An Extension of the Class Of Unitary Time-Warping Projectors To Discrete-Time Sequences

This paper establishes a new coherent framework to extend the class of unitary warping operators (R. Baraniuk, 1995) to the case of discrete-time sequences. Providing some a priori considerations on signals, we show that the class of discrete-time warping operators finds a natural description in linear shift-invariant spaces. On such spaces, any discrete-time warping operator can be seen as a non-uniform weighted resampling of the original signal. Then, gathering different results from the non-uniform sampling theory, we propose an efficient iterative algorithm to compute the inverse discrete-time warping operator and we give the conditions under which the warped sequence can be inverted. Numerical examples show that the inversion error is of the order of the numerical round-off limitations after few iterations