On the realization of 2-D orthogonal state-space systems

Synthesis of 2-D lossless FIR filter transfer function matrix

“…Obtained results show that it is possible to realize, so popular in image processing, 3x3 kernel filters using lossless structures. After the embedding, next steps would be Roesser model synthesis [13] and implementation using Givens rotations structures [15]. These steps determine future research directions for the authors.…”

“…However, if a system with equal number of inputs and outputs is required, it can be obtained for a state-space representation. An efficient technique for such a task is presented in [15].…”

Synthesis and Realization of 3-D Orthogonal FIR Filters Using Pipeline Structures

“…Next, we extend A UBU C UD to be a square matrix [27,29] which leads to final state space realization, given by …”

“…Each H e i (z h , z v ) is an single-input single-output system, so we can apply the algorithm presented in [27,28] to synthesize 2-D orthogonal state space equations, given by (11), spanned on 3-D. The factors k e i obtained from the 2-D synthesis are applied to the corresponding elements ofĤ d (z d ).…”

“…As (40) is a horizontal vector, it cannot satisfy (7). So, to obtain an orthogonal structure, we take into account a transposed version of (40) (10) which is a square matrix [27]. Then, the result is transposed back to the orthogonal realization of (40), which is 1-D state space equations (9) spanned on 3-D (dimensions h and v are not processed), given by…”