In an earlier work, we introduced a new form of signal representation called the pseudo power signature (PPS) that was essentially independent of the duration of the signal. The signatures were obtained based on the continuous wavelet transform, and were shown to be reliable and discriminating for classification purposes. In this paper, we take a fresh look at the problem of obtaining PPS by carrying out our analysis in the frequency domain. The main advantages of this approach over our earlier one, are that it is more versatile, permits the development of efficient computational algorithms, offers a solution to some unresolved uniqueness problems in our original formulation, and allows the study of the effect of the choice of analyzing wavelet to better aid the classification process.