Approximation Error of Shifted Signals in Spline Spaces

Spline signal spaces offer several advantages for the representation of signals compared with the more traditional signal spaces of bandlimited signals. Among them are the finite support of B-splines, simple manipulations like differentiation and integration, etc. A major disadvantage, however, is that spline signal spaces are not closed under signal shifts. In order to assess the approximation error introduced by shifting a spline signal, the approximation error norm and its average are evaluated. Furthermore, an upper bound on the expected normalized approximation error is derived using Reid’s inequality.