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

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