SIGNALS AND SYSTEMS ( a ) x(r - 2 ) is sketched in Fig. 1-18(a). ( 6 ) x ( 2 0 is sketched in Fig. 1-18(b). ( c ) x(t/2) is sketched in Fig. 1-18(c). ( d ) X ( - t ) is sketched in Fig. 1-1Nd). (c) F g 1-18 i. . A discrete-time signal x [ n ] is shown in Fig. 1-19. Sketch and label each of the following signals. ( a ) x [ n - 21; ( b ) x [ 2 n ] ; ( c ) x[-n]; (d) x[-n + 21 F g 1-19 i. .CHAP. 11 SIGNALS AND SYSTEMS (a) (b) (c). | 20 SIGNALS AND SYSTEMS CHAP. 1 x t - 2 is sketched in Fig. 1- 18 a . 6 x 2t is sketched in Fig. 1-18 6 . c x r 2 is sketched in Fig. l-18 c . d x -t is sketched in Fig. l-18 t . a 6 c d Fig. 1-18 . A discrete-time signal is shown in Fig. 1-19. Sketch and label each of the following signals. a x n - 2 6 x 2n c - d x -n 4- 2 CHAP. 1 SIGNALS AND SYSTEMS 21 a x n - 2 is sketched in Fig. l-20 a . b x 2n is sketched in Fig. 1-2O Z . c x -n is sketched in Fig. 1-20 c . d x -n 2 is sketched in Fig. l-20 d . x -n x -n 2 3 3 - - 1 . Given the continuous-time signal specified by x i i-kl 0 otherwise determine the resultant discrete-time sequence obtained by uniform sampling of x t with a sampling interval of u s b s and c s. It is easier to take the graphical approach for this problem. The signal x t is plotted in Fig. l-21 a . Figures l-21 b to d give plots of the resultant sampled sequences obtained for the three specified sampling intervals. a Ts s. From Fig. l-21 b we obtain x n . 0 1 0 . I h Ts s. From Fig. l-21 c we obtain x n . 0 l 0 . I 22 SIGNALS AND SYSTEMS CHAP. 1 c Ts 1 s From Fig. 1-21 we obtain . Using the discrete-time signals xjn and x2 n shown in Fig. 1-22 represent each of the following signals by a graph and by a sequence of numbers. a yjn x n x2 n b y2 n 2xj n c y3 n x1 n x2 n Fig. .
