White noise with two-sided power spectral density 1/2 N₀ is added to a signal having the power spectral density shown in Figure 8.22. The sum (signal plus noise) is filtered with an ideal low pass filter with unity pass band gain and bandwidth B > W. Determine the SNR at the filter output. By what factor will the SNR increase if B is reduced to W?

Figure 8.22

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S,(f) S,(f) = kf²