why in MATLAB for notch filter design, the order of filter must be even?!

in filter visualization tools in MATLAB, we can design notch filters as belows:

%Notch filter Design
F0=60   % Notch point : 60Hz
Fs= 600; % Sampling frequency : 600 Hz
f = fdesign.notch('N,F0,Q',2,60,8,600);
h=design(f);
hfvt = fvtool(h);

but N(the order of filter) must be even, if not;it occurs an error!!!

Answer 1

[Walter Roberson]

Simple linear algebra. A filter is a polynomial (or ratio of polynomials.) A polynomial of odd order must map -infinity and +infinity to results of different sign, and thus cannot be a notch filter as a notch filter requires that the value at the starting frequency be the same sign as the value at infinity.