physics 434 module 4 - t. burnett 1 physics 434 module 4 acoustic excitation of a physical system:...
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Frequency vs. time Physics 434 Module 4 - T. Burnett 3 What is the frequency composition of these signals?TRANSCRIPT
Physics 434 Module 4 - T. Burnett 1
Physics 434 Module 4
Acoustic excitation of a physical system: time domain
Physics 434 Module 4 - T. Burnett 2
Frequency domain
Last week you measured the frequency domain response to the system
where, =2f, and G() is the (complex) response. (Why complex?).
Hin() G() Hout()
)()()( inout HGH
Frequency vs. time
Physics 434 Module 4 - T. Burnett 3
What is the frequency composition of these
signals?
Frequencies in a pulse
Physics 434 Module 4 - T. Burnett 4
)sin(2 adte
a
a
ti
Note: exactly the same as a single-slit diffraction pattern
Physics 434 Module 4 - T. Burnett 5
More generally
dttheH
dHeth
ti
ti
)()(
inverse and the
)()( 21
Any time-varying signal is composed of a spectrum of frequencies:
Where H() is the Fourier transform, or frequency domain representation of the signal
Physics 434 Module 4 - T. Burnett 6
The response to a time-varying signal:
dttheG
dGeth
tth
dtdtheGeth
dttheH
dHGeth
outti
tiout
in
intiti
out
inti
in
inti
out
)()(
so response, theofansform Fourier tr inverse just the is
)()(
finally)()( :0at t pulsefunction -delta a beinput let the
)()()(
then
)()(
where
)()()(
21
21
21
Physics 434 Module 4 - T. Burnett 7
Time domain: Goals
Apply a pulse to the system, measure the response Adapt the test VI to accumulate and average
multiple shots Understand the signal processing requirements, and
capabilities of the DAQ system Use a Fast Fourier Transform (FFT) VI to obtain the
spectrum Understand how a FFT works
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Setup: almost same as Module 3…
Pulse output&
trigger
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Triggering!
digitalTrigger: PFI 0 #73
Digital pulse outPFI12 #89
Ground #90
To scope and speaker in
We use the output pulse to both trigger the acquisition and drive the speaker
The scope
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Ch1,very short pulse to speaker; scope trigger
Ch2: microphone
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Run the demo:ImpulseTest.vi
Response of an ideal tube!
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A second advantage: signal averaging
NB: you will convert this guy to r,
Summary (from the document)
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Once the system is running and you have good data from the standard settings, try the varying the following parameters of the experiment:1. What is the effect of the pulse width on the experiment? Try
settings like 0.1, 1.0, and 10 msec. Report your observations in your documentation.
2. What is the effect of the acquisition rate? Try settings like 1000, 10000 and 100000 points per sec. Also note what the minimum buffer size and scan rate is needed to describe the response up to 2000 Hz.
3. Try the effect of signal averaging on the appearance of the power spectrum. For this experiment, reduce the gain of the audio amplifier until the signal is barely detectable
Finally, run the analysis VI from Module 3 and compare some of the resonant frequencies. Submit your fully commented VI as before, saved with a sample output, and with the documentation section containing answers to the questions above.
Physics 434 Module 4 - T. Burnett 14
Next week: FFT