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As I understand it, to convolve $f$ and $g$ means to find $\displaystyle \int_{\mathbb R} f(a)g(t-a)da$, which is also apparently commutative, and therefore $\displaystyle \int_{\mathbb R}f(a)g(t-a)da = \displaystyle \int_{\mathbb R}f(t-a)g(a)da$

That means, if $f(a) = 1$, then $\displaystyle \int_{\mathbb R}g(t-a)da = \displaystyle \int_{\mathbb R}g(a)da$. For $g(t) = t$, for example, is not true. So what am I misunderstanding?

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    Neither integral converges for g(t)=t.2011-03-01
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    For your purposes you should only consider functions with finite integral.. preferably their absolute value has finite integral. Otherwise you're comparing infinities which gets icky and sometimes not well-defined.2011-03-01

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