Several methods for testing stability of first quadrant quarter-plane two dimensional (2-D) recursive digital filters have been suggested in 1970's and 80's. Though Jury's row and column algorithms, row and column concatenation stability tests have been considered as highly efficient mapping methods. They still fall short of accuracy as they need infinite number of steps to conclude about the exact stability of the filters and also the computational time required is enormous. In this paper, we present procedurally very simple algebraic method requiring only two steps when applied to the second order 2-D quarter - plane filter. We extend the same method to the second order Non-Symmetric Half-plane (NSHP) filters. Enough examples are given for both these types of filters as well as some lower order general recursive 2-D digital filters. We applied our method to barely stable or barely unstable filter examples available in the literature and got the same decisions thus showing that our method is accurate enough.

This paper treats the problem of realizing high speed 2-D denominator separable digital filters. Partitioning a 2-D data plane into square blocks, filtering proceeds block by block sequentially. A fast intra-block parallel processing method was developed using block state space realization, which allows simultaneous computation of all the next block states and the outputs of one block. As the block state matrix of the filter has high sparsity, the rows and columns are interchanged respectively to reduce the matrix size. The filter is implemented by a multiprocessor system, where for each matrix's row one processor is assigned to perform the row-column vector multiplication. All processors wirk in synchronized fashion. Number of processors of this implementation are equal to the number of rows of the reduced state matrix and throughput is raised with block lengths.

This paper proposes a technique for designing two-dimensional (2-D) digital filters approximating an arbitrary magnitude function. The technique is based on 2-D spectral factorization and rational approximation of the complex exponential function. A 2-D spectral factorization technique is used to obtain a recursively computable and stable system with nonsymmetric half-plane support from the desired 2-D magnitude function. Since the obtained system has an exponential function type transfer function and cannot be realized directly in a rational form, a class of realizable 2-D digital filters is introduced to approximate the exponential type transfer function. This class of filters referred to as two-dimensional log magnitude approximation (2-D LMA) filters can be viewed as an extension of the class of 1-D LMA filters to the 2-D case. Filter coefficients are given by the 2-D complex cepstrum coefficients, i.e., the inverse Fourier transform of the logarithm of the given magnitude function, which can be efficiently computed using 2-D FFT algorithm. Consequently, computation of the filter coefficients is straightforward and efficient. A simple stability condition for the 2-D LMA filters is given. Under this condition, the stability of the designed filter is guaranteed. Parallel implementation of the 2-D LMA filters is also discussed. Several examples are presented to demonstrate the design capability.