Interpreting the Phase Response

What does it mean to have a phase response of

$\displaystyle \Theta(\omega) = -\frac{\omega T}{2} = -\pi\frac{f}{f_s}, \qquad \vert f\vert\le f_s/2?$
We see, again but perhaps more clearly, that the phase response is linear in frequency.
In general, to obtain the phase delay (time delay) in seconds, divide by $-\omega$ :

$\displaystyle P(\omega) \triangleq -\frac{\Theta(\omega)}{\omega}$ seconds $\displaystyle .$

``Mus 270a: Introduction to Digital Filters'' by Tamara Smyth, Department of Music, University of California, San Diego.