Approximation of 2-D separable in denominator filters

The use of strictly causal filters in the approximation of two-dimensional asymmetric half-plane filters

“…Let the filter to approximate the impulse response (1) be specified as ?j) + B u(i j) ,j) HI 0 ' I> i,j>O (2) where xh(i, j) is the n ~1 horizontal state vector, x"(i, j) is the m x 1 vertical state vector, u(i, j) is the y x 1 input vector, v(i, j) is the X ~1 output vector, and A,, A,, A,, B, C are real constant matrices of appropriate dimensions. The filter (2) is a special form of the Roesser state-space model [6] and is simpler than one used in [5]. This filter also includes the Attasi state-space model [7], [ll].…”

“…In this example [l], [5] the problem is to approximate the impulse response of the "Gaussian Filter" given by Fig. 1.…”

“…1. The other results of the application of the algorithm to this example are summarized in comparison with [l], [5] in Table I and the number of parameters is given in terms of a rational transfer function. Table I shows that the resulting filter does not have a better approximation than that in 151 in the case where the filter order is -_ _ .…”

“…This mapping technique enables one to use an algorithm for designing quarter-plane causal 2-D digital filters for the purpose of designing asymmetric half-plane weakly causal 2-D digital filters [2]. Lashgari et al [5] has presented a technique based on singular value decomposition to approximate a quarter-plane causal 2-D digital filter by one being separable in the denominator. This technique is used for the approximation in PI.…”

“…The data in the transfered domain (open first quadrant) are approximated by a strictly causal 2-D digital filter being separable in the denominator. This is done via singular value decomposition of two finite Hankel matrices as in [5], [ll]. Finally, the resultant filter is transfered back to the original coordinates.…”