# Analysis of z transform to time domain, poles and zeros

From a given z transform X(z) = {1- z^-10}/{1 - z^-1} the discrete time domain form x(n) is deduced using complex manipulation and inverse transforms to arrive at x(n) = x(n-1) + u(n) - u(n-10)

The second part shows how to convert the given X(z) into a polynomial in z as X(z) = 1 + z^-1 + z^-2 + .... + z^-9

Finally the third part goes on to show the poles and zeros of X(z) and plot these in the complex z plane as zeros , z(n) = 0.2n*pi, magnitude 1, Poles at 0

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From a given z transform X(z) = {1- z^-10}/{1 - z^-1} the discrete time domain form x(n) is deduced using complex ...

#### Solution Summary

From a given z transform X(z) = {1- z^-10}/{1 - z^-1} the discrete time domain form x(n) is deduced using complex manipulation and inverse transforms to arrive at x(n) = x(n-1) + u(n) - u(n-10)

The second part shows how to convert the given X(z) into a polynomial in z as X(z) = 1 + z^-1 + z^-2 + .... + z^-9

Finally the third part goes on to show the poles and zeros of X(z) and plot these in the complex z plane as zeros , z(n) = 0.2n*pi, magnitude 1, Poles at 0