A white Gaussian noise process
is input to two filters with impulse responses,
as shown in the accompanying figure. The corresponding outputs
respectively.
(a) Derive an expression for the cross-correlation function of the two outputs, ![](https://test.transtutors.com/qimg/9cd1ff00-060f-4641-a3cc-b3f205c33b1d.png)
(b) Derive an expression for the cross-spectral density of the two outputs ![](https://test.transtutors.com/qimg/ccf72fe8-f045-473c-a342-a9763087aed7.png)
(c) Under what conditions (on the filters) are the two outputs independent when sampled at the same instants in time? That is, when are
Independent for arbitrary t1 and t2 Express your constraints in terms of the impulse responses of the filters and also in terms of their transfer functions.