A cascade system having the impulse responses $h_{1}(n)= \{ \underset{\uparrow}{1}-1 \}$ and $h_{2}(n)= \{ \underset{\uparrow}{1}-1, 1 \}$ is shown in the figure below, where symbol $\uparrow$ denotes the time origin.
The input sequence $x(n)$ for which the cascade system produces an output sequence $y(n)=\{\underset{\uparrow}{1}-1, 2, 1, -1, -2, -1 \}$ is
- $x(n)= \{\underset{\uparrow}{1}-1, 2, 1, 1\}$
- $x(n)= \{\underset{\uparrow}{1}-1, 1, 2, 2 \}$
- $x(n)= \{\underset{\uparrow}{1}-1, 1, 1, 1 \}$
- $x(n)= \{\underset{\uparrow}{1}-1, 2, 2, 1 \}$