CONSISTENT SAMPLING WITH MULTI-, PRE- AND POST-FILTERINGS

Abstract

We consider the approximate consistent sampling process in the space L-2(R) of signals of finite energy, where multi-, pre- and post-filters {h(i)}(i=1)(M) and {phi(j)}(j=1)(N) are from L-2(R). We take {(f * h(i))(qk) vertical bar 1 <= i <= M, k is an element of Z} as measurements(or generalized samples) of an input signal f and then seek its consistent approximation (f) over bar in the reconstruction space V(Phi), which is a shift-invariant subspace of L-2(R) generated by N post-filters {phi(j)}(j=1)(N). Here q = m/n is a rational number and the consistency means that f and (f) over bar have the same measurements. We find equivalent conditions for the existence of such consistent approximation in L-2(R) together with some relevant properties such as performance analysis.