Pseudo Affine Spectral Correlation Analysis: Definition and the Kernel Formulation

In this paper, we introduce a new set of tools for spectral correlation analysis: the pseudo affine spectral correlation analysis. Based on the affine Wigner distributions of J. and P. Bertrand and the pseudo affine Wigner distribution of Paulo Goncalves, these new spectral correlation analysis support efficient online operation at the same computational cost as the continuous wavelet transform. Moreover, they take advantage of the proportional bandwidth smoothing inherent in the sliding structure of their implementation to suppress cumbersome interference components. To formalize their place within the echelon of the affine class of time-scale distributions (TSD´s), we introduce and study an alternative set of spectral correlation generators and kernel for this class