Wrong phase plot generated by angle()

I was trying to plot the phase spectrum of using the angle function, however matlab gives me which is incorrect since the phase of this signal is , and ω is undefined at -1 and 1. The correct plot should be . I wonder if I did something wrong or if it's something intertal of the angle() function.

Answer 1

[Paul]

The four-quadrant arctangent is needed to find the angle of a (non-zero) complex number:

syms w real
X(w) = 1/(1 + 1j*w)^2;
phase(w) = atan2(simplify(imag(X)),simplify(real(X)))

phase(w) = 

angle(X(1))

ans = 

phase(1)

ans =