Is this signal linear, time variant?

[Larrytsai]

Homework Statement

y[n] = x[-n] + 2Is this signal linear?

for signal to be linear,
y3[n] = a*y1[n] + b*y2[n] IF x3[n] = a*x1[n] + b*x2[n]
--------------------------------------------------------------
x1[n] -> y1[n] = x1[-n] + 2
x2[n] -> y2[n] = x2[-n] + 2

x3[n] = a*x1[n] + b*x2[n]

y3[n] = x3[-n] + 2
= a*x1[-n] + b*x2[-n] + 2

y3[n] != a*y1[n] + b*y2[n] = a*x1[-n] + b*x2[-n] + 4

Hence not linear...

Is this signal time invariant?

for signal to be time invariant, if we delay the signal before it enters the system, the signal should be the same as if the signal enters the signal and delays it. *Not sure if this is correct.

so if i delay the signal before it enters the system, we have

y[n] = x[-(n-n0)] + 2

delay after it leaves the system

w[n] = x[-n-n0] + 2

Hence is time varying.can you guys kindly check if my work is correct, and if it is wrong explain what concept I have broken?

thanks.

 

[KataKoniK]

Your reasoning for the signal not being linear is correct. However, your reasoning for the signal being time varying is incorrect. Time varying means that the system is dependent on time, meaning that the output will vary if the input is delayed or advanced in time. In this case, the output will remain the same regardless of when the input is delayed or advanced. Therefore, the signal is time invariant.