Final answer:
To convert the transfer function H(z) into its difference equation, we can use the inverse Z-transform. By performing partial fraction decomposition and using the method of residues, we can obtain the difference equation in the form y[n] = a0*x[n] + a1*x[n-1] + b1*y[n-1] + b2*y[n-2]. For the given transfer function H(z) = (z² - 0.25)/(z² + 1.1z + 0.18), the difference equation is y[n] = 0.36*x[n-1] - 0.36*x[n-3] + 0.3613*y[n-1] - 0.3243*y[n-2].
Step-by-step explanation:
The transfer function H(z) can be written as a ratio of polynomials. To convert it into its difference equation, we can use the inverse Z-transform. The inverse Z-transform of H(z) can be found using partial fraction decomposition and the method of residues. The difference equation will have the form y[n] = a0*x[n] + a1*x[n-1] + b1*y[n-1] + b2*y[n-2], where a0, a1, b1, and b2 are coefficients obtained from the partial fraction decomposition.
In this case, H(z) = (z² - 0.25)/(z² + 1.1z + 0.18) can be decomposed into H(z) = 0.36/(z - 0.25) - 0.36/(z + 0.9).
Using the method of residues, we can find the corresponding difference equation as y[n] = 0.36*x[n-1] - 0.36*x[n-3] + 0.3613*y[n-1] - 0.3243*y[n-2].