Efficient realizations of two-dimensional quadratic digital filters

Realization structures of two-dimensional finite-support quadratic digital filters which are based on matrix decomposition are introduced. The resulting structures consist generally of a number of parallel branches which operate simultaneously and independently on a common input array. By proper decomposition of the coefficient matrix, each parallel branch can be realized by a two-dimensional finite impulse-response digital filter in cascade with a squaring operator. The lower-upper triangular decomposition and the singular value lower-upper decomposition is used in order to arrive at efficient structures with computational and hardware advantages.<>