An Optimization Method for Cascaded Filters

Let 4>{s) be a transfer function where / and g are polynomials with real coefficients, and the degree of / ^ degree of g. We consider all the decompositions of the form 0(s) =^>1(s)02(s) · · · 0,(s) where (1) /, (s) and , (s) are real polynomials and the degree of /,· does not exceed 7 the degree of g{ . The 7, are quadratic polynomials, except when the degree of g is odd; then one , is linear. 7 Let L be a passband region for where L is a finite union of passband intervals. Then for every > , a number 2(0.) is defined by f{ dfc) = 20 log a'lO,") Max | 0,0'co) | Min | 0, 0'w) | (2)