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

This paper proposes a new technique for designing variable two-dimensional (2-D) linear phase recursive digital filters, the stability of which is always guaranteed. The method finds each variable filter coefficient as a multidimensional (M-D) polynomial of a few parameters. The parameters specify different frequency responses, 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 responses. To guarantee the stability, we first perform denominator coefficient transformations such that they satisfy the stability conditions. Then, both denominator and numerator coefficients are determined as M-D polynomials.