3 - The Game Simplified

Lets look at what happens if our signals are not periodic. We can achieve this by setting our period T to infinity such that $\underset{T\to \mathrm{\infty }}{\lim }\sum _{n=-\mathrm{\infty }}^{\mathrm{\infty }}(1/T\underset{-T/2}{\overset{T/2}{\int }}x(t^{\text{'}})e^{-j2\pi n{t}^{\text{'}}/T}d{t}^{\text{'}})e^{j2\pi nt/T},$
where
$1/T\underset{-T/2}{\overset{T/2}{\int }}x(t^{\text{'}})e^{-j2\pi n{t}^{\text{'}}/T}d{t}^{\text{'}}={\alpha }_n$
first we need to remove the restiction x(t) = x(t + T) by following these steps.
1/T $⟹df$
n/T $⟹df$
<math> \sum_{n=-\infty} ^\infty