Frequency spectra of a sampled process
Sampling in the time domain is equivalent to periodic repetition in the frequency domain with $1/T_s$ as the period. So formally you'd have something like
$$R_{sampled}(f) = \sum_{n=-\infty}^{\infty}R_z(f-2\cdot n)$$

If you evaluate this, you actually get $R(f) = 2$. It's easier to see if you draw it: take the initial spectrum, shift it by -6,-4,-2,0,2,4,6... and sum it all graphically