Reducing the dynamic range of lifting-based quaternion multipliers

Structural transformations are studied which facilitate finite-precision implementation of lifting-based quaternion multipliers. The idea is to substitute the original multiplier with that whose hypercomplex coefficient has permuted parts. The latter multiplier needs only simple pre- and postprocessing to play the role of the former, and the permutation can be selected so that the real coefficients of the corresponding lifting scheme have reduced dynamic ranges, which simplifies fixed-point scaling.