Final answer:
The unit impulse response of the given LTID system is h(n) = 0.5δ(n) - 0.6δ(n-1) + 1.1δ(n-2). The system is stable as the sum of the absolute values of the coefficients is finite. The filter is a combination of low-pass and high-pass filters.
Step-by-step explanation:
The given system represents a linear time-invariant discrete-time system. To find the unit impulse response h(n) of the system, we can set x(n) = δ(n), where δ(n) is the discrete unit impulse function. Substituting this into the difference equation, we get y(n) = 0.5δ(n) - 0.6δ(n-1) + 1.1δ(n-2). Therefore, the unit impulse response h(n) is h(n) = 0.5δ(n) - 0.6δ(n-1) + 1.1δ(n-2).
Since the system is stable if the impulse response h(n) is absolutely summable, we need to check if the sum of the absolute values of the coefficients is finite. In this case, |0.5| + |-0.6| + |1.1| = 2.2, which is a finite value, so the system is stable.
The type of the filter can be determined by the coefficients of the difference equation. In this case, the coefficients are positive and negative, indicating that the system is a combination of both low-pass and high-pass filters.