Theory of the generalized interpolation of approximately band-limited signals

摘要

In this paper, we present some sets of signals for which the optimum discrete n-dimensional interpolation functions ψ{sub}k (n) (n = integer vectors ) exist which minimize various measures of approximation error defined at discrete sample points X{sub}n = n (n = integer vectors ), simultaneously. The presented discrete interpolation functions ψ{sub}k (n) (n = integer vectors) vanish outside the prescribed domain in the integer-vector space. Hence, these interpolation functions are realized by multi-dimensional FIR filters. Besides, these interpolation functions satisfy the discrete orthogonality. Further, the interpolation functions have much flexibility in their frequency characteristics if appropriate analysis filters are selected. These features of the presented theory will be useful in applying those results to UWB radars and so on.