A note on unser-zerubia generalized sampling theory for the linear interpolator

In this correspondence, we calculate the condition number of the linear operator mapping sequences of samples /(2fc), /(2fc+a),fc g Z of an unknown continuous / g L2 (R) consistently (in the senses of the Unser-Zerubia generalized sampling theory) onto the set of continuous, piecewise linear functions in L2(R) with nodes at the integers as a function of a g (0, 2). It turns out that the minimum condition numbers occur at a = √2/3 and a = 2 - √2/3 and not at a = 1, as we might have expected.