An improved method for designing variable recursive digital filters with guaranteed stability

Variable recursive digital filters require lower orders and less computational complexity to satisfy the same desired variable magnitude responses than nonrecursive filters, but the stability is difficult to guarantee since their coefficients are also varied in some manner. This paper proposes a new method for designing variable recursive one-dimensional (1-D) digital filters with guaranteed stability, which is an improved version of the existing one. The basic idea is to find both the numerator and the denominator coefficients of a variable recursive filter as multi-dimensional polynomials of the spectral parameters that define variable magnitude characteristics. To guarantee the stability, we first substitute the denominator coefficients by another set of variables which can take arbitrary values but without affecting the stability. Then both the numerator and the new denominator coefficients are determined as the polynomials of the spectral parameters. The new design method is simpler than the existing one, but does not degrade the final design accuracy.