JOURNAL OF COMPUTERS (JCP)

ISSN : 1796-203X

Volume : 2 Issue : 6 Date : August 2007

**Toward The Use Of The Time–Warping Principle With Discrete–Time Sequences**

Arnaud Jarrot, Cornel Ioana, and André Quinquis

Page(s): 49-55

Full Text: PDF (457 KB)

**Abstract**

This paper establishes a new coherent framework to extend the class of unitary warping operators

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.

**Index Terms**

Time–frequency, Unitary equivalence, Implementation of time–warping operators, Non–stationary

filtering.

ISSN : 1796-203X

Volume : 2 Issue : 6 Date : August 2007

Page(s): 49-55

Full Text: PDF (457 KB)

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.

filtering.