The exponential x(t) = e-at can be written as x(t) = e-at u(t) + e-at u(-t) where the first term represent the

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  1. anti- causal part of x(t)
  2. causal part of x(t)
  3. non- causal part of x(t)
  4. formal part of x(t)

Answer (Detailed Solution Below)

Option 2 : causal part of x(t)
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Detailed Solution

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Concept:

The impulse response is the output of a system when the input is an impulse, i.e.

F1 S.B Madhu 03.03.20  D2

The impulse response of a system can be used to evaluate various system properties. Causality is one such property, that states, “if the output of the system at any time depends only on the past and present values of the input, the system is said to be causal.”

If the impulse response is known, the system is said to be causal, if h(t) = 0 for t < 0.

Analysis:

x(t) = e-at u(t) + e-at u(-t) 

F1 Neha Madhuri 20.11.2021 D15

F1 Neha Madhuri 20.11.2021 D16

Therefore, the first term is the causal part of the signal x(t). 

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