Mapping of s-plane into z-plane
The poles of the Laplace transform(s) of an analog signal x(t) are:
P1,2 = -1 +/- j1
P3 = 0
P4,5 = +/- j1
There are no zeros. If we use the transformation z = esTs with Ts = 1:
a.) Determine where the given poles are mapped into the z-plane.
b.) How would you determine if these poles are mapped inside, on, or outside the unit circle in the z-plane? Explain.
c.) Carefully plot the poles and zeros of the analog and the discrete-time signals in the Laplace and the z-planes.