Meeting harmonic limits using wide-spectrum passive harmonic filter
The Simple Harmonic Oscillatorpeople.ece.umn.edu/.../noiseInEngBio2010/lectures/week3a.pdf ·...
Transcript of The Simple Harmonic Oscillatorpeople.ece.umn.edu/.../noiseInEngBio2010/lectures/week3a.pdf ·...
![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](https://reader033.fdocuments.us/reader033/viewer/2022050507/5f98a32c4296de7d664ed4ff/html5/thumbnails/1.jpg)
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](https://reader033.fdocuments.us/reader033/viewer/2022050507/5f98a32c4296de7d664ed4ff/html5/thumbnails/2.jpg)
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](https://reader033.fdocuments.us/reader033/viewer/2022050507/5f98a32c4296de7d664ed4ff/html5/thumbnails/3.jpg)
NormalityMonday, February 01, 2010
7:28 PM
Week3a Page 3
![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](https://reader033.fdocuments.us/reader033/viewer/2022050507/5f98a32c4296de7d664ed4ff/html5/thumbnails/4.jpg)
Jointly Gaussanity of X and VMonday, February 01, 2010
7:32 PM
Week3a Page 4
![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](https://reader033.fdocuments.us/reader033/viewer/2022050507/5f98a32c4296de7d664ed4ff/html5/thumbnails/5.jpg)
Mean of X and VMonday, February 01, 2010
7:33 PM
Week3a Page 5
![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](https://reader033.fdocuments.us/reader033/viewer/2022050507/5f98a32c4296de7d664ed4ff/html5/thumbnails/6.jpg)
Mean of X and VMonday, February 01, 2010
7:36 PM
Week3a Page 6
![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](https://reader033.fdocuments.us/reader033/viewer/2022050507/5f98a32c4296de7d664ed4ff/html5/thumbnails/7.jpg)
Mean of X and VMonday, February 01, 2010
7:39 PM
Week3a Page 7
![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](https://reader033.fdocuments.us/reader033/viewer/2022050507/5f98a32c4296de7d664ed4ff/html5/thumbnails/8.jpg)
Variance of VTuesday, February 02, 2010
12:46 AM
Week3a Page 8
![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](https://reader033.fdocuments.us/reader033/viewer/2022050507/5f98a32c4296de7d664ed4ff/html5/thumbnails/9.jpg)
Ode for var{V}Tuesday, February 02, 2010
1:00 AM
Week3a Page 9
![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](https://reader033.fdocuments.us/reader033/viewer/2022050507/5f98a32c4296de7d664ed4ff/html5/thumbnails/10.jpg)
Ode for Var{X}Tuesday, February 02, 2010
1:05 AM
Week3a Page 10
![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](https://reader033.fdocuments.us/reader033/viewer/2022050507/5f98a32c4296de7d664ed4ff/html5/thumbnails/11.jpg)
Ode for Cov{X,V}Tuesday, February 02, 2010
1:08 AM
Week3a Page 11
![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](https://reader033.fdocuments.us/reader033/viewer/2022050507/5f98a32c4296de7d664ed4ff/html5/thumbnails/12.jpg)
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](https://reader033.fdocuments.us/reader033/viewer/2022050507/5f98a32c4296de7d664ed4ff/html5/thumbnails/13.jpg)
Solution for second order statisticsTuesday, February 02, 2010
1:22 AM
Week3a Page 13
![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](https://reader033.fdocuments.us/reader033/viewer/2022050507/5f98a32c4296de7d664ed4ff/html5/thumbnails/14.jpg)
Thermal EquilibriumTuesday, February 02, 2010
1:25 AM
Week3a Page 14