A GENERAL SAMPLING THEORY FOR NONIDEAL ACQUISITION DEVICES

We first describe the general class of approximation spaces generated by translation of a function rho(x), and provide a full characterizati on of their basis functions. We then present a general sampling theore m for computing the approximation of signals in these subspaces based on a simple consistency principle. The theory puts no restrictions on the system input which can be an arbitrary finite energy signal; bandl imitedness is not required. In contrast to previous approaches, this f ormulation allows for an independent specification of the sampling (an alysis) and approximation (synthesis) spaces. In particular, when both spaces are identical, the theorem provides a simple procedure for obt aining the least squares approximation of a signal. We discuss the pro perties of this new sampling procedure and present some examples of ap plications involving bandlimited, and polynomial spline signal represe ntations. We also define a spectral coherence function that measures t he ''similarity'' between the sampling and approximation spaces, and d erive a relative performance bound for the comparison with the least s quares solution.