Which is the correct representation of Commutative Continuous time LTI system?Group of answer choices∫h(α) + x(t-α) = ∫x(α) + h(t-α)∫h(α) * x(t-α) = ∫x(α) * h(t-α)∫h(α) – x(t-α) = ∫x(α)h(t-α)∫h(α)x(t-α) = ∫x(α)h(t-α)
Question
Which is the correct representation of Commutative Continuous time LTI system?Group of answer choices∫h(α) + x(t-α) = ∫x(α) + h(t-α)∫h(α) * x(t-α) = ∫x(α) * h(t-α)∫h(α) – x(t-α) = ∫x(α)h(t-α)∫h(α)x(t-α) = ∫x(α)h(t-α)
Solution
The correct representation of a Commutative Continuous time LTI (Linear Time-Invariant) system is:
∫h(α) * x(t-α) = ∫x(α) * h(t-α)
This is because in a commutative system, the order of the operations does not change the result. In this case, the convolution of the input signal x(t) with the system's impulse response h(t) is the same as the convolution of h(t) with x(t). This property is fundamental to LTI systems and is a direct result of their time-invariance and linearity.
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