Convolution of the step function, three times

Thread starter nightshade123
Start date Nov 13, 2009
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Convolution Function Step function

AI Thread Summary

The discussion focuses on the convolution of the step function u(t) with itself three times. It is established that the convolution of u(t) with itself results in t u(t). The participant attempts to calculate the convolution of (t u(t)) with u(t) and derives the integral of τ dτ from 0 to t. The final result presented is 1/2 t^2 u(t), which the participant believes is correct. The solution process and final answer are confirmed as satisfactory.

Nov 13, 2009

nightshade123

Homework Statement

u(t) * u(t) * u(t)

* indicates convolution

Homework Equations

i know u(t) * u(t) = t u(t)

The Attempt at a Solution

so (t u(t)) * u(t) = \int \tau d \tau limits of integration are 0 to t
so the answer is 1/2 t^2 u(t)?

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Nov 16, 2009

Redbelly98

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Looks good to me

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