Realisation of a 2-dimensional f.i.r. digital filter using separable filters

The scheme for the expansion of a 2-dimensional f.i.r. digital filter function into a sum of separable functions is generalised. Using the generalised procedure a m × m order filter function can be expressed in as many as m!n!/(|m-n| + 1)! ways. Further it is also proved that the number of terms in the expansion will be equal to the rank of the matrix.