Problem 1) A certain telephone channel has He(w) = 10-3 over the signal band. The message...

Transcribed Image Text:

Problem 1) A certain telephone channel has He(w) = 10-3 over the signal band. The message signal PSD is Sm (w) = Brect (w/2a), with a = 8000. The channel noise PSD is S, (w) = 10-8. If the output SNR at the receiver is required to be at least 30 dB, what is the minimum transmitted power required? Calculate the value of ß corresponding to this power. Problem 2) For a DSB-SC system with a channel noise PSD of Sn (w) = 10-8 and a baseband signal of bandwidth 4 kHz, the receiver output SNR is required to be at least 30 dB. The receiver is as shown below. m(1) Channel √2 cost Noise Tx Channel Bandpass Filter @±2¬B √2 cost S₁, N₁ y,(1) Receiver Baseband Filter (LPF) Demodulator S., N. y (1) (a) What must be the signal power S, received at the receiver input? (b) What is the receiver output noise power No? (c) What is the minimum transmitted power ST if the channel transfer function is He(w) = 10-4 over the transmission band? Problem 3) In a DSB-SC system, the carrier frequency is f-600kHz, and the modulating signal m(t) has a uniform PSD band-limited to 5 kHz. The modulated signal is transmitted over a distortionless channel with a noise PSD Sn (w) = 1/(w² + a²), where a 10°r. The useful signal power at the receiver input is 3uW. The received signal is bandpass filtered, multiplied by 2cos(@ct), and then low-pass filtered to obtain the output so(t) + no(t). Determine the output SNR. = Problem 1) A certain telephone channel has He(w) = 10-3 over the signal band. The message signal PSD is Sm (w) = Brect (w/2a), with a = 8000. The channel noise PSD is S, (w) = 10-8. If the output SNR at the receiver is required to be at least 30 dB, what is the minimum transmitted power required? Calculate the value of ß corresponding to this power. Problem 2) For a DSB-SC system with a channel noise PSD of Sn (w) = 10-8 and a baseband signal of bandwidth 4 kHz, the receiver output SNR is required to be at least 30 dB. The receiver is as shown below. m(1) Channel √2 cost Noise Tx Channel Bandpass Filter @±2¬B √2 cost S₁, N₁ y,(1) Receiver Baseband Filter (LPF) Demodulator S., N. y (1) (a) What must be the signal power S, received at the receiver input? (b) What is the receiver output noise power No? (c) What is the minimum transmitted power ST if the channel transfer function is He(w) = 10-4 over the transmission band? Problem 3) In a DSB-SC system, the carrier frequency is f-600kHz, and the modulating signal m(t) has a uniform PSD band-limited to 5 kHz. The modulated signal is transmitted over a distortionless channel with a noise PSD Sn (w) = 1/(w² + a²), where a 10°r. The useful signal power at the receiver input is 3uW. The received signal is bandpass filtered, multiplied by 2cos(@ct), and then low-pass filtered to obtain the output so(t) + no(t). Determine the output SNR. =