  In [8] the author of this paper continued the research on the complex-valued
discrete random variables $X_l(m,N)$ ($0\le l\le N-1$, $1\le M\le N)$ recently
introduced and studied in [24]. Here we extend our results by considering
$X_l(m,N)$ as sub-Gaussian random variables. Our investigation is motivated by
the known fact thatthe so-called Restricted Isometry Property (RIP) introduced
in [4] holds with high probability for any matrix generated by a sub-Gaussian
random variable. Notice that sensing matrices with the RIP play a crucial role
in Theory of compressive sensing.
  Our main results concern the proofs of the lower and upper bound estimates of
the expected values of the random variables $|X_l(m,N)|$, $|U_l(m,N)|$ and
$|V_l(m,N)|$, where $U_l(m,N)$ and $U_l(m,N)$ are the real and the imaginary
part of $X_l(m,N)$, respectively. These estimates are also given in terms of
related sub-Gaussian norm $\Vert \cdot\Vert_{\psi_2}$ considered in [28].
Moreover, we prove a refinement of the mentioned upper bound estimates for the
real and the imaginary part of $X_l(m,N)$.
