Design of variable 2-D linear phase IIR filters with guaranteed stability

This paper proposes a new method for designing variable two-dimensional (2-D) linear phase recursive digital filters whose stability is always guaranteed. The method finds each variable filter coefficient as a multidimensional (M-D) polynomial of a few variables. The variables specify different frequency-domain characteristics, thus they are called the spectral parameters. In applying the resulting variable filters, substituting different spectral parameter values into the M-D polynomials will obtain different filter coefficients and thus different frequency-domain characteristics. To guarantee the stability, we first perform coefficient transformations on the denominator coefficients such that they satisfy the stability conditions. These both denominator and numerator coefficients are determined as M-D polynomials.