I know the z-transform of an upsampler is:
$$ y[n] = \begin{cases} x(n/L) &n=0,\pm L, \pm 2L, ...\\ 0&otherwise \end{cases} \longrightarrow Y(z)= X(z^{L}) $$
if $x[n]_L$ is defined to zero for $n <0$ and $n \ge L$ and to be non-zero over interval $[0, L-1]$...then, what's the Z-transform of:
$$ y[n] = \begin{cases} x[n]_L & 0 \le n \le L-1\\ 0&otherwise \end{cases} \longrightarrow Y(z) = ??? $$
its kind of like:
$$ y[n] = x[n]\ u[-n + L]\ u[n] $$
I have this z-transform for LPF that is similar, but doesn't match:
$$ \begin{cases} y[n]=a^{n}&0 \le n \le L-1 \\ \\ 0& otherwise \end{cases} \longrightarrow Y(z) = \frac{1-a^Lz^{-L}}{1-a{\ z}^{-1}} $$