Is there a way to simplify two functions being convoluted with the same function, i.e. can I simplify:
\begin{align} \left[ f(t) * w(t) \right] \left[ g(t) * w(t) \right] = \int_{-\infty}^{\infty} f(\tau) w(t - \tau) d\tau \int_{-\infty}^{\infty} g(\tau) w(t - \tau) d\tau \end{align}
I could solve the two integrals seperately, but I'm looking for a more elegant approach.