaptively design kernel based on the
-Iv-
ambiguity function of muliticomponent LFM signals is generalized and the effect
of different kind of kernels on TFD is also discussed.
~ Based on the 揅LEANZ~ algorithm, with respect to muliticomponent LFM signals.
in which each component has slowly-varying envelope and different time duration,
a new method called FC-WVD to suppress crossterrns in Wigner distribution is
presented. The basic idea of FC-WVIY is to first decompose the multicomponents
into separate subcomponents by use of band-pass filters with the 揅LEAN?
algorithm in frequency domain, and then each subcomponent is analyzed using
TFD. The influence of the band-pass filter on different component and its Wigner
distribution is discussed in detail, and the experiment with simulated and real-
world cl~a show satisfactory results of the FC-WVD in improving the time-
frequency resolution of multieomponent signals. FC-WVD is also suitable for the
time-frequency analysis of signals close to LFMs?or sinusoids.
~ The relationship between the decomposition algorithm based on the 揅LEAN?in
the frequency domain and the Fractional Fourier Trax~form (FRFT), the Radon-
Wigner Transform (RWT) is analyzed. Furthermore, the comparison between FC-
WVD and RWI?Filtered Back-projection algorithm is n~mde. These work makes the
FC-WVD method more meaningful
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