Infinity-Norm Rotation Transforms

Abstract

Abstract-A new general paradigm of dynamic-range-preserving one-to-one mapping-infinity-norm rotations, analogous to the general 2-norm rotations, are proposed in this paper. Analogous to the well-known discrete cosine transforms, the linear 2-norm rotation transforms which preserve the 2-norm of the rotated vectors, the proposed infinity-norm rotation transforms are piecewise linear transforms which preserve the infinity-norm of vectors. Besides the advantages of perfect reversibility, in-place calculation and dynamic range preservation, the infinity-norm rotation transforms also have good energy-compact ability, which is suitable for signal compression and analysis.