Cross-term Reduction Using Wigner Hough Transform and Back Estimation

This paper presents some algorithms to reduce the cross-terms, which are unfortunate mathematical artifacts in the calculation of Wigner Ville Distribution (WVD) of a multi-component signal. The experiments are carried out for linear FM signals which have a line representation in the spectral domain. When the WVD of a multi-component signal is calculated, sometimes the cross-terms will show higher peaks compared to the main signal components. There have been many methods proposed to filter out these cross terms, so that the signal can be precisely represented in the time-frequency domain. In this paper, a method based on Hough Transform is used for the same purpose. A line in the time-frequency domain can be represented as a point in the Hough transformed domain. Once we identify the coordinates of this point in the transformed domain, we can estimate the properties of the line in the time-frequency domain which corresponds exactly to the actual signal components. This paper proposes a new idea of back estimation to filter out only the components corresponding to cross-terms from the time-frequency domain of WVD. This paper also briefs about the implementation of the algorithms in Matlab for different values of signal to noise ratios.