Difference Equations Solving System Responses with Stored Energy

Initial conditions summarize the effect of all past inputs to the system.

The steady-state response of a system described by a difference equation describes the transition from the initial condition to the steady-state condition.

The transient response of a system described by a difference equation describes how the system responds to the input after a long time has passed.

If the input to a system described by a difference equation is $x[n]=(3/4)^n$, which of the following could represent the steady-state response of the system? Select all that apply.

If the roots of the system’s characteristic equation are $1/3$ and $2/3$, which of the following could represent the transient response of the system? Select all that apply.