Consider the system shown in Figure 8.23 The signal x(t) is defined by 

x(t) = A cos (2Ï€f_ct)

The low pass filter has unity gain in the pass band and bandwidth W, where f_c < W. The noise n(t) is white with two-sided power spectral density 1/2 N₀ . The signal component of y(t) is defined to be the component at frequency f_c. Determine the SNR of y(t).

Figure 8.23

Lowpass filter d x(t) y(t) ()dt S()dt dt dt | n(t)