First-Order Complex Resonators

For distinct poles, the recursive terms in the complete partial fraction expansion of Eq.$\,$(9.2) can be realized as a parallel sum of complex one-pole filter sections, thereby producing a parallel complex resonator filter bank. Complex resonators are efficient for processing complex input signals, and they are especially easy to work with. Note that a complex resonator bank is similarly obtained by implementing a diagonalized state-space model [Eq.$\,$(G.22)].