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PROBLEM 1: Given figure shows the effect of eliminating higherharmonic components of a square wave and retaining only a few lower harmonic components. What would the signal look like in the opposite case; that is, retaining all higher harmonics and eliminating a few lower harmonics?
BLM256 DATA COMMUNICATIONS TUTORIAL FOR CHAPTER PROBLEM 1: Given figure shows the effect of eliminating higher-harmonic components of a square wave and retaining only a few lower harmonic components What would the signal look like in the opposite case; that is, retaining all higher harmonics and eliminating a few lower harmonics? SOLUTION: The signal would be low-amplitude, rapidly changing waveform like following signal PROBLEM 2: Given an amplifier with an effective noise temperature of 10,000oK and a 10-MHz bandwidth, what thermal noise level may we expect at its output? SOLUTION: N = 10 log k + 10 log T + 10 log B = -228.6 dBW + 10 log 104 + 10 log 107 = -228.6 + 40 +70 = - 118.6 dBW PROBLEM 3: What is the thermal noise level of a channel with a bandwidth of 10 kHz carrying 1000 watts of power operating at 50oC? SOLUTION: N=1.38x10-23x(50+273)x10,000 = 4.5x10-17 watts PROBLEM 4: Given a channel with an intended capacity of 20 Mbps, the bandwidth of the channel is MHz Assuming white thermal noise, what signal to noise ratio is required to achieve this capacity? SOLUTION: C=B log2 (1+SNR) 20x106=3x106x log2 (1+SNR) log2 (1+SNR)=6.67 1+SNR=102 SNS=101 PROBLEM 5: If an amplifier has a 30 dB voltage gain, what voltage ratio does the gain represent? SOLUTION: For a voltage ratio, we have NdB=30=20log (V2/V1) V2/V1=1030/20=101.5=31.6 PROBLEM 6: If the solid curve in following figure represents sin( 2π ) , what does the dotted curve represent? That is, the dotted curve can be written in the form A sin( 2πft + φ ) ; what are A, f , and φ ? SOLUTION: sin( 4πt + π ); A = 2, f = 2, φ = π PROBLEM 7: Assume that the TV picture is to be transmitted over a cannel with 4.5-MHz bandwidth and a 35-dB signal-to-noise ratio Find the capacity of the channel (bps) SOLUTION: PROBLEM 8: Suppose a transmitter produced 50 W of power a) Express the transmit power in units of dBm and dBW b) If the transmitter’s power is applied to a unity gain antenna with a 900-MHz carrier frequency, which is the received power in dBm at a free space distance of 100 m? SOLUTION: PROBLEM (Chapter Problem 3.7): SOLUTION: PROBLEM 10 (Chapter Problem 3.8): SOLUTION: PROBLEM 11: The square wave of Figure 3.7 c, with T=1 ms, is passed through a lowpass filter that passes frequencies up to kHz with no attenuation a) Find the power in the output waveform b) Assume that at the filter input there is a thermal noise voltage with N0=0.1 µ Watt /Hz, find the output signal to noise ratio in dB SOLUTION: PROBLEM 12: If the received signal level for a particular digital system is -151 dBW and the receiver system effective noise temperature is 1500 K, what is Eb/N0 for a link transmitting 2400 bps? SOLUTION: PROBLEM 13: What is the channel capacity for a teleprinter channel with a 300 Hz bandwidth and a signalto-noise ratio of dB, where the noise is white thermal noise? SOLUTION: PROBLEM 14: Adigital signaling system is required to operate at 9600 bps a) If a signal element encodes a bit word, what is the minimum required bandwidth of the channel? b) Repeat part (a) for the case of 8-bit words SOLUTION: PROBLEM 15: What is the thermal noise level of a channel with a bandwidth of 10 kHz carrying 1000 watts of power operating at 500C? SOLUTION: PROBLEM 16 (Chapter Problem 3.13,a,b,7): SOLUTION: