Consider a narrowband desired signal, X( f ), with the variance: where 𝛽 ≪ f 0 and 𝛽 + f 0 which is uncorrelated with X( f ). a) Compute the broadband input SNR. b) Show that the optimal Wiener...

Consider a narrowband desired signal, X( f ), with the variance:

where 𝛽 ≪ f₀
and 𝛽 + f₀
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which is uncorrelated with X( f ).

a) Compute the broadband input SNR.

b) Show that the optimal Wiener gain is given by

c) Show that the MMSE is given by

d) Show how the MMSE changes if the variance of the noise is