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22-Elec-A3 Signals and Communications: May 2014

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

  1. Question 1 Sampling and Reconstruction of a Squared-Sinc Signal
  2. Question 2 Sampling a Two-Tone Message, With and Without Aliasing
  3. Question 3 Scaling, Shifting and Modulation of a Sinc Pulse
  4. Question 4 Reading an FM Spectrum with Bessel Coefficients
  5. Question 5 PCM Design for a Television Signal
  6. Question 6 AM Signal Parameters, Power Budget and Efficiency
  7. Question 7 Testing a Cascade for Linearity and Distortionlessness
  8. Question 8 Regions of Convergence and Impulse Responses of a Discrete System
  9. Question 9 M-ary PCM Bandwidth for an Audio Channel
  10. Question 10 Matched Filtering and Decoding of Split-Phase Manchester Data

Start with Question 1 →

Paper format. National Exams, May 2014 — 07-Elec-A3 Signals and Communications. Three hours, open book, any non-communicating calculator permitted. Ten questions of equal value (20 marks each); the rubric states that five questions constitute a complete paper and only the first five presented are marked. All ten are solved here, since the set is intended as a study resource. A table of Fourier-transform pairs and properties, a table of z-transform pairs, trigonometric identities and Bessel-function graphs/tables are supplied with the paper and are used freely below.

Reference texts. B. P. Lathi and Z. Ding, Modern Digital and Analog Communication Systems, 4th ed. (sampling, PCM, AM/FM, matched filtering); B. P. Lathi, Linear Systems and Signals, 2nd ed. (Fourier analysis, LTI properties); A. V. Oppenheim and A. S. Willsky, Signals and Systems, 2nd ed. (z-transform, regions of convergence); S. Haykin, Communication Systems, 5th ed. (digital transmission, eye diagrams).

Convention used throughout. This paper's own transform table defines the sinc function as $\operatorname{sinc}(x)=\sin x / x$ (Lathi's convention, not the normalised $\sin(\pi x)/(\pi x)$). Every bandwidth below follows from that table, in particular $2B\operatorname{sinc}(2\pi Bt)\leftrightarrow\operatorname{rect}(f/2B)$ and $B\operatorname{sinc}^2(\pi Bt)\leftrightarrow\Delta(f/2B)$.