The impulse response of a causal linear time-invariant system is given as h(t). Now consider the following two statements:
Statement (I): Principle of superposition holds
Statement (II): h(t) = 0 for t

Question

The impulse response of a causal linear time-invariant system is given as h(t). Now consider the following two statements:
Statement (I): Principle of superposition holds
Statement (II): h(t) = 0 for t < 0
Which one of the following statements is correct?

Accepted Answer

Both Statement (I) and Statement (II) are correct. The principle of superposition applies to linear systems, meaning that the response to a combination of inputs is the sum of the responses to each input individually, which is true for causal linear time-invariant systems. Additionally, the definition of a causal system requires that the impulse response h(t) is zero for all times before t=0, confirming that both statements are indeed correct.

The impulse response of a causal linear time-invariant system is given as h(t). Now consider the following two statements: Statement (I): Principle of superposition holds Statement (II): h(t) = 0 for t < 0 Which one of the following statements is correct?

Solution

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