Discrete Wigner-Ville Distribution with Wide Frequency Observation Range

Abstract

The Wigner-Ville distribution (WVD) is a high-resolution time-frequency analysis method. However, the discrete WVD (DWVD) has the problem of a narrow frequency observation range. This is because the time sampling of the symmetric instantaneous auto-correlation function (SIAF) changes simultaneously in the positive and negative directions. As a result, the sampling period of the SIAF in the case of DWVD is doubled and the frequency observation range is halved. Therefore, we propose a DWVD that does not narrow the frequency observation range. Specifically, when deriving the SIAF, in addition to the conventional sample that varies in both the positive and negative directions, we consider a sample averaged over two samples that vary only in the positive or negative direction. The proposed process allows the DWVD to be performed without halving the frequency observation range. However, this process causes a small aliasing component, which can be reduced by the use of window functions. This study will demonstrate this effect by using the proposed method for chirp waveforms.