Multichannel Sampling of Parametric Signals with a Successive Approximation Property

Recently the sampling theory for certain parametric signals based on rate of innovation has been extended to all sampling kernels that satisfy the Strang-Fix conditions, thus including many attractive choices with finite support. We propose a new sampling scheme in which samples are taken simultaneously at the outputs of multiple channels. This new scheme is closely related to previously known cases, but provides a successive approximation property that can be used for detecting undermodeling. We also draw connections to splines and multi-scale sampling of signals.