Consider the following pairs of signal x[n] and y[n], which are the input and ou
ID: 2990025 • Letter: C
Question
Consider the following pairs of signal x[n] and y[n], which are the input and output of a system shown in Fig. 2. For each pair, determine whether there is a discrete-time LTI system for which y[n] is the output when the corresponding x[n] is the input. If such a system exists, determine whether the system is unique (i.e., whether there is more than one LTI system with the given input-output pair). Also determine the frequency response of an LTI system with the desired behaviour. If no such LTI system exists for a given x[n], y[n] pair, explain why. X[n] = (0-5)n and y[n] = (0.25)n x[n]= (0.5)nu[n] and y[n] = (0.25)nu[n] x[n] = 0.5nu[n] and y[n] = 4nu[-n] x[n] = ejn/8 and y[n] = 2ejn/8 x[n] = ejn/8u[n] and y[n] = 2ejn/8u[n] x[n] = jn and y[n] = 2jn (1 - j) x[n] = cos(pin/3) and y[n] = cos(pin/3) + 3 sin(pin/3) x[n] and y1[n] shown in Fig. 3. x[n] and y2[n] shown in Fig. 3. Figure 3: Periodic input signal x[n] and two periodic output signals y1[n] and y2[n]Explanation / Answer
(a). y[n] = (x[n])^2 , not a LTI system
for LTI system:- y'[n] = (a*x[n])^2 not eequal to a*y[n]
(b).
y[n] = (x[n])^2 , not a LTI system
for LTI system:- y'[n] = (a*x[n])^2 not eequal to a*y[n]