So say there's a filter with an impulse response of $h(t) = (0.8)^t u(t)$. I'd like to pass white noise through this and figure out the autocorrelation and power spectral density of the output.
I'm having a bit of trouble figuring out exactly how to do this. I know if you pass a signal through a filter, you simply take the Fourier transforms of the signal and the impulse response, multiply them together, and that's the output.
However, not being any mathematical expression for the noise, I'm unsure how to proceed. Any tips would be appreciated.