Say I have the function,
$$ \delta\left(\tau-\frac{T}{2}\right)\mathrm d\tau $$ where T = $$\frac{2π}{ω}$$
Is this even or odd? Or neither?
Reason I ask is to find out whether I can cancel some cosine and sine terms for a convolution computation.
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$\begingroup$ The expression looks funny. $\partial$ ? $\endgroup$– herb steinbergFeb 15, 2020 at 22:21
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3$\begingroup$ I have no idea what your bizarre notation means $\endgroup$– MPWFeb 15, 2020 at 22:22
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1$\begingroup$ Are you trying to write $\delta (t -\frac{T}{2})\mathrm dt$? Either way, this doesn't seem to denote any function. $\endgroup$– Brian61354270Feb 15, 2020 at 22:23
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1$\begingroup$ @Macuser That looks like a differential, not a function. Are you simply asking whether or not the Dirac delta function is even or odd? $\endgroup$– Brian61354270Feb 15, 2020 at 22:27
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3$\begingroup$ @Macuser Do you know the definitions of even and odd functions? Have you checked whether or not they apply? Please add this context to your question with an edit $\endgroup$– Brian61354270Feb 15, 2020 at 22:29
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1 Answer
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$\delta(x)$ is an even function which peaks at $x=0$ and $\delta(-x)=\delta(x)$. But $f(t)=\delta(t-T/2)$ peaks at $t=T/2$ and it is symmetric about $t=T/2$ as $$f(T-t)=\delta(T-t-T/2)=\delta(T/2-t)=\delta(t-T/2)=f(t)$$
