A note on Unser-Zerubia generalized sampling theory applied to the linear interpolator

In this correspondence, we calculate the condition number of the linear ope rator that maps sequences of samples f(2k), f(2k + a), k is an element of Z of an unknown continuous f is an element of L-2 (R) consistently (in the s ense of the Unser-Zerubia generalized sampling theory) onto the set of cont inuous, piecewise linear functions in L-2 (R) with nodes at the integers as a function of a is an element of(0, 2). It turns out that the minimum cond ition numbers occur at a = root 2/3 and a = 2 - root 2/3 and not at a = 1 a s we might have expected.