  Improving the efficiency of discrete time scale invariant (DSI) processes, we
consider some flexible sampling of a continuous time DSI process ${X(t),
t\in{R^+}}$ with scale $l>1$, which is in correspondence to some
multi-dimensional self-similar process. So we consider $q$ samples at arbitrary
points $s_0, s_1, ..., s_{q-1}$ in interval $[1, l)$ and proceed in the
intervals $[l^n, l^{n+1})$ at points $l^n s_0,l^n s_1, ..., l^n s_{q-1}$, $n\in
Z$. So we study an embedded DT-SI process $W(nq+k)=X(l^n s_k)$, $q\in N$, $k=
0, ..., q-1$, and its multi-dimensional self-similar counter part
$V(n)=\big(V^0(n), ..., V^{q-1}(n)\big)$ where $V^k(n)=W(nq+k)$. We study
spectral representation of such process and obtain its spectral density matrix.
Finally by imposing wide sense Markov property on $W(\cdot)$ and $V(\cdot)$, we
show that the spectral density matrix of $V(\cdot)$ can be characterized by
${R_j(1), R_j(0), j=0, ..., q-1}$ where $R_j(k)=E[W(j+k)W(j)]$.
