Instantaneous scale and the short-time scale transform

The concept of instantaneous scale, c_i, is developed and it is shown that it is given by c_i=tØ´(t) where Ø´( t) is the derivative of the phase of the signal. Formulas for average scale, scale bandwidth, and scale group delay are obtained. The scale transform, the short time scale transform, the analytic scale signal, and other related concepts are defined