Explicit formula for generalized half-band maximally flat diamond-shaped filters
S. Samadi, Akinori Nishihara · 2002
An explicit polynomial solution to the functional equation H(z/sub 1/, z/sub 2/)/spl plusmn/H(-z/sub 1/, -z/sub 2/)-z/sub 1/(-D/sub 1/)z/sub 2/(-D/sub 2/) is derived. The solution gives rise to an intriguing class of half-band diamond-shaped FIR digital filters encompassing linear-phase filters as well. The functional equation is solved so that the number of vanishing partial derivatives of the frequency response of H(z/sub 1/, z/sub 2/) at wl/sub 1/=w/sub 2/=/spl pi/ are maximized. This results in a maximally flat magnitude response with a flat group delay response in the passband.