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22-Elec-B1 Digital Signal Processing: December 2019

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

  1. Question 1 Sampling Followed by Ideal Reconstruction
  2. Question 2 Six-Point DFT, Circular Shift and Circular Convolution
  3. Question 3 Impulse Response, Output and Stability of a First-Order System
  4. Question 4 Stability and Structures for a Parallel System
  5. Question 5 Kaiser Window Design of a Three-Band FIR Filter
  6. Question 6 IIR Design Choices and Linear-Phase FIR Types

Start with Question 1 →

Paper format. National Exams, December 2019 — 16-Elec-B1, Digital Signal Processing. Closed book, 3 hours. Six questions, each worth 12 marks; the rubric states that five questions constitute a complete paper. All six 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. (Pearson) — the syllabus text for this code; J. G. Proakis and D. G. Manolakis, Digital Signal Processing: Principles, Algorithms and Applications, 4th ed.; S. K. Mitra, Digital Signal Processing: A Computer-Based Approach. Formula sheets supplied with the paper (DTFT/DFT/z-transform tables) are reproduced only where a step uses them.

Question 3 system function. The printed system function for Question 3 is $H(z)=(1-z^{-1})/\left(1+\tfrac{3}{4}z^{-1}\right)$, and all work below follows it.