Symmetric basis functions and their unitary transforms

It is shown that continuous functions obtained from symmetric contours generalize into functions whose magnitude component r(t) is some function of a trigonometric polynomial. The authors consider this general set of functions and show that they form a Reisz basis for L/sup 2/(a,b). The compaction efficiency of the unitary transforms obtained from sampling these functions depends on the sampling grid and on the symmetry of the functions rather than on its functional form. This symmetry can be used to obtain fast transforms. The fact that such a family can be parametrized makes it extremely suitable for adaptive algorithms in coding, computer vision, and pattern analysis.<>