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Digital Signal Processing Solutions to Midterm Exam 2009

This document contains solutions and discussions related to the 2009 Midterm Exam in Digital Signal Processing, edited by Shih-Ming Huang and confirmed by Prof. Jar-Ferr Yang. The content addresses key concepts including stability, causality, time invariance, and linear systems. Each problem is explored step-by-step, providing a thorough understanding of fundamental DSP principles. Additional resources are also mentioned to enhance learning in the field of Digital Signal Processing.

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Digital Signal Processing Solutions to Midterm Exam 2009

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  1. Digital Signal ProcessingSolutions to Midterm Exam 2009Edited by Shih-Ming HuangConfirmed by Prof. Jar-Ferr YangLAB: 92923 R, TEL: ext. 621E-mail: smhuang@video5.ee.ncku.edu.twPage of MediaCore: http://mediawww.ee.ncku.edu.tw

  2. 1. (1) a e (2) c d (3) d (4) a b c e 2. Stable: b c e f Casual: e Memory: All 3. (a) stable, casual, initial value = 1/3 at position 1 (b) unstable, non-casual, final value = -1 at position 1 (c) unstable, non-casual, final value = 2 at position 2 (d) stable, non-casual, None (e) unstable, non-casual, final value = 1 at position 2 (f) unstable, non-casual, initial value = 1/2 at position -1

  3. 1 (1) is y[n] = nx[2n] linear? Sol: Step 1: y1[n]=T(x1[n])=nx1[2n] Step 2: y2[n]=T(x2[n])=nx2[2n] Step 3: y3[n]=T(x1[n] + x2[n])=n(x1[2n]+x2[2n]) Step 4: y3[n] = y1[n]+y2[n]

  4. 1 (2) is y[n] = x2[n] time-invariant? Sol: Step 1: y1[n]= x2[n-n0] Step 2: y[n- n0]= x2[n- n0] = y1[n]= x2[n-n0]

  5. 4 a b c d

  6. 5 a b

  7. 6

  8. 7 a b

  9. 8. a b

  10. 9. a b

  11. 10. (a) (b)

  12. -p/T -p -3p p/T p 3p 11. 1/T x[n] 0 xc(t) 1/T … v[n] 2p -2p 0 -p p p/3 -p/3 1/3T … … w[n] 0 yc(t) p -3p 3p -p T’/3T 1/3T … … y[n] p -3p 3p -p p/3T -p/3T 2p -2p 4p 0 0

  13. 12. with 0.5rL < ROCY < 0.5rU

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