1. A lossless data transformation system for transforming input data into rotated transformed data, the system for use in data communications equipment for maintaining data fidelity, the system comprising, one or more process units adapted to implement at least portions of a shared Haar transform and an appended transform, the shared Haar transform for transforming the input data into Haar transformed data, and the appended transform for transforming the Haar transformed data into the rotated transform data, the rotated transform data is lossless transform data in inverse transformation to the input data.