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A continuous, linear time-invariant filter has an impulse response h(t) described by h(t) = { 3 for 0 ≤ t ≤ 3 { 0 otherwise When a constant input of value 5 is applied to this filter, the steady state output is _____.

1. 0
2. 5
3. 15
4. 45

Correct answer: 45

Solution

The output of a linear time-invariant filter to a constant input can be calculated by multiplying the input value by the area under the impulse response. Here, the area under h(t) is 3 (height) multiplied by 3 (width), which equals 9, and when this is multiplied by the constant input of 5, the result is 45.

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