22-Elec-A3 Signals and Communications, December 2019: worked solutions

Paper format. National Examinations, December 2019 — 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 submit a clear statement of any assumption made where a question admits more than one reading.

Reference texts.

B. P. Lathi and Z. Ding, Modern Digital and Analog Communication Systems, 4th ed. — Ch. 2–3 (Fourier series and transforms), Ch. 4 (amplitude modulation, DSB and SSB), Ch. 5 (angle modulation, Carson's rule), 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 and 9 (discrete-time systems and the z-transform).
A. V. Oppenheim and A. S. Willsky, Signals and Systems, 2nd ed. — Ch. 3 (Fourier series), Ch. 4 (Fourier transform), Ch. 8 (modulation), Ch. 10 (z-transform).
J. G. Proakis and D. G. Manolakis, Digital Signal Processing, 4th ed. — Ch. 2 (LTI systems and convolution), Ch. 5 (frequency-domain analysis), Ch. 9 (FIR filter structures).
S. Haykin, Communication Systems, 5th ed. — Ch. 3 (amplitude modulation), Ch. 4 (angle modulation), Ch. 5 (pulse-code modulation and quantisation noise).

Note on scope. This sitting carries no printed figures: every system in Questions 4 and 5 is specified analytically, so all block diagrams and plots below are constructed from the given equations. Where the examiner asks for a "plot", a labelled sketch with the correct line positions, weights and signs is what earns the marks — each figure here is drawn to that standard.

22-Elec-A3 Signals and Communications: December 2019