Applied Mathematics and Computation vol:62 issue:2-3 pages:259-277
The invertibility and propagation properties of binary shift-invariant transformations are treated. Linear shift-invariant transformations can be modeled by polynomial multiplication modulo 1 + x(n). Nonlinear transformations require a more ad hoc approach. A distinction is made between ''local'' invertibility and ''global'' invertibility. Proofs of invertibility are given for a number of examples in the form of an algorithm to compute the inverse transformation. Multiplication modulo 2n-1 by a constant is shown to be a shift-invariant transformation.