New 2D FIR direct-form minimal circuit and state-space filter structures

This paper examines newly formed two dimensional (2D) direct-form finite impulse response (FIR) structured digital filters, with a minimal number of delays. These filters also have an minimal state-space vector. The three new arrangements include delay elements on the top or the bottom of the structure, delays equally split between the top and the bottom, and delays having alternating orientation. It is noted that all filter structures share the same transfer function while their state-space realizations are different. In addition, second-order 2D representations are provided in order to show to the reader the overall internal structures of the circuit and state-space realization FIR digital filters for comparison purposes.