EE390 Final Exam Fall Term 2002 Friday, December 13, 2002

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1 Name Page 1 of 11 EE390 Final Exam Fall Term 2002 Friday, December 13, 2002 Notes 1. This is a 2 hour exam, starting at 9:00 am and ending at 11:00 am. The exam is worth a total of 50 marks, broken down as follows: Question 1-10 marks Question 2-10 marks Question 3-10 marks Question 4-10 marks Question 5-10 marks 2. This is a closed-book exam. Only the exam pages, a formula sheet (both sides of an 8.5 x11 sheet, provided by you), a calculator, and writing instruments are allowed. Use the backs of the exam pages for rough calculations, if necessary. No scrap paper allowed. 3. Please write your solutions on the test paper in the spaces provided (write on the back of pages where necessary). Hand in all pages that were provided to you. 4. Sign the class list before you leave. 5. Good luck. Marking Question 1 /10 Question 2 /10 Question 3 /10 Question 4 /10 Question 5 /10 Total /50

2 Name Page 2 of 11 Question 1 a. Consider sampling the signal g(t)=1000 sinc(1000πt). Determine the Nyquist rate, f S min, and the Nyquist interval. (3 marks) b. Is the signal g(t) (from part a.) a power or an energy signal? Calculate the appropriate quantity (energy or power). (3 marks)

3 Name Page 3 of 11 c. Estimate the information content of the signal g(t) from part a. In a couple of sentences, explain your estimate. (2 marks) d. The signal g(t) from part a. is passed through an ideal low-pass filter (LPF) with cutoff frequency at 400 Hz. What percentage of the signal energy or power passes through the LPF? (2 marks)

4 Name Page 4 of 11 Question 2 a. Consider sending a baseband audio signal, with bandwidth of 30 khz, by pulse-code modulation (uniform quantization). A signal to noise ratio greater than 50 db is specified. Determine the minimum number of bits required to encode each sample, by assuming that the audio signal is a pure sinusoid with peak value equal to the peak value accepted by the analog to digital convertor. (4 marks). b. Assume the signal in part a. is sampled at 20 % above the Nyquist rate, and is encoded with the number of bits per sample determined in a. (if you didn t do part a., just assume a reasonable number of bits per sample). Determine the binary symbol rate (bits per second) of the PCM signal, and estimate the theoretical minimum channel (transmission) bandwidth required. (3 marks)

5 Name Page 5 of 11 c. Assume that the transmission bandwidth can be increased by 50% for the pcm signal above. Estimate the reduction in transmit power that this allows while keeping the SNR fixed (assume the same sampling rate as in b.). (3 marks)

6 Name Page 6 of 11 Question 3 Consider using the baseband signal shown below to modulate a high-frequency carrier. a. Sketch the time-domain waveform of the modulated signal if double-sideband suppressed-carrier (DSB-SC) modulation is used. (1 mark) b. Sketch the time-domain waveform of the modulated signal if frequency modulation (FM) is used. (2 marks) c. Sketch the time-domain waveform of the modulated signal if phase modulation (PM) is used. (3 marks)

7 Name Page 7 of 11 d. For the phase modulation case, assume k p =20π, and estimate the essential bandwidth occupied by the modulated signal. Justify (briefly) any assumptions you make. Is this wideband or narrowband phase modulation? (4 marks)

8 Name Page 8 of 11 Question 4 a. Consider sampling a 25 khz bandwidth baseband analog signal and sending it using binary digital transmission (ie. PCM encoded). The quantization error should be no greater than 1% of the peak amplitude of the baseband signal. Assuming uniform quantization, sampling at 50% greater than the Nyquist rate (ie. f s =1.5f S min ), and zero ISI pulses with roll-off factor r=0.25, determine the required transmission bandwidth, B T. (5 marks) b. The signal in part a. (25 khz baseband bandwidth) is to be sent using an m-ary digital line code over a channel with bandwidth of 50 khz. It has been determined that 64 quantization levels and sampling at only 20% greater than the Nyquist rate provides adequate fidelity in this case. What is the minimum value for m, assuming that it is possible to send the maximum rate of information (2 symbols per second per Hz) over the channel? (5 marks)

9 Name Page 9 of 11 Question 5 (1 mark per multiple choice question, 10 marks total) Select the appropriate answer (by circling one of a, b, c, or d) for each of the questions below: I. From the perspective of signal fidelity, FM broadcast radio is superior to AM broadcast radio. Which of the following is not a reason: a. In FM, more bandwidth is allowed for the baseband audio signal. b. In FM, more transmission bandwidth is allowed. c. In FM, clipping circuits can be used at the receiver, so that transmit power (thus SNR) can be higher. d. FM signals have inherent immunity to nonlinearities. II. It is not possible for a modulator to be a linear time invariant (LTI) system, because: a. LTI systems have impulse response that extends over all time, and cannot be realized in practice. b. LTI systems are based on assumption of power signals, while all real signals are energy signals. c. All real systems are at least slightly nonlinear. d. LTI systems never shift energy from one frequency to another. III. According to the maximum rate of information rule: a. binary digital communication allows maximum rate of information over a given channel, since it occupies the most bandwidth. b. Channel bandwidth limits the rate of change of a time signal, and therefore the number of independent symbols that can be sent per second. c. Noise and bandwidth are fundamental limitations to the maximum bit rate. d. We can never completely eliminate errors in a digital communication system. IV. In practice, a signal cannot be exactly reconstructed from its quantized samples. Which of the following is not a reason for this: a. it would require an unrealizable filter that completely attenuates a range of frequencies. b. Real signals are time-limited and therefore are not exactly band-limited. c. Quantization always introduces some error. d. It is impossible to generate a train of Dirac delta functions (ideal impulses). V. Standard pulse-code modulation (PCM) is inherently bandwidth inefficient because: a. the sampling rate is chosen to exceed the Nyquist rate of the highest significant frequency in the baseband signal. b. uniform quantization results in a signal to noise ratio that varies with signal power. c. Square pulses have significant power in high frequency harmonics. d. The number of quantization levels used must be a power of 2. VI. Digital transmission benefits from regenerative repeaters, because: a. repeaters completely negate the impact of noise on a communication channel. b. repeaters ensure that signal impairments due to noise stay within acceptable limits. c. Repeaters are insensitive to channel distortion. d. Repeaters can store binary data until channel characteristics are optimal.

10 Name Page 10 of 11 VII. Which did Nyquist demonstrate to be true?: a. Intersymbol interference can be completely negated using practical filters. b. a raised cosine filter characteristic can be realized without infinite delay. c. Practical filters can be employed to greatly reduce intersymbol interference. d. Ideal low pass filters are possible in digital systems, because of noise immunity. VIII. Entropy coding is the science of: a. assigning code word lengths based on the amount of information in a particular message. b. adding redundant bits to a digital message as a means of error control. c. Shaping pulses to ensure that there is a DC null in their power spectral density. d. Embedding color information in unused portions of the black and white video spectrum. IX. The four main criteria for comparing digital line codes are: a. bits per symbol, power efficiency, inter-symbol interference, bandwidth. b. Transparency, spectral shape, bandwidth, power efficiency. c. Bandwidth, pulse shape, SNR, roll-off factor. d. Power efficiency, chip rate, transparency, vestigial bandwidth. X. The two fundamental limitations faced by a communication engineer are: a. Time and distance. b. Ice and snow. c. Lectures and Labs. d. Bandwidth and noise!! Have a good holiday.

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TSEK02: Radio Electronics Lecture 2: Modulation (I) Ted Johansson, EKS, ISY

TSEK02: Radio Electronics Lecture 2: Modulation (I) Ted Johansson, EKS, ISY 2 Basic Definitions Time and Frequency db conversion Power and dbm Filter Basics 3 Filter Filter is a component with frequency