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ME 392 Chapter 5 Signal Processing February 20, 2012 week 7 part 1

ME 392 Chapter 5 Signal Processing February 20, 2012 week 7 part 1. Joseph Vignola. Signal Processing. We have been talking about recording signal from sensors like microphones of accelerometers. Signal Processing.

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ME 392 Chapter 5 Signal Processing February 20, 2012 week 7 part 1

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  1. ME 392Chapter 5Signal ProcessingFebruary 20, 2012week 7 part 1 Joseph Vignola

  2. Signal Processing We have been talking about recording signal from sensors like microphones of accelerometers

  3. Signal Processing We have been talking about recording signal from sensors like microphones of accelerometers and expressing the result as either a time history

  4. Signal Processing We have been talking about recording signal from sensors like microphones of accelerometers expressing the result as either a time history or frequency spectrum

  5. Signal Processing Now we want to think about manipulating these signal once they are recorded expressing the result as either a time history or frequency spectrum

  6. Integration and Differentiation With motion data we often need to integrate of differentiate experimental data

  7. Integration and Differentiation With motion data we often need to integrate of differentiate experimental data

  8. Integration and Differentiation With motion data we often need to integrate of differentiate experimental data

  9. Integration and Differentiation With motion data we often need to integrate of differentiate experimental data

  10. Integration and Differentiation With motion data we often need to integrate of differentiate experimental data

  11. Integration and Differentiation With motion data we often need to integrate of differentiate experimental data

  12. Integration and Differentiation Integration is a process of finding the area under a curve

  13. Integration and Differentiation Integration is a process of finding the area under a curve For discreet data (sampled data) We can find the area of each of the trapezoids shown in the figure and add them up

  14. Integration and Differentiation Integration is a process of finding the area under a curve For discreet data (sampled data) We can find the area of each of the trapezoids shown in the figure and add them up

  15. Integration and Differentiation Integration is a process of finding the area under a curve For discreet data (sampled data) We can find the area of each of the trapezoids shown in the figure and add them up So …

  16. Integration and Differentiation Differentiation can be thought of as finding the local slope For discreet data (sampled data) We can find approximate the local Slope by the ratio of the rise over the run As a practical matter is the Sampling interval

  17. Integration in Frequency Domain You know that So all I need to do to integrate discreet data is divide by Assuming that And that

  18. Differentiation in Frequency Domain You know that And you remember that any signal can be reduced to sines and cosines So all I need to do to differentiate discreet data is multiply by Assuming that And that

  19. What Could Go Wrong? For example

  20. Time Shifting Shift Theorem If is Fourier Transform of then is Fourier Transform of

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