5. Show

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1 − ae−2????fi

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2 = 1 − 2a ⋅ cos(2????f ) + a2 and

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1 − a1e−2????fi − a2e−4????fi

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2 =

1 − 2a1 cos(2????f ) − 2a2 cos(4????f ) + 2a1a2 cos(2????f ) + a21

+ a22

[this is just the real expansion of the denominator of the AR(2) power spectrum].