LinearSystems

Convert a rational polynomial defined with zeros Z and poles P and gain K in to a product of second order sections. The numerator in the last section will be scaled by K and all polynomials are assumed to have only real coefficents. (Poles and zeros can still be complex, if they have complex conjugated pairs.) 

Second order sectios are stored in destination vector in the order: Num1, Den1, Num2, Den2... DenN. Each section consists of 3 items (a,b,c) from the formula : a*x^2 + b*x + c

          num_sos1(s)              num_sosN(s)       (s-sz1)*...*(s-szn)
  H(s) = ------------- *  ...  * ------------- =   K*-------------------
          den_sos1(s)              den_sosN(s)       (s-sp1)*...*(s-spn)

  szn - n'th zero
  spn - n'th pole
  K - system gain

Functions