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22-Elec-B1 Digital Signal Processing: Undated paper

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

  1. Question 1 Sampling rate for an ideal C/D – filter – D/C chain
  2. Question 2 Periodic convolution from a product of discrete Fourier series
  3. Question 3 Why a longer zero-padded DFT runs faster
  4. Question 4 Partial fractions, stability and causality from the ROC
  5. Question 5 Five signal flow graphs for one third-order system
  6. Question 6 Kaiser-window design of a linear-phase bandpass filter

Start with Question 1 →

Paper format. National Exam, May 2019 — 16-Elec-B1 Digital Signal Processing. Three hours, closed book; two approved calculators (Casio or Sharp) and one double-sided aid sheet are permitted. Six questions, each worth 12 marks; the printed rubric states that any five of the six constitute a complete paper. Marking scheme as printed: Q1 (a) 6 (b) 6; Q2 (a) 6 (b) 6; Q3 (a) 6 (b) 6; Q4 (a) 7 (b) 5; Q5 (a) 3 (b) 2 (c) 2 (d) 3 (e) 2; Q6 (a) 5 (b) 3 (c) 4. All six questions are solved here, because the set is a study resource rather than an exam script.

Reference texts. A. V. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing, 3rd ed. — the standard EGBC reference for this subject (sampling Ch. 4, the z-transform Ch. 3, the DFS/DFT Ch. 8, filter structures Ch. 6, FIR design by windowing Ch. 7). Supporting: J. G. Proakis and D. G. Manolakis, Digital Signal Processing: Principles, Algorithms and Applications, 4th ed.; A. V. Oppenheim and A. S. Willsky, Signals and Systems, 2nd ed. The paper supplies its own aid sheet (DTFT analysis/synthesis pair, Parseval, a table of z-transform properties, a table of common z-transform pairs including the finite-length geometric pair, the geometric sum and series, the DFT/CTFT/DTFT property table, and the Kaiser design formulas), and the solutions below use only those.

Source-quality disclosure. Two places where the paper itself is still partly illegible are flagged in check notes at the questions concerned (Q4(b) numerator coefficient, Q5 expanded denominator); in both cases the printed information elsewhere in the same expression fixes the value uniquely. Readers comparing against another copy of the paper should treat those two items as reconstructed.