(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

find

[tex]\int_{-\infty}^{+\infty} x(t) \delta (\beta t - t_{0}) dt [/tex]

for [tex] x(t) = e^{a t} u(t) [/tex]

there is no information conserning a, β, or [tex]t_{0}[/tex]...

3. The attempt at a solution

assuming that [tex]t_{0}[/tex] is a constant

[tex]\int_{-\infty}^{+\infty} x(t) \delta (\beta t - t_{0}) dt =

\int_{-\infty}^{+\infty} e^{at}u(t) \delta (\beta t - t_{0}) dt

= \int_{0}^{+\infty} e^{at} \delta (\beta t - t_{0}) dt

= \int_{0}^{+\infty} e^{\frac{a}{b}t_{0}} dt

= +\infty

[/tex]

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# Dirac delta integration

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