In the noise analyzer of Figure a, the low-pass filters are ideal with a bandwidth equal to one-half that of the narrowband noise n (t) applied to the input. Using this scheme, derive the following result:

(a) Equation (1.101), defining the power spectral densities of the in-phase noise component n1 (t) and quadrature noise components nQ (t) in terms of the power spectral density of n (t).

(b) Equation (1.102), defining the cross-spectral densities of n1 (t) and nQ (t)