Minimum FIR deconvolver orders for MIMO systems in one or several variables

The problem of computing exact finite impulse response (FIR) inverses for multiple-input multiple-output (MIMO) FIR systems is considered. Results allow for arbitrary n-dimensional inputs and outputs and thus are applicable to time signals, images and video. A generic bound on the orders of the inverse filters is derived and is shown to be approximately inversely proportional to the ratio of the number of outputs to that of inputs. Further, the bounds are shown to be sharp for many special cases of practical interest.