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salam February 2016
### Decomposing the numerator and the denominator polynomials into their even and odd parts

Here there is a 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)`

where `w = frequency symbol.`

Now, how is it possible to decompose the numerator and the denominator
polynomials of Eq. (1) into their even and odd parts and get the `G(jw)`

as (Using Matlab) :

You could probably take the real and imaginary parts after the substitution with `s=j*w`

. However, you can actually select the even and odd parts of your polynomials:

```
% G(s) = N(s)/D(s);
syms s;
N = s^3+4*s^2-s+1;
p = sym2poly(N);
%// do this in fewer lines:
%{
/*
if mod(length(p),2)==0 %// then first index is odd
imin_o = 1; %// for odd part
imin_e = 2; %// for even part
else
imin_o = 2; %// for odd part
imin_e = 1; %// for even 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);
% even 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 the same for the denominator.

Asked in February 2016

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Voted 6

Answered 1 times

Viewed 3,370 times

Voted 6

Answered 1 times