The DFT of a finite-duration sequence corresponds to samples of its z-transform on the u...

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 P8.50-1.We wish to find the equally spaced samples of X(z) on the contour shown in Figure P8.50-2; i.e., we wish to obtain

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).