Abstract

Abstract—Except some extremely special cases, signal resampling was generally considered to be irreversible because of strong attenuation of high frequencies after interpolation. In this paper, we prove that signal resampling based on polynomial interpolation can be reversible even for integer signals, i.e., the original signal can be reconstructed losslessly from the resampled data. By using matrix factorization, we also propose a reversible method for uniform shifted resampling and uniform scaled and shifted resampling. The new factorization yields three elementary integer-reversible matrices. The method is actually a new way to compute linear transforms and a lossless integer implementation of linear transforms with the factor matrices. It can be applied to integer signals by in-place integer-reversible computation, which needs no auxiliary memory to keep the original sample data for the transformation during the process or for “undo ” recovery after the process. Some examples of low-order resampling solutions are also presented in this paper and our experiments show that the resampling error relative to the original signal is comparable to that of the traditional irreversible resampling. Index Terms—Factorial polynomials, integer-to-integer transforms, PLUS factorization of matrices, resampling, Stirling

Citations