The DFT of a finite-duration sequence corresponds to samples of its z-transform on the unit circle. For example, the DFT of a 10-point sequence x[n] corresponds to samples of X(z) at the 10 equally spaced points indicated in Figure. We wish to find the equally spaced samples of X(z) on the contour shown in Figure i.e., we wish to obtain 

X(z)| _{z= 0.5e j[(2πk/10) + (π/10)]}.

Show how to modify x[n] to obtain a sequence x1[n] such that the DFT of x1[n] corresponds to the desired samples of X(z).

Im z-plane 2 Radians 10 Unit circle, Re Im Circle with z-plane 2 radius = 2 10 2 20 Re