Z-transform of not quite an upsampler I know the z-transform of an upsampler is:

$$
y[n] = \begin{cases}
x(n/L) &amp;n=0,\pm L, \pm 2L, ...\\
0&amp;otherwise
\end{cases} 
\longrightarrow  Y(z)= X(z^{L})
$$

if $x[n]_L$ is defined to zero for $n &lt;0$ and $n \ge L$ and to be non-zero over interval $[0, L-1]$...then, what's the Z-transform of:

$$
y[n] = \begin{cases}
x[n]_L &amp; 0 \le n \le L-1\\
0&amp;otherwise
\end{cases} 
\longrightarrow  Y(z) = ???
$$

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:

$$
\begin{cases}
y[n]=a^{n}&amp;0 \le n \le L-1 \\
\\
0&amp; otherwise
\end{cases}
\longrightarrow  Y(z) = \frac{1-a^Lz^{-L}}{1-a{\ z}^{-1}}
$$
Ok, its a trick question...its $Y(z) = X(z)$ because $y[n]$ and $x[n]_L$ are identical sequences.

$$
y[n] = \begin{cases}
x[n]_L &amp; 0 \le n \le L-1\\
0&amp;otherwise
\end{cases} 
\longrightarrow  Y(z) = X(z)
$$