A pseudo-Bertrand distribution for time-scale analysis

Using the pseudo-Wigner time-frequency distribution as a guide, we derive two new time-scale representations: the pseudo-Bertrand and the smoothed pseudo-Bertrand distributions. Unlike the Bertrand distribution, these representations support efficient online operation at the same computational cost as the continuous wavelet transform. Moreover, they take advantage of the affine smoothing inherent in the sliding structure of their implementation to suppress cumbersome interference components.