Final answer:
To determine the LTID system's zero-state response to the given input signal, one needs to perform a convolution of the system's impulse response with the input signal or apply z-transform methods.
Step-by-step explanation:
The student is asking about the zero-state response (yzs[k]) of a Linear Time-Invariant Discrete (LTID) system with a given transfer function H(z) when the input signal f[k] is specified. The system's transfer function is H(z) = (z²+1/2z)/(z²+ z+1), and the input signal is f[k] = {1 if k=0,1; 0 otherwise}. To find the zero-state response of the system, one must perform a convolution between the input signal and the system's impulse response h[k], which is obtained by performing an inverse z-transform of H(z).
However, without the use of computational tools or additional information such as initial conditions or the system's impulse response, the exact expression for yzs[k] cannot be determined directly from the information given. One would typically apply the z-transform to the input signal, multiply it by the transfer function, and then perform an inverse z-transform to get the zero-state response.