An alternative simultaneous maximally flat approximation for a low-pass recursive digital filter

Digital filters with either maximally flat magnitude or maximally flat group delay are known [1]-[3]. This paper offers an approach to the design of a recursive digital filter with simultaneous approximation to both magnitude and phase. Although the same Taylor norm is used, this described technique is different from the previous approach [4] in the sense that it employs a power series expansion around ω = 0 in the z-plane. It gives an alternative insight into the problem for the designers who are more familiar with the z-plane than the Richards' λ-plane. The filter transfer functions are obtained explicitly in closed forms.