Title :
Reproducing kernel structure and sampling on time-warped Kramer spaces
Author :
Azizi, Shahrnaz ; Cochran, Douglas
Author_Institution :
Dept. of Electr. Eng., Arizona State Univ., Tempe, AZ, USA
Abstract :
Given a signal space of functions on the real line, a time-warped signal space consists of all signals that can be formed by composition of signals in the original space with an invertible real-valued function. Clark´s (1985) theorem shows that signals formed by warping bandlimited signals admit formulae for reconstruction from samples. This paper considers time warping of more general signal spaces in which Kramer´s (1959) generalized sampling theorem applies and observes that such spaces admit sampling and reconstruction formulae. This observation motivates the question of whether Kramer´s theorem applies directly to the warped space, which is answered affirmatively by introduction of a suitable reproducing kernel Hilbert space structure. This result generalizes one of Zeevi (1993), who pointed out that Clark´s theorem is a consequence of Kramer´s
Keywords :
bandlimited signals; signal reconstruction; signal sampling; Clark´s theorem; Kramer´s generalized sampling theorem; bandlimited signals; functions; invertible real-valued function; kernel sampling; real line; reproducing kernel Hilbert space structure; reproducing kernel sampling; reproducing kernel structure; signal reproduction; signal space; time-warped Kramer spaces; time-warped signal space; Convergence; Hilbert space; Kernel; Sampling methods; Signal processing; Signal sampling;
Conference_Titel :
Acoustics, Speech, and Signal Processing, 1999. Proceedings., 1999 IEEE International Conference on
Conference_Location :
Phoenix, AZ
Print_ISBN :
0-7803-5041-3
DOI :
10.1109/ICASSP.1999.756308