多项式Wigner-Ville分布的频域卷积实现
doi: 10.3724/SP.J.1146.2006.01835
Realization of the Polynomial Wigner-Ville Distribution (PWVD) Based On the Convolution In Frequency Domain
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摘要: 多项式Wigner-Ville分布(PWVD)是分析多项式相位信号(PPS)时频特性的一种有力工具。该文根据PWVD的结构特点，提出一种通过频域卷积来实现PWVD的方法，将其分解成一系列Wigner-Ville分布(WVD)或L-Wigner-Ville分布(LWVD)的卷积，而WVD或LWVD可由短时Fourier变换(STFT)来计算，这样既可消除信号分量间的互交叉项影响，同时又保持较高的时频聚集性。文中分析了该算法的离散实现方法以及相应的计算量，并通过计算机仿真实验验证了该算法的有效性。Abstract: The Polynomial Wigner-Ville Distribution (PWVD) is a time-frequency signal analysis tool for representing Polynomial Phase Signal (PPS). An algorithm for implementation of the PWVD based on the convolution in frequency domain according to the structure of the PWVD is presented in this paper. By decomposing the PWVD into a series of convolutions of WVD or LWVD, the cross-terms can be reduced just because the WVD or LWVD can be calculated by the STFT, which is a linear transform. At the same time, the PWVD have a high time frequency convergence. The discrete implementation method and the corresponding computation complexity are analyzed and the effectiveness of the method is illustrated with numerical examples.
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