New method for designing stable variable filters

Digital filters with adjustable frequency-domain characteristics are called variable filters. Variable filters are used in many signal processing fields, but recursive variable filters are extremely difficult to design due to the stability problem. This paper proposes a new method for designing recursive one-dimensional (1-D) variable filters whose stability is always guaranteed. To guarantee the stability, we first perform coefficient substitutions on the denominator coefficients such that for arbitrary real-valued coefficients, the stability condition is always satisfied. Then both the denominator coefficients and the numerator coefficients after substitutions are determined as M-D polynomials of spectral parameters that specify variable magnitude characteristics. In applying the resulting variable filters, substituting different values of the spectral parameters into the M-D polynomials will obtain different filter coefficients and thus different magnitude characteristics.