How to separate the real and imaginary parts of a transfer function?

Question

Here is a transfer function:

S = [tf([10 2 4],[1 95 2000 3450])];

How can I get real(S) and Imag(S)?

Answer 1

It sounds like you want the Fourier form of your transfer function. As far as I know, there's no builtin function for this so you'll need to use symbolic math:

num = [10 2 4];
den = [1 95 2000 3450];
syms s;
syms omega real; % Define as real-valued
f1 = poly2sym(num,s)/poly2sym(den,s)
f2 = subs(f1,s,1i*omega)
f2_real = simplify(real(f2))
f2_imag = simplify(imag(f2))

which returns

f1 =
 
(10*s^2 + 2*s + 4)/(s^3 + 95*s^2 + 2000*s + 3450)


f2 =
 
(- 10*omega^2 + omega*2i + 4)/(- omega^3*1i - 95*omega^2 + omega*2000i + 3450)


f2_real =
 
(4*(237*omega^4 - 7720*omega^2 + 3450))/(omega^6 + 5025*omega^4 + 3344500*omega^2 + 11902500)


f2_imag =
 
-(2*omega*(5*omega^4 - 9907*omega^2 + 550))/(omega^6 + 5025*omega^4 + 3344500*omega^2 + 11902500)

You can then use subs and vpa/double to evaluate these for a particular value of omega.