22-Elec-A3 Signals and Communications, December 2018: worked solutions

Paper format. National Examinations, December 2018 — 16-Elec-A3 Signals and Communications. Three hours, closed book (an approved Casio or Sharp calculator is permitted). Answer all 5 questions; all 5 questions are of equal value (20 marks each, 100 marks total). Candidates are urged to state any assumption made where a question admits more than one reading.

Reference texts.

B. P. Lathi and R. Ding, Modern Digital and Analog Communication Systems, 4th ed. — Ch. 2–4 (Fourier series and transforms), Ch. 4 (amplitude modulation, DSB/SSB), Ch. 6 (sampling and PCM).
B. P. Lathi, Linear Systems and Signals, 2nd ed. — Ch. 6–7 (Fourier analysis of periodic and aperiodic signals), Ch. 5 (discrete-time systems).
A. V. Oppenheim and A. S. Willsky, Signals and Systems, 2nd ed. — Ch. 3 (Fourier series), Ch. 7 (sampling), Ch. 10 (z-transform).
J. G. Proakis and D. G. Manolakis, Digital Signal Processing, 4th ed. — Ch. 3 (z-transform), Ch. 5 (frequency-domain analysis of LTI systems), Ch. 9 (filter structures).
S. Haykin, Communication Systems, 5th ed. — Ch. 3 (amplitude modulation), Ch. 5 (pulse-code modulation and quantisation noise).

Note on the Question 4 figure. The block diagram shows both summing junctions drawn as plain adders — there are no minus signs at any input — so the printed arm gains are the multipliers exactly as shown: −3/4 on the first delay output into the input adder, +1/2 on the second delay output into the same adder, and +1/2 on the first delay output feeding forward to the output adder. The consequence, developed in Question 4, is that one pole falls outside the unit circle. That is a genuine property of the printed network, and the answer below treats it as such.

22-Elec-A3 Signals and Communications: December 2018