Obtaining impulse response by means of cross-correlation between input and output
we can calculate it!

define $y=h*t$, $r_{xy} -$
is the cross correlation

$r_{xy}(\tau)=\int_{-\infty}^ \infty x(t)y(\tau+t)dt = (y*x^-)(\tau) = (x^-*h*x)(\tau) =(r_{xx}*h)(\tau)\underbrace{=}_{r_{xx}=\delta}h(\tau)$

so actually the cross correlation is the impulse response