Two signals g1(t) and g2(t) have average powers 4 and 5, respectively, and their zero-lag cross-correlation is 6. What is the average power of the sum signal g1(t) + g2(t)?

Introduction / Context:In signal analysis, the average power of a sum of signals depends on the individual powers and their correlation. This question checks understanding of how cross-correlation (at zero lag) contributes to the composite power of two simultaneous signals.

Given Data / Assumptions:

• P1 = average power of g1(t) = 4.
• P2 = average power of g2(t) = 5.
• R12(0) = zero-lag cross-correlation between g1 and g2 = 6.
• Signals are wide-sense stationary or time averages are meaningful for power calculation.

Concept / Approach:The time-average power of the sum is P{g1 + g2} = P1 + P2 + 2R12(0). The last term arises from the cross term 2g1(t)g2(t) when squaring and averaging. If R12(0) > 0, the sum’s power increases by twice the correlation value.

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