A complex filter is whose impulse response is complex valued, and its transfer function in spectral domain could be asymmetric with respect to DC (0 hertz frequency). Let's say bf is the numerator and af is the denominator of this complex filter's transfer function in z-domain already. For example, Hd = (0.007823+6.136e-05i)/(z - (0.9921+0.01558i)),[A,B,C,D] = tf2ss(Hd.Numerator{:},Hd.Denominator{:}) will yield A = 0.9921 + 0.0156i, B = 1, C = 0.0078 + 0.0001i, and D = 0. Can I trust this ABCD matrix will work for the state equations: y(k) = C*x+D*u(k), x=A*x+B*u(k), with x,y and u all being complex valued numbers?
