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22-Elec-B1 Digital Signal Processing: May 2014

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

  1. Question 1 Pole-Zero Diagrams, ROC, Stability and Causality
  2. Question 2 FIR and IIR Notch Filter Design from a DFT Spectrum
  3. Question 3 Applying the DFT Twice: Recovering the Original Sequence
  4. Question 4 One Output, Four Methods: Iteration, Convolution, Circular Convolution and the DFT
  5. Question 5 System Reconstruction from Poles, Zeros and d.c. Gain
  6. Question 6 Impulse Response, Frequency Response and Sinusoidal Steady State
  7. Question 7 Computing the IDFT with a Forward-DFT Block

Start with Question 1 →

Paper format. National Exams May 2014, 07-Elec-B1 Digital Signal Processing — 3 hours, open book, any non-communicating calculator permitted. Seven questions are printed; five constitute a complete paper and the first five appearing in the answer book are marked. All questions are of equal value (20 marks each; the printed marking scheme gives the sub-part split). A table of symbols, trigonometric identities, DFT definitions, DTFT tables and z-transform tables is supplied at the back of the paper. All seven questions are solved below, so the set works as a complete study resource.

Reference texts. Proakis & Manolakis, Digital Signal Processing, 4th ed. (z-transform and ROC, Ch. 3; DFT and FFT, Ch. 7; filter structures, Ch. 9); Oppenheim & Schafer, Discrete-Time Signal Processing, 3rd ed. (the DTFT symmetry and transform tables reproduced at the back of this paper are Tables 2.1–2.3 of that text); B. P. Lathi, Linear Systems and Signals, 2nd ed. (discrete-time convolution and system response).