A method, including: obtaining a scale-depth or scale-time phase image of a continuous wavelet transform of an input signal, the scale-depth or scale-time phase image including oval-shaped circular patterns observed on the mirrored phase image; and extracting, with a computer, hierarchical multiscale intervals from the scale-depth or scale-time phase image, wherein the hierarchical multiscale intervals correspond to the oval-shaped circular patterns observed on the mirrored scale-depth or scale-time phase image of the continuous wavelet transform of the input signal. Another method includes: characterizing, with a computer, curve shapes of intervals of a signal using beta distribution; and visualizing and analyzing, with the computer, shape parameters of the curve shapes on a shape-parameter crossplot.