4. (10%) A white Gaussian noise with two-sided power spectral density (PSD) \( N_0 / 2 \) is added to a signal having PSD given by \( S_{x}(f) = f^{4} \) for \( |f| \leq W \) and \( S_{x}(f) = 0 \) otherwise. The sum is filtered by an ideal low pass filter with gain 1 and bandwidth \( B > W \). Determine the signal-to-noise ratio (SNR) at the output. How much do we gain in SNR if we change the bandwidth to \( B = W \)?