Bandlimited Random Processes Plot the power spectral density of the amplitude modulated signal Y() in Example,...

  

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Bandlimited Random Processes Plot the power spectral density of the amplitude modulated signal Y() in Example, assuming fc > W; fc < W. Assume that A() is the signal in Problem. Example Example Demodulation of Noisy Signal The received signal in an AM system is Y(t) = A(t) cos(2mft + 0) + N(1), where M(t) is a bandlimited white noise process with spectral density No 2 SN(f) If ± fcl <W elsewhere. Find the signal-to-noise ratio of the recovered signal. Equation allows us to represent the received signal by N(1) = N(1) cos(2#fd + e) - N,(t) sin(2nf + 0). (Eq) Y(t) = {A(1) + N(1)} cos(2nf + ) - N,(t) sin(2mfd + 0). The demodulator in Fig. is used to recover A(f). After multiplication by 2 cos(27fct + Ⓒ), we have Fig X(1) 2 cos (2mfd + 0) LPF -Y(1) 2Y (1) cos(2mf1 + 0) = (A(1) + N(1)}2 cos² (2mf1 + 0) - N,(t)2 cos(2#f1 + 0) sin(2af1 + 0) - {A(1) + N(1)} (1 + cos(4mf1 +20)) - N₂(1) sin(4mf + 20). After lowpass filtering, the recovered signal is A(t) + Ne(t). The power in the signal and noise components, respectively, are - [SA(f) af -W No PN. - [SN,(f) df = [(+2) df. -W The output signal-to-noise ratio is then SNR df = 2W No- 2W No (b) Find Rz(1) and SZń). Problem (b) Find the autocorrelation corresponding to the power spectral density Sx(f) = g(f/w). Bandlimited Random Processes Plot the power spectral density of the amplitude modulated signal Y() in Example, assuming fc > W; fc < W. Assume that A() is the signal in Problem. Example Example Demodulation of Noisy Signal The received signal in an AM system is Y(t) = A(t) cos(2mft + 0) + N(1), where M(t) is a bandlimited white noise process with spectral density No 2 SN(f) If ± fcl <W elsewhere. Find the signal-to-noise ratio of the recovered signal. Equation allows us to represent the received signal by N(1) = N(1) cos(2#fd + e) - N,(t) sin(2nf + 0). (Eq) Y(t) = {A(1) + N(1)} cos(2nf + ) - N,(t) sin(2mfd + 0). The demodulator in Fig. is used to recover A(f). After multiplication by 2 cos(27fct + Ⓒ), we have Fig X(1) 2 cos (2mfd + 0) LPF -Y(1) 2Y (1) cos(2mf1 + 0) = (A(1) + N(1)}2 cos² (2mf1 + 0) - N,(t)2 cos(2#f1 + 0) sin(2af1 + 0) - {A(1) + N(1)} (1 + cos(4mf1 +20)) - N₂(1) sin(4mf + 20). After lowpass filtering, the recovered signal is A(t) + Ne(t). The power in the signal and noise components, respectively, are - [SA(f) af -W No PN. - [SN,(f) df = [(+2) df. -W The output signal-to-noise ratio is then SNR df = 2W No- 2W No (b) Find Rz(1) and SZń). Problem (b) Find the autocorrelation corresponding to the power spectral density Sx(f) = g(f/w).