Final answer:
In this case where the system is stable, the unit sample response shift towards y[n] = 0 for all n.
Step-by-step explanation:
The given system is a linear, discrete-time, shift-invariant system. We are asked to determine the unit sample response of the system.
To find the unit sample response, we need to find the output when the input is a unit sample, which is 1 at time n=0 and 0 at all other times.
By substituting x[n] = 1 and y[n] = y in the given equation, we get: y[n - 1] - 10/3 y[n] + y[n + 1] = 1.
If we assume the system is at equilibrium, then the equilibrium response is y[n] = 0 for all n.
Substituting this assumption into the equation, we get: -10/3 * 0 + 0 + 0 = 1, which is not true.
Therefore, the system is not at equilibrium.
If the system is not at equilibrium, it will need to shift towards a direction to reach equilibrium.
In this case, the system will need to shift towards y[n] = 0 for all n.