Mapping of z-plane into the s-plane
Consider the inverse relation given by z=eSTs - that is, how to map the z-plane into the s-plane.
a.) Find an expression for s in terms of z from the relation z = STs.
b.) Consider the mapping of the unit circle (I.E. z = 1ejw, - pi <= w < pi). Obtain the segment in the s-plane resulting from mapping.
c.) Consider the mapping of the inside and outside of the unit circle. Determine the regions in the s-plane resulting from the mappings.
d.) From the above results, indicate the region in the s-plane to which the whole z-plane is mapped into. Since w = w + 2*pi, is this mapping unique? Explain.