A noise process has a power spectral density given by Sn$($ f $)=1081|$ f $|108|$ f $|<1080|$ f $|>108$ This noise is passed through an ideal bandpass filter with a bandwidth of $2$ MHz centered at $50$ MHz$.1.$ Find the power content of the output process. $2.$ Write the output process in terms of the in$-$phase and quadrature components, and find the power in each component. Assume f$0=50$ MHz$.3.$ Find the power spectral density of the in$-$phase and quadrature components. $4.$ Now assume that the filter is not an ideal filter and is described by $|$H$($ f $)|2=|$ f $|1064949$ MHz $<|$ f $|<51$ MHz $0$ otherwise Repeat parts $1,2,$ and $3$ with this assumption.