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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,

(b) Derive an expression for the cross-spectral density of the two outputs

(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.

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Electrical & Electronics, Engineering

Category:- Electrical & Electronics
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