4. For a continuous time system, the s-domain transfer function is (40%)
G(s) = Y(s) 2s X(s) (3s + 1)(2s + 1)
If the input x(t) is a step function,
a. For a sampling frequency 1k Hz, use the bilinear transform method to find the
transform based transfer function G(z)... b. What is the difference equation (in terms of y[n] and x[n]) of G(z)?
C. Is this system stable? Why?
d. What is the z-transform of the output?
e. If the initial condition is known, y[n] = 0, n ≤0, what are the values of the first 3 elements of the output, ie., y[1],y[2],y[3]?