matlab - Decomposing the numerator and the denominator polynomials into their even and odd parts -

here there continues time transfer function (g(s)) in form of:

g(s) = n(s)/d(s); g(s) = (s^3+4s^2-s+1)/(s^5+2s^4+32s^3+14s^2-4s+50)     (1) 

and (s = j*w) w = frequency symbol.

now, how possible decompose numerator , denominator polynomials of eq. (1) , odd parts , g(jw) (using matlab) :

you take real , imaginary parts after substitution s=j*w. however, can select , odd parts of polynomials:

% g(s) = n(s)/d(s);  syms s; n = s^3+4*s^2-s+1;  p = sym2poly(n);  %// in fewer lines: %{ /* if mod(length(p),2)==0  %// first index odd     imin_o = 1;  %// odd part     imin_e = 2;  %// part else     imin_o = 2;  %// odd part     imin_e = 1;  %// part end */ %}  imin_o = mod(length(p),2) + 1; imin_e = 2 - mod(length(p),2);  % odd part of numerator p_o = zeros(size(p)); p_o(imin_o:2:end) = p(imin_o:2:end); % part of numerator p_e = zeros(size(p)); p_e(imin_e:2:end) = p(imin_e:2:end);  % restore n_o = poly2sym(p_o,s); n_e = poly2sym(p_e,s); 

and same denominator.