Student Name Student ID Last 4 digits only EE4330 Section 001 Fundamentals of Telecommunications Systems INSTRUCTOR Dr K R Rao Fall 2006 Test 1 Thursday 28 September 2006 11 00 am 12 20 pm 1 Hour and 20 minutes INSTRUCTIONS 1 Closed books and closed notes 2 Any additional information required is attached to the test you can only use the four page cheat sheet handout 3 Choose only one answer from the options given and show all your work 4 Please print your name and last four digits of your ID 2 Q1 Find the average power of the periodic signal x t in Fig 1 x t 1 Fig 1 t 2 A B C D 1 0 1 2 3 1 Watt 1 2 Watts 1 3 Watts 1 6 Watts Q2 Find bandwidth in Hz of the signal x t 2 sinc t A B C D 1 2 Hz 1 Hz 2 Hz 4 Hz Q3 Find the value of t e j t dt A 1 B e jT C 2 sin T D None is correct Q4 Determine the average power of x t 10 sin 3t cos 6t cos 10t Hint sin A cos B sin A B sin A B Average power of K cos K2 2 Average power of K sin K2 2 A 5 5 Watts B 1 25 Watts C 2 5 Watts D 12 5 Watts 3 Q5 Ring modulator in Fig 2 is used to generate the DSB SC signal D1 a c D4 m t vi t Bandpass DSB SC filter D2 b D3 c t A cos ct d 0 c t A cos ct t Fig 2 Which assumption is TRUE A B C D During negative half cycle of c t D1 and D3 open D2 and D4 conduct During positive half cycle of c t D1 and D2 conduct D3 and D4 open Both A and B are correct None is correct Q6 From Q5 ring modulator is equivalent to modulation with square wave w t The equivalent diagram is given in Fig 3 The Fourier series expansion of w t is given by w t 1 2 c 1 w t 4 cos ct 1 3 cos 3 ct vi t m t t 4 c 1 5 cos 5 ct Bandpass filter 1 7 cos 7 ct u t BPF 1 0 2 c 3 c w t Fig 3 If the bandpass filter has bandwidth 2 c and center frequency at 3 c determine the modulated output u t Given bandwidth of m t is much less than c A 4 m t B 4 m t cos ct C 34 m t cos 3 ct D 4 m t cos ct 4 3 m t cos 3 ct 4 5 m t cos 5 ct 4 c 4 Q7 For amplitude modulation DSB with carrier with modulation index which is TRUE A B C D Envelope detection cannot be applied Envelope detection is NOT possible when 1 Envelope detection is NOT possible when 1 Envelope detection is always possible Q8 Periodic triangle signal m t shown in Fig 4 is modulated with the carrier The result is AM DSB with carrier A m t cos ct 10 sec m t 3 V t 3 V Fig 4 Given carrier amplitude A 5 find the AM modulation index A B C D 1 0 83 0 6 0 3 Q9 From Q1 signal x t in Fig 1 is modulated with the carrier 2 cos ct The result is AM DSB with carrier 2 x t cos ct Find the power efficiency x t 1 t 2 1 0 Fig 1 from Q1 A 1 B 4 C 10 D 25 1 2 3 5 Q10 Tone signal B cos mt is modulated with the carrier A cos ct The modulated signal is given by A B cos mt cos ct If the tone signal magnitude B is reduced by half WITHOUT changing the modulation index what is TRUE about the average power of the carrier A B C D Carrier power does not change Carrier power increases 2 times Carrier power decreases 2 times Carrier power decreases 4 times Q11 Coherent demodulation of AM signal is given in Fig 5 The lowpass filter and message signal m t have the same bandwidths A m t sin ct i Lowpass filter ii dc blocker Fig 5 sin ct Determine the signal at i A B C D j A m t A m t A m t 2 A m t sin2 ct Q12 From Q11 determine the signal at ii A B C D j m t m t m t 2 0 Q13 The power efficiency for tone modulation under the best condition is A B C D 25 33 3 56 6 83 3 6 Q14 Given QAM diagram in Fig 6 the two baseband signals m1 t 2 cos 10t and m2 t cos 50t are modulated and are transmitted simultaneously m1 t cos ct i 2 sin ct Fig 6 m2 t Determine the QAM signal at i A B C D 2 cos ct cos 10t cos ct cos 50t sin ct 2 cos ct cos 10t cos ct cos 50t sin ct cos ct cos 10t cos ct cos 50t sin ct 2 cos ct cos 10t cos ct cos 50t sin ct Q15 From Q14 determine the bandwidth in rad sec of the QAM signal at i A B C D 120 rad sec 100 rad sec 60 rad sec 50 rad sec Q16 Given a signal m t 4 cos 10t cos 30t find mh t Where mh t is Hilbert transform of m t A B C D 2 sin 40t 2 sin 20t 2 sin 40t 2 sin 20t 2 cos 40t 2 cos 20t 2 cos 40t 2 cos 20t Q17 Single sideband modulation given the modulating signal m t cos 20t and carrier frequency c 100 rad sec find the USB upper sideband expression A B C D sin 20t cos 20t cos 80t cos 120t 7 Q18 Envelope detection of SSB signal with a carrier SSB C given carrier frequency c rad sec and message signal m t sin 10t The modulated SSB C signal is given by SSB C t 10 cos ct sin 10t cos ct cos 10t sin ct Rewrite the SSB C signal such that SSB C t E t cos ct t Determine the envelope E t A B C D 101 20 cos10t 101 20 cos10t 101 20 sin 10t 101 20 sin 10t Q19 VSB modulator in Fig 7 uses the vestigial filter Hi f given in Fig 8 to generate the VSB signal VSB t The carrier frequency fc is 10 kHz The message signal m t has bandwidth 3 kHz Determine the bandwidth in Hz of the VSB signal m t Bandpass filter VSB filter Hi f VSB t 1 Hi f 0 5 11 10 13 2 cos 2 fct Fig 7 9 0 9 10 11 12 13 Fig 8 A 3 kHz …