A discrete-time, linear time invariant system with input sequence $$x_{n}$$, and output sequence $$Y_{n}$$ is characterised by
$$y_{n}=0.1x_{n}+0.9 y_{n-1}$$
If two such systems are connected in series, which of the following is the governing difference equation of the overall system?

A

$$y_{n}-1.8y_{n-1}+0.81 y_{n-2}=0.01 x_{n}$$

B

$$y_{n}+0.81 y_{n-1}=0.01 x_{n}$$

C

$$y_{n}-0.81 y_{n-1}+1.8 y_{n-2}=0.01 x_{n}$$

D

$$y_{n}-0.81 y_{n-i}=0.01 x_{n}$$