Final answer:
The transfer function H(z) of the given LTID system is (1 - 3z^-1) / (1 - 0.4z^-1 + 0.03z^-2), representing the ratio of the output to input in the Z-domain.
Step-by-step explanation:
The question asks for the transfer function H(z) of a Linear Time-Invariant Discrete (LTID) system given by the difference equation y(n) = x(n) - 3x(n-1) + 0.4y(n-1) - 0.03y(n-2). To find the transfer function, we first take the Z-transform of both sides of the equation, remembering that the Z-transform of y(n) is Y(z) and that of x(n) is X(z). With the initial conditions provided as x(-1) = y(-1) = y(-2) = 0, the equation transforms to Y(z)(1 - 0.4z-1 + 0.03z-2) = X(z)(1 - 3z-1). Therefore, the transfer function H(z) = Y(z)/X(z) becomes (1 - 3z-1)/(1 - 0.4z-1 + 0.03z-2), which represents the ratio of the output to the input in the Z-domain.