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The true statement for the system equation given below
y(t)=2x(at)
(i) If a = 1, y(t) is static causal.
(ii) If a < 1, y(t) is dynamic causal.
(iii) If a > 1, y(t) is dynamic and non-causal.
(iv) If a > 1, y(t) is dynamic and causal.
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- (i) and (ii) only
- (i) and (iii) only
- (i), (ii) and (iii) only
- (i), (ii) and (iv) only
Correct Option: C
Given equation
y(t)=2x(at) …(I)
Case I: When a = 1, equation (I) becomes
y(t)=2x(t) …(A)
Equation (A) is static and causal.
Case II: When a < 1 say 1/2 Equation (I) becomes
| y(t) = 2x |  | t |  | ...........(B) | |
| 2 |
Equation (B) is causal and dynamic.
Case III: If a > 1, say a = 2
Equation (I) becomes
y(t)=2x(2t) …(C)
Equation (C) becomes non-causal and dynamic.
Hence, alternative (C) is the correct choice.
