Ajem. Janssen et T. Kalker, A note on Unser-Zerubia generalized sampling theory applied to the linear interpolator, IEEE SIGNAL, 47(8), 1999, pp. 2332-2335
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.