Sampling at Minimum Sampling Rate for Signals in Shift Invariant Spaces

This paper is focus on to design a sampling system with minimum sampling rate for signals in the shift invariant Hilbert space. To achieve this goal, we propose a method to calculate the rate of innovation (RI) of signals in the Hilbert space. The RI is then used to identify a suitable sampling kernel as well as the sampling rate for a specific signal. We show that the RI of the kernel should be greater or equal to the RI of the signal for the signal to be perfectly reconstructible. The minimum sampling rate depends on the RI of the signal. Examples are included to demonstrate how our method is applied to calculate the RI. Some known sampling theories can also be fitted into the framework of sampling system with minimum sampling rate.