Question

/. For the i determin whe eher the sstem s 1) Causal 2, Find the Fourier rmiform xjw) for xw, rie) 2 o otherwise 5keech Xjw)

Answer 1

Given angle of TI system, h(t) = e^-2t u(t + 1) It is an Anti - causal system because it only depends on future values of i/p for i/p rightarrow (- infinity, infinity) o/p of e^-2t rightarrow ' infinity' when t rightarrow - infinity '0' when t rightarrow 'infinity' u(t + 1) rightarrow input [-1, infinity] input (- infinity, -1) rightarrow '1' output '0' /boundary therefore of the LTI system rightarrow input rightarrow (- infinity, -1]: output rightarrow 0 input rightarrow [-1, infinity): exponential \r\n it is a dynamic, because it has depending on future input. So it is not a memory less system. Given signal, x(t) { 2: -2 lessthanorequalto t lessthanorequalto 2 0: 0.w implies d(x(t)/dt = 2 delta(t + 2)-2 delta (t - L) (jw)'.X (jw) = [1.e^jw2 - 1.e^-jwL] \r\n x(jw) = 2/w [e^j2w - e^-j2w/j] x(jw) = 2/w [2 sin (2w)/ 2w] times 2w x (jw) = 8