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Page 1: The Simple Harmonic Oscillatorpeople.ece.umn.edu/.../noiseInEngBio2010/lectures/week3a.pdf · 2010-02-10 · Week3a Page 12 . Solution for second order statistics Tuesday, February

The Simple Harmonic Oscillator

Week3a Page 1

Page 2: The Simple Harmonic Oscillatorpeople.ece.umn.edu/.../noiseInEngBio2010/lectures/week3a.pdf · 2010-02-10 · Week3a Page 12 . Solution for second order statistics Tuesday, February

Position, Velocity are Gaussian

Week3a Page 2

Page 3: The Simple Harmonic Oscillatorpeople.ece.umn.edu/.../noiseInEngBio2010/lectures/week3a.pdf · 2010-02-10 · Week3a Page 12 . Solution for second order statistics Tuesday, February

NormalityMonday, February 01, 2010

7:28 PM

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Page 4: The Simple Harmonic Oscillatorpeople.ece.umn.edu/.../noiseInEngBio2010/lectures/week3a.pdf · 2010-02-10 · Week3a Page 12 . Solution for second order statistics Tuesday, February

Jointly Gaussanity of X and VMonday, February 01, 2010

7:32 PM

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Page 5: The Simple Harmonic Oscillatorpeople.ece.umn.edu/.../noiseInEngBio2010/lectures/week3a.pdf · 2010-02-10 · Week3a Page 12 . Solution for second order statistics Tuesday, February

Mean of X and VMonday, February 01, 2010

7:33 PM

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Page 6: The Simple Harmonic Oscillatorpeople.ece.umn.edu/.../noiseInEngBio2010/lectures/week3a.pdf · 2010-02-10 · Week3a Page 12 . Solution for second order statistics Tuesday, February

Mean of X and VMonday, February 01, 2010

7:36 PM

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Page 7: The Simple Harmonic Oscillatorpeople.ece.umn.edu/.../noiseInEngBio2010/lectures/week3a.pdf · 2010-02-10 · Week3a Page 12 . Solution for second order statistics Tuesday, February

Mean of X and VMonday, February 01, 2010

7:39 PM

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Page 8: The Simple Harmonic Oscillatorpeople.ece.umn.edu/.../noiseInEngBio2010/lectures/week3a.pdf · 2010-02-10 · Week3a Page 12 . Solution for second order statistics Tuesday, February

Variance of VTuesday, February 02, 2010

12:46 AM

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Page 9: The Simple Harmonic Oscillatorpeople.ece.umn.edu/.../noiseInEngBio2010/lectures/week3a.pdf · 2010-02-10 · Week3a Page 12 . Solution for second order statistics Tuesday, February

Ode for var{V}Tuesday, February 02, 2010

1:00 AM

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Page 10: The Simple Harmonic Oscillatorpeople.ece.umn.edu/.../noiseInEngBio2010/lectures/week3a.pdf · 2010-02-10 · Week3a Page 12 . Solution for second order statistics Tuesday, February

Ode for Var{X}Tuesday, February 02, 2010

1:05 AM

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Page 11: The Simple Harmonic Oscillatorpeople.ece.umn.edu/.../noiseInEngBio2010/lectures/week3a.pdf · 2010-02-10 · Week3a Page 12 . Solution for second order statistics Tuesday, February

Ode for Cov{X,V}Tuesday, February 02, 2010

1:08 AM

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Page 12: The Simple Harmonic Oscillatorpeople.ece.umn.edu/.../noiseInEngBio2010/lectures/week3a.pdf · 2010-02-10 · Week3a Page 12 . Solution for second order statistics Tuesday, February

Solution for second order statisticsTuesday, February 02, 2010

1:13 AM

Week3a Page 12

Page 13: The Simple Harmonic Oscillatorpeople.ece.umn.edu/.../noiseInEngBio2010/lectures/week3a.pdf · 2010-02-10 · Week3a Page 12 . Solution for second order statistics Tuesday, February

Solution for second order statisticsTuesday, February 02, 2010

1:22 AM

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Page 14: The Simple Harmonic Oscillatorpeople.ece.umn.edu/.../noiseInEngBio2010/lectures/week3a.pdf · 2010-02-10 · Week3a Page 12 . Solution for second order statistics Tuesday, February

Thermal EquilibriumTuesday, February 02, 2010

1:25 AM

Week3a Page 14