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Digital Signal Processing, 10th Edition
book

Digital Signal Processing, 10th Edition

by Maurice Bellanger, Benjamin A. Engel
April 2024
Intermediate to advanced
400 pages
12h 28m
English
Wiley
Content preview from Digital Signal Processing, 10th Edition

Exercises: Solutions and Hints

Chapter 1

  1. 1.1 upper I Subscript normal upper L Baseline left-parenthesis t right-parenthesis equals one half plus StartFraction 2 Over normal pi EndFraction sigma-summation Underscript p equals 1 Overscript 4 Endscripts StartFraction left-parenthesis negative 1 right-parenthesis Superscript p plus 1 Baseline Over 2 p minus 1 EndFraction cosine 2 pi left-parenthesis 2 p minus 1 right-parenthesis StartFraction t Over upper T EndFraction
  2. 1.2 s(nT) = sin (nπ + ϕ) = (−1)n sin ϕ.

    The possibility of reconstruction depends on ϕ. left-parenthesis phi equals StartFraction pi Over 2 EndFraction y e s semicolon phi equals 0 n o right-parenthesis.

  3. 1.3 upper H left-parenthesis StartFraction f Subscript s Baseline Over 2 EndFraction right-parenthesis equals StartFraction 2 StartRoot 2 EndRoot Over pi EndFraction left-parenthesis 0.92 d upper B right-parenthesis period
  4. 1.4 f2 < fs < 2f1.
  5. 1.5 s left-parenthesis italic n upper T right-parenthesis equals s Subscript r Baseline left-parenthesis italic n upper T right-parenthesis plus italic j s Subscript i Baseline left-parenthesis italic n upper T right-parenthesis equals e Superscript j left-parenthesis pi slash 2 right-parenthesis n Baseline StartStartFraction sine StartFraction 3 pi Over 8 EndFraction n OverOver sine left-parenthesis StartFraction pi Over 8 EndFraction n right-parenthesis EndEndFraction period
  6. 1.6 Maximum value of s(n) = 8;
    s left-parenthesis n right-parenthesis equals 0 for phi Subscript k Baseline equals minus 2 pi StartFraction k Over 8 EndFraction n plus k pi
  7. 1.7 ƒs = 2 MHz; Δƒ = 1 kHz.
  8. 1.8 p left-parenthesis 1 right-parenthesis equals StartFraction 1 Over pi EndFraction StartFraction 1 Over StartRoot upper A squared minus s squared EndRoot EndFraction semicolon r left-parenthesis tau right-parenthesis equals 2 left-parenthesis f 2 minus f 1 right-parenthesis StartFraction sine pi left-parenthesis f 2 minus f 1 right-parenthesis tau Over pi left-parenthesis f 2 minus f 1 right-parenthesis tau EndFraction cosine pi left-parenthesis f 2 plus f 1 right-parenthesis tau period
  9. 1.9 Periodic part; Fourier coefficient: upper C Subscript n Baseline equals StartStartFraction p sine StartFraction pi Over 2 EndFraction n OverOver pi n EndEndFraction period

    Non-periodic part; spectrum: normal upper S 2 left-parenthesis f right-parenthesis equals p left-parenthesis 1 minus p right-parenthesis normal upper T StartFraction 1 minus cosine pi f normal upper T Over pi squared f squared normal upper T squared EndFraction.

  10. 1.10 Signal-to-noise ratio in the band: 300–500 Hz = 75 dB (ƒs = 16 kHz; gain 3 dB).
  11. 1.11 Quantizing distortion: line at three eighths f Subscript normal s Baseline semicolon power: 0.01952.
  12. 1.12 If the characteristic is centered:
    a 1 equals 0 for 0 less-than-or-equal-to StartAbsoluteValue alpha EndAbsoluteValue less-than-or-equal-to one half semicolon a 1 equals StartFraction 4 q Over pi EndFraction StartRoot 1 minus StartFraction 1 Over 4 alpha squared EndFraction EndRoot for one half less-than-or-equal-to StartAbsoluteValue alpha EndAbsoluteValue less-than-or-equal-to 1

    Centering at ...

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