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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. - PowerPoint PPT Presentation
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ME 392Chapter 5
Signal Processing
February 20, 2012week 7 part 1
Joseph Vignola
Signal ProcessingWe have been talking about recording signal from sensors like microphones of accelerometers
Signal ProcessingWe have been talking about recording signal from sensors like microphones of accelerometers and
expressing the result as either a time history
Signal ProcessingWe have been talking about recording signal from sensors like microphones of accelerometers
expressing the result as either a time history or frequency spectrum
Signal ProcessingNow we want to think about manipulating these signal once they are recorded
expressing the result as either a time history or frequency spectrum
Integration and DifferentiationWith motion data we often need to integrate of differentiate experimental data
Measured with
Displacement LVDT
velocity Laser Vibrometer
acceleration accelerometer
Integration and DifferentiationWith motion data we often need to integrate of differentiate experimental data
Measured with
Displacement LVDT
velocity Laser Vibrometer
acceleration accelerometer
Integration and DifferentiationWith motion data we often need to integrate of differentiate experimental data Measured with
Displacement LVDT
velocity Laser Vibrometer
acceleration accelerometer
Integration and DifferentiationWith motion data we often need to integrate of differentiate experimental data Measured with
Displacement LVDT
velocity Laser Vibrometer
acceleration accelerometer
Integration and DifferentiationWith motion data we often need to integrate of differentiate experimental data Measured with
Displacement LVDT
velocity Laser Vibrometer
acceleration accelerometer
Integration and DifferentiationWith motion data we often need to integrate of differentiate experimental data Measured with
Displacement LVDT
velocity Laser Vibrometer
acceleration accelerometer
Integration and DifferentiationIntegration is a process of finding the area under a curve
Integration and DifferentiationIntegration 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
Integration and DifferentiationIntegration 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
Integration and DifferentiationIntegration 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 …
Integration and DifferentiationDifferentiation 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
So all I need to do to integrate discreet data is divide by
Integration in Frequency DomainYou know that
Assuming that
And that
So all I need to do to differentiate discreet data is multiply by
Differentiation in Frequency DomainYou know that
And you remember that any signal can be reduced to sines and cosines
Assuming that
And that
What Could Go Wrong?For example
Time ShiftingShift TheoremIf is Fourier Transform of then is Fourier Transform of