Question

Consider the following difference equation representing a causal LTID system:

y[n]+0.6y[n−1]+0.09y[n−2]=x[n]−0.6x[n−1]+0.09x[n−2]
Find the transfer function of the system.

Answer 1

To find the transfer function of the given difference equation, write it in the form of a z-transform. The transfer function is given by H(z) = (1 - 0.6z^(-1) + 0.09z^(-2)) / (1 + 0.6z^(-1) - 0.09z^(-2)).

Step-by-step explanation:

To find the transfer function of the system represented by the given difference equation, notice that the equation can be written in the form of a z-transform. Let's assume Y(z) is the z-transform of y[n] and X(z) is the z-transform of x[n]. The transfer function H(z) is then given by:

H(z) = Y(z) / X(z) = (1 - 0.6z^(-1) + 0.09z^(-2)) / (1 + 0.6z^(-1) - 0.09z^(-2))

This is the transfer function of the system.