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ME 392Chapter 5
Signal Processing
February 20, 2012week 7 part 1
Joseph Vignola
Signal Processing
We have been talking about recording signal from sensors like microphones of accelerometers
Signal Processing
We have been talking about recording signal from sensors like microphones of accelerometers and
expressing the result as either a time history
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
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
Integration and Differentiation
With motion data we often need to integrate of differentiate experimental data
Measured with
Displacement LVDT
velocity Laser Vibrometer
acceleration accelerometer
Integration and Differentiation
With motion data we often need to integrate of differentiate experimental data
Measured with
Displacement LVDT
velocity Laser Vibrometer
acceleration accelerometer
Integration and Differentiation
With motion data we often need to integrate of differentiate experimental data Measured with
Displacement LVDT
velocity Laser Vibrometer
acceleration accelerometer
Integration and Differentiation
With motion data we often need to integrate of differentiate experimental data Measured with
Displacement LVDT
velocity Laser Vibrometer
acceleration accelerometer
Integration and Differentiation
With motion data we often need to integrate of differentiate experimental data Measured with
Displacement LVDT
velocity Laser Vibrometer
acceleration accelerometer
Integration and Differentiation
With motion data we often need to integrate of differentiate experimental data Measured with
Displacement LVDT
velocity Laser Vibrometer
acceleration accelerometer
Integration and Differentiation
Integration is a process of finding the area under a curve
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
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
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 …
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
So all I need to do to integrate discreet data is divide by
Integration in Frequency Domain
You know that
Assuming that
And that
So all I need to do to differentiate discreet data is multiply by
Differentiation in Frequency Domain
You 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 Shifting
Shift TheoremIf is Fourier Transform of then is Fourier Transform of