A link between shape and phase

Signals can be treated as ordered sets and shape as a property of the order. It is shown that the degree of asymmetry or relative contrast of various ordered subsets is a good measure of this property. Statistical measures provide robustness while shape measures provide sensitivity to changes in order. The concept of phase is examined within this framework. What shape information is found in the instantaneous phase? A relationship between instantaneous phase and a measure of shape is derived. Moments, Fourier and wavelet transforms, edges and segments are examined from the new perspective on measures of shape and robustness