Pseudo affine wigner distributions: definition and kernel formulation

In this paper we introduce a new set of tools for timevarying spectral analysis: the pseudo affine Wigner distributions. Based on the affine Wigner distributions of J. and P. Bertrand these new time-scale distributions support efficient on-line 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 we extend the definition of this class by introducing the notion of a natural generator.