Design of separable-denominator variable 2-D digital filters with guaranteed stability

Abstract

Stability guarantee is the most important issue in designing variable recursive digital filters since unstable variable filters cannot be applied in signal processing applications. This paper proposes a technique for designing separable-denominator variable two-dimensional (2-D) digital filters having variable magnitude characteristics, and the stability of the designed variable recursive 2-D filters is always guaranteed. The method assumes each coefficient of the variable 2-D recursive digital filter as a polynomial of the spectral parameters that specify different variable magnitude responses. Since the filter coefficients are represented by different polynomials, substitution of different values of the spectral parameters into the polynomials gives different filter coefficients and thus different magnitude responses. To guarantee the stability, we first perform coefficient transformations on the denominator coefficients of the recursive transfer function such that the stability conditions of the recursive filter are always satisfied for arbitrary values of the new coefficients. Then both the denominator and the numerator coefficients are determined as the polynomials of the spectral parameters. The proposed technique is effective in designing separable-denominator variable 2-D digital filters with guaranteed stability.