Pick an input and an impulse response, then slide the flipped one across with your finger. The overlap is shaded, its area is the output at that instant, and the output curve grows point by point. A discrete mode shows the sum of products term by term.
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Flip , slide it to , multiply, and take the area. That area is one point of .
Input
Impulse response
x(τ) stays still, h(t − τ) is flipped and slides
Their product. The shaded area is y(t): 0.500
Output so far
The output starts at 0, the sum of the two start times. It ends at 3, the sum of the two end times, so its length is the sum of the two lengths.