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I want to convolve two triangles. The equation satisfied by one triangle is

$$f(y) = \begin{cases} y + 1 & −1 < y < 0\\ \\ 1 − y & 0 \leq y < 1 \end{cases}.$$

So, the overall duration of a triangle is $\;-1\;$ to $\;1$.

What I have found is that the convolution of a triangle with itself is a $\operatorname{sinc}$ function but does one obtain this $\operatorname{sinc}$ from the above equation?

Secondly, what should be the limits of integral for calculating convolution?

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    It might be worthwhile asking the moderators to migrate this question to dsp.SE. With regard to your question about the limits on the integral for calculating convolutions, there is not a single integral that you have to compute, but different integrals depending on your choice for the _argument_ of the _function_ that is the _result_ of the convolution. For a _detailed exposition_ of how to go about convolving two signals, see [my answer to a similar question](http://dsp.stackexchange.com/a/1405/235) on dsp.SE2012-12-22

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