Question

Q1. The signal x(t) shown in Figure Q1 is zero except as shown. [No Partial Credit] x(t) 2 1 -1 0 1 2 3 4 5 t Figure Q1 Clearly indicate the significant points in the time axis and y-axis. a) Plot x(t + 2) b) Plot x(2t - 3) c) Plot x(2-t) [2 marks) [2 marks] [2 marks]

Answer 1

Given, 24t) 2 → Z D 2 3 4 5 с are - Property using for parts a, b and Time shift: for altt to) alt+to) means graph will shift to units . to the Left side. alt-to) means graph will shift to units to the right side. Time Reverse for xl-t t to) ₃xl-t+to) means graph will shift to units to the right side. ₃xl-t-to) means graph will shift to units the to Left side . Tirne scaling: for x(04) if a<」 that means H time axis will expand a times. if azt that means will compress from a time axis times

(0) Plot for x 1t+2) graph of alt) that means to =2 which implies shift 2 units of time towards left side. x lt+2) 2. t -3 0 -2. 2 3 both property So (b) Plot for xl2t-3) that means here of time shift and time scaling will be done. to =-3 and a-2 graph of original act) will be shifted 3 time units to the right side and time here SO axis a=2 (a)!) compression will be done further . zel2t-3) alt-3) 2 2 1 't 0 1 2 3 5 7 0 2.5 Ł 3.5

to =2 () Plotting for x(2-t) al-t+2) that means but with time reversal with mirror image Shifting the graph of axis (time reversal) al-t) 2 >t -5 -4 -3 -2 -1 D Then shifting this plot 2 units to the right side. el-t+2) » x(2-t) 2 1 0 - t -3 -2. -1 I 2 3