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Solved Problems-7

Problems-7
Determine whether the following continuous-time systems are causal or non-causal:
  1. Description: Description: Description: 3025.png
  2. Description: Description: Description: 3021.png
  3. Description: Description: Description: 3017.png
  4. Description: Description: Description: 3011.png
  5. Description: Description: Description: 3005.png
Solution
  1. Description: Description: Description: 3001.png
Here, y(t) depends on the present input x(t).
 
A cosine function can be evaluated at (t + 1).
 
Therefore, the system is causal.
  1. Description: Description: Description: 2997.png
Here, if t = 5, then Description: Description: Description: 2991.png
 
Thus, the output y(t) depends on the future input.
 
Therefore, the system is non-causal.
  1. Description: Description: Description: 2987.png
Here, if  t = –3, then Description: Description: Description: 2975.png
 
Thus, the output y(t) depends on the future input.
 
Therefore, the system is non-causal.
  1. Description: Description: Description: 2971.png
Here, y(t) depends upon the present value of x(t).
 
Therefore, the system is causal.
  1. Description: Description: Description: 2967.png
Here, y(t) depends upon the present and the past values of x(t), but not on the future value.
 
Therefore, the system is causal.
 




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