This paper describes a general solution to the system identification problem. The technique is referred to as ‘ intermediate domain processing ’ and can result in faster and more efficient computations. The paper begins by outlining a general theory of translation invariant linear systems. By making specific choices within this general framework, different special cases can be derived. A method is developed which facilitates the conversion between data vectors associated with each of these special cases. This conversion technique is used in deriving a generalized solution to the system identification problem. A practical example is considered in which the unknown system is assumed to be time invariant linear (TIL), whereas computations are carried out in the domain of an equivalent and computationally advantageous dyadic invariant linear (DIL) system.