Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. Professional Engineers Ontario / Engineers Canada national examination 07-Elec-A3 — Signals and Communications, December 2016. Three hours, closed book; a standard non-programmable calculator is the only permitted aid. Six questions of equal value (20 marks each); any five constitute a complete paper. All six are solved below, because this set is a study resource rather than an examination script.
Reference texts. B. P. Lathi and Z. Ding, Modern Digital and Analog Communication Systems, 4th ed. (Ch. 2–4 Fourier analysis, Ch. 4 amplitude modulation, Ch. 5 angle modulation, Ch. 6 sampling and pulse-code modulation); A. V. Oppenheim and A. S. Willsky, Signals and Systems, 2nd ed. (Ch. 3 Fourier series, Ch. 10 the z-transform); J. G. Proakis and D. G. Manolakis, Digital Signal Processing, 4th ed. (Ch. 3 z-transform, Ch. 7 realisation structures); S. Haykin and M. Moher, Communication Systems, 5th ed. (Ch. 3 amplitude modulation, Ch. 4 angle modulation, Ch. 7 digital transmission).
Notation used throughout. The normalised sinc function is $\operatorname{sinc}(x)=\dfrac{\sin \pi x}{\pi x}$, so that $\operatorname{sinc}(0)=1$ and the zeros sit at the non-zero integers. Average power of a periodic signal is $P=\frac{1}{T_0}\int_{T_0}|x(t)|^{2}\,dt$, and the exponential Fourier series is $x(t)=\sum_{n=-\infty}^{\infty} c_n e^{j n \omega_0 t}$ with $P=\sum_n |c_n|^{2}$ (Parseval).
