Inverse Z-transform and poles and zeros
When finding the inverse Z-transform of functions with z-1 terms in the numerator, the fact that z-1 can be thought of as a delay operator can be used to simplify the computation. Consider:
X(z) = 1 - z-10/1 - z-1
a.) Use the z- transform of u[n] and the properties of the z-transform to find x[n].
b.) If we consider X(z) a polynomial in negative powers of z, what would be its degree and the values of its coefficients?
c.) Find the poles and the zeros of X(z) and plot them on the z-plane. Is there a pole or zero at z = 1? Explain.