Improved precision of fixed-point algorithms by means of common factors

We describe a general technique for improving the precision of fixed-point implementations of signal processing algorithms (such as filters, transforms, etc.) relying on the use of "common factors". Such factors are applied to groups of real constants in the algorithms (e.g. filter coefficients), turning them into quantities that can be more accurately approximated by dyadic rational numbers. We show that the problem of optimal design of such approximations is related to the classic Diophantine approximation problem, and explain how it can be solved and used for improving practical designs.