Asymmetric Multichannel Sampling in Shift Invariant Spaces
Résumé
We consider a multi-channel sampling with asymmetric sampling rates in shift invariant spaces, while related previous works have supposed that each channel has a symmetric (uniform) sampling rate. Motivated by the fact that shift invariant spaces are isomorphic images of L2[0; 2pi], we obtain a sampling expansion in shift invariant spaces by using frame or Riesz basis expansion in L2[0; 2pi]. The samples in the expansion are expressed in terms of frame coefficients of an appropriate function with respect to a certain frame in L2[0; 2pi]. The involved reconstruction functions are given explicitly by using the frame operator. We also present relation between asymmetric multichannel sampling and symmetric one.
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