This theorem indicates the presence of a maximum at the finer scales where a singularity occurs. In the general case, is sequence of modulus maxima is detected which converges to the singularity. A PDF file shows the connection between wavelet modulus maxima and the signal singularities. When the wavelet is the n th derivative of a gaussian, the maxima curves are connected and go through all of the finer scales. The modulus maxima are displayed as a function of the scale in log-log axes, and the slope gives the estimated singularity order.
Fine scales are on the left.