In Property 4 of Section 10.2, it was stated that if x[n] is a right-sided sequence and

Chapter 10, Problem 10.49

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In Property 4 of Section 10.2, it was stated that if x[n] is a right-sided sequence and if the circle lzl = r0 is in the ROC, then all finite values of z for which 1z1 > r0 will also be in the ROC. In this discussion an intuitive explanation was given. A more formal argument parallels closely that used for Property 4 of Section 9 .2, relating to the Laplace transform. Specifically, consider a right-sided sequence x[n] = 0, n < NJ, and for which L, ix[n]jr0n L, jx[n]jr0n < oo. n=-oo n=N1 Then if ro :::; r1, (P10.49-1) where A is a positive constant. (a) Show that eq. (Pl0.49-l) is true, and determine the constant A in terms of r0 , r 1, andN1 (b) From your result in part (a), show that Property 4 of Section 10.2 follows. (c) Develop an argument similar to the foregoing one to demonstrate the validity of Property 5 of Section 1 0.2.