The text says this can be considered as an approximation of a Low Pass Filter. A low pass filter in continuous signal system is something that would block frequencies above a cutoff. But here in the discrete system, how is this to be understood? In a discrete time system, "frequency" is just angle/sample. Does the picture above mean "the system allows samples taken at the rate (0 to $2\pi/5$) / sample and blocks the rest" ?
Is it like this: say there is signal with a frequency range 20Hz to 50Hz. The sampling frequency in 100Hz. The lower frequency components get smaller $\omega$ and for higher frequency (50Hz) it gets close to $\pi$. If I have a low pass filter, it would block out those samples with large $\omega$. And this functionality now resembles a continuous time low pass filter. Is this a correct interpretation?