Realization of 2-D denominator-separable digital filter transfer functions using complex arithmetic

In this paper the problem of realizing 2-D denominator-separable digital filter transfer functions is considered for processing of real sequences. The approach is based on expressing the given 2-D transfer function as a sum of two reduced-order rational transfer functions with complex coefficients. New structures are obtained for equivalent reduced-order, complex-coefficient, 2-D transfer functions. All the realizations are basically parallelform structures with minimum-norm, low round-off noise and freedom from overflow limit cycles. A comparison of the different structures is also made.     

Evaluation of the quantization error in denominator-separable 2-Drecursive filters

The evaluation of the quantization error in two-dimensional (2-D) digital filters involves the computation of the infinite square sum J=Σ^∞_m=φΣ ^∞_n=φy² (m, n). A simple method is presented for evaluating J based on partial fraction expansion and using the residue method provided the Z-transform Y(Z₁, Z₂) of the sequence y(m, n) having quadrant support is a causal bounded input, bounded output (BIBO) stable denominator-separable rational function. The value of J is expressed as a sum of simple integrals which can easily be evaluated. The simple integrals are tabulated for ready reference. The proposed method is suitable for analytical as well as numerical computation and can easily be programmed     

General approach to efficient implementation of 2-D denominator-separable digital transfer functions

A functional theoretical framework is reported for obtaining efficient 2-D digital filter realisations. A given 2-D transfer function having a separable denominator polynomial is developed into certain expansions which may be realised as two-stage structures. In such structures, only suitable 1-D substructures need to be searched for to obtain a complete realisation by connecting 1-D substructures using the corresponding weighting matrix.<>     

Highly molecular systolic structures for denominator-separable 2-Drecursive filters

Two systolic realization structures for the implementation of 2-D denominator-separable recursive filters are presented. These structures possess a high degree of modularity and parallelism with low roundoff noise. The number of delays and multipliers is fewer than for similar realizations in the literature. The proposed structures are more suitable for special-purpose hardware and amenable to VLSI design     

Orthonormal minimal structure for n-dimensional denominator-separable digital filters for multiprocessor implementation

A new structure for n-dimensional-separable digital filters is derived based on an orthonormal expansion. The new structure processes well behaved filter parameters that are easily calculated, needs the minimum number of delays and has only lossless and passive substructures that are free from overflow oscillations and have low sensitivity and low roundoff noise. It can be mapped into a systolic multiprocessor array in a straightforward manner.<>     

Formation of the block toeplitz matrix for two-dimensional PLSI Polynomials

The planar least-squares inverse (PLSI) polynomials are used for stabilization of two-dimensional unstable recursive filters. In order to obtain the PLSI polynomials, the main work involved consists in forming a set of linear equations and then solving them. In this paper we present an efficient and simple method to form the necessary set of linear equations (i.e., the required coefficient matrix) for a chosen pattern and order of the desired PLSI polynomial, starting from the denominator polynomial of a two-dimensional unstable recursive filter.This work was financed by the Alexander von Humboldt Foundation, Bonn.On leave from the Department of Electrical and Electronics Engineering, S.V. University, Tirupati-517502, A.P., India.     

On the Stabilization of Multidimensional Recursive Digital Filters

It is brought to light that a one-dimensional lacunar leastsquares inverse (LSI) polynomial is not necessarily stable and that theproof of the theorem [1] about the stability of multidimensional LSIpolynomials is questionable, even though the theorem seems to be true.     

Implementation of 2-D denominator-separable digital filters using first-order all-pass sections

It is established that denominator-separable transfer functions which characterize an important subclass of 2-D filters can be expressed as a linear combination of first-order (1-D or 2-D separable) all-pass transfer functions with real or complex coefficients. This type of expansion is referred to as all-pass expansion of the corresponding transfer function. Based on this all-pass expansion, we derive some efficient structures for the realization of 2-D denominator-separable filters using all-pass sections.On leave from S.V. University College of Engineering. Tirupati-517502, India.