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22-Elec-B1 Digital Signal Processing: May 2015

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

  1. Question 1 Reconstructing a real causal sequence from six transform clues (12 marks)
  2. Question 2 Sampling a band-limited periodic signal (12 marks)
  3. Question 3 Pole-zero transformations of a causal stable system (12 marks)
  4. Question 4 Parallel and cascade realisations of an IIR system (12 marks)
  5. Question 5 Circular versus linear convolution, and the FFT route (12 marks)
  6. Question 6 IIR design by transformation and the four linear-phase FIR types (12 marks)

Start with Question 1 →

Paper format. National Exams, May 2015 — 07-Elec-B1 Digital Signal Processing. Three hours, closed book; candidates may use one approved Casio or Sharp calculator and one aid sheet written on both sides. Six questions are printed and five constitute a complete exam, each worth 12 marks (72 printed, 60 counted). Every question and sub-part is worked below, because this set is intended as a study resource rather than an exam script. The tables of z-transform pairs and DFT properties bound into the back of the paper are reproduced from Oppenheim & Schafer and are quoted where used.

Reference texts.

  • A. V. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing, 3rd ed., Pearson — Ch. 2 (LTI systems and the DTFT), Ch. 3 (the z-transform, Tables 3.1 and 3.2), Ch. 4 (sampling), Ch. 6 (filter structures), Ch. 7 (IIR and FIR design), Ch. 8 (the DFT and circular convolution), Ch. 9 (the FFT). This is the text the printed appendix tables are taken from.
  • J. G. Proakis and D. G. Manolakis, Digital Signal Processing: Principles, Algorithms and Applications, 4th ed., Pearson — Ch. 5 (DFT), Ch. 8 (IIR design), Ch. 10 (FIR design).
  • A. V. Oppenheim and A. S. Willsky, Signals and Systems, 2nd ed., Prentice Hall — Ch. 3 (Fourier series), Ch. 7 (sampling).