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.
$\endgroup$ 81 Answer
$\begingroup$$\delta(x)$ is an even function which peaks at $x=0$ and $\delta(-x)=\delta(x)$. But $f(t)=\delta(t-T/2)$ peaks at $t=T/2$ and it is symmetric about $t=T/2$ as$$f(T-t)=\delta(T-t-T/2)=\delta(T/2-t)=\delta(t-T/2)=f(t)$$
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