- #1
alena_S
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Member warned about posting with no effort shown
Homework Statement
I am trying to figure out following problem.
Let A ⊂ R. Then we can define the characteristic function:
\begin{align}
\chi_A : R → \{0, 1\}, x = \begin{cases}
1 & \text{if } x \in A \\
0 & \text{else }
\end{cases}
\end{align}
Let a be bigger than 0. I am trying to find a following convolution:
\begin{align}
\chi_{[-a,a]} * \chi_{[-a,a]} * \chi_{[-a,a]}
\end{align}
Homework Equations
Convolution is given as
\begin{align}
f*g = \int f(x-y) g(y) dy
\end{align}
The Attempt at a Solution
I have started to do convolution of 1st 2 terms, my results are as follows(not sure about correctness)[/B]
\begin{align}
\phi * \phi (x) = \begin{cases}
0 & x \leq -a \\
x & \text{ if } -a \leq x \leq a\\
2a - x & \text{ if } a \leq x \leq 2a\\
0 & x \geq 2a
\end{cases}
\end{align}
but I am being stuck what should follow.
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