山东大学2017-2018学年2学期数字信号处理（双语）课程试卷（) n].N=2 1n1n1n1 210124561 签 家 得分圆卷人 5.(15 pts)Suppose]is a periodic sequence with period N. Then:]is also periodic with period 3N.Let]denote the DFS 器 coefficients of considered as a periodic sequence with period N. and let]denote the DFS coefficients of considered as a periodic sequence with period 3N. (a)Express]in terms of]. (b) By explicitly calculating]and],verify your result in part (a)when] is as given in the following figure. 第4项共5页2017-2018 2 数字信号处理（双语） （A） 4 5 5．(15 pts) Suppose x n[ ] is a periodic sequence with period N. Then: x n[ ] is also periodic with period 3N. Let X k[ ] denote the DFS coefficients of x n[ ] considered as a periodic sequence with period N. and let 3 X k[ ] denote the DFS coefficients of x n[ ] considered as a periodic sequence with period 3N. (a) Express 3 X k[ ] in terms of X k[ ]. (b) By explicitly calculating X k[ ] and 3 X k[ ] , verify your result in part (a) when x n[ ] is as given in the following figure. 得分 阅卷人