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Let continuous-time signals x1(t) and x2(t) be x1(t) = { 1, t ∈ [0,1] { 2 − t, t ∈ [1,2] { 0, otherwise and x2(t) = { t, t ∈ [0,1] { 2 − t, t ∈ [1,2] { 0, otherwise Consider the convolution y(t) = x1(t) * x2(t). Then ∫_(−∞)^(∞) y(t) dt is

1. 1.5
2. 2.5
3. 3.5
4. 4

Correct answer: 1.5

Solution

Integral of y = (integral of x1)(integral of x2). Integral x1 = 1 (on [0,1]) + 0.5 (triangle) = 1.5; integral x2 = 0.5+0.5 = 1. Product = 1.5.

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