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ECEN3513 Signal Analysis Lecture #26 23 October 2006

ECEN3513 Signal Analysis Lecture #26 23 October 2006. Read 6.8, 6.9 Problems 6.5-5, 6.5-6, 6.8-2 Test #2 on 27 October Chapters 4 & 6 Read 6.12 Problems: 6.9-1, 6.9-2, 6.12-1 Test #2 next time!! Chapters 4-6 Quiz 7 results: Hi =7.6, Low = 0.5, Ave = 4.56 Standard Deviation = 1.70.

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ECEN3513 Signal Analysis Lecture #26 23 October 2006

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  1. ECEN3513 Signal AnalysisLecture #26 23 October 2006 • Read 6.8, 6.9 • Problems 6.5-5, 6.5-6, 6.8-2 • Test #2 on 27 October • Chapters 4 & 6 • Read 6.12 • Problems: 6.9-1, 6.9-2, 6.12-1 • Test #2 next time!! Chapters 4-6 • Quiz 7 results: Hi =7.6, Low = 0.5, Ave = 4.56Standard Deviation = 1.70

  2. after filtering δ(f-0.1) δ(f+0.1) δ(f) y(t)

  3. output magnitude & phase |Y(f)|

  4. filter impulse response H(f) h(t)

  5. filter magnitude & phase response |H(f)|

  6. filter magnitude & phase response To avoid distortion All frequencies should be delayed same time Higher frequencies should see larger phase shifts (1 second delay = 360 degrees for 1 Hz, 720 degrees for 2 Hz, etc.) i.e. phase delay should =  f Filter phase response should be a straight line

  7. Square wave made up of 100 cosinesEvery other cosine has phase = 180○

  8. Improperly aligned phases

  9. filter magnitude & phase response To avoid phase distortion Phase delay should =  f Filter phase response should be a straight line

  10. 2vp, 1 second pulse in x(t)

  11. pulse magnitude & phase |X(f)|

  12. pulse out y(t)

  13. output magnitude & phase |Y(f)|

  14. Quiz 7 - Filter Impulse Response 0.02 y(t) x(t) + ∑ ← H(f) + .8 delay = 2 .8y(t-2) h(t)

  15. Quiz 7: Transfer Function H(f) Little or no phase distortion.

  16. Quiz 7 - Energy Spectrum 0.02 ← |H(f)|2 (1|H(f)|2= SYY(f) if delta function input) ↕ RYY(τ) for output if delta function input.

  17. Energy Spectrum Energy Transfer Response |H(f)|2

  18. Output y(t) when input = u(t) δ(f) H(f)U(f) = Y(f) y(t)

  19. |Y(f)| and phase plot

  20. Need to find power? • Evaluate time average. • Limit 1∫ x(t)2dtT→∞ T T • Evaluate power RXX(τ) at τ = 0. • Find area under power spectrum SXX(f). • Units are W/Hz. Integrate out Hz & left with Watts • Convert X(f) to SXX(f) via Lim 1 |X(f)|2 • Find area under curve T→∞ T • Limit = |X(f)|2 if line spectra

  21. Need to find energy? • Evaluate time average. • Limit ∫ x(t)2dtT→∞ T • Evaluate energy RXX(τ) at τ = 0. • Find area under energy spectrum GXX(f). • Units are J/Hz. Integrate out Hz & left with Joules • Convert X(f) to GXX(f) = |X(f)|2 • Find area under curve

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