physics 434 module 4 - t. burnett 1 physics 434 module 4 acoustic excitation of a physical system:...
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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
Review the pre-test
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(
2a
dtea
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 AT-E data acquisition board Use a Fast Fourier Transform (FFT) VI to obtain the
spectrum Understand how a FFT works
Physics 434 Module 4 - T. Burnett 8
Setup: almost same as Module 3…
Physics 434 Module 4 - T. Burnett 9
Triggering!
TRIG1
GPCTR0_OUT
digital ground
To scope and
speaker in
To scope and microphone in
Physics 434 Module 4 - T. Burnett 10
Run the demo VI
Response of an ideal tube!
Physics 434 Module 4 - T. Burnett 11
A second advantage: signal averaging
Physics 434 Module 4 - T. Burnett 12
Next week: FFT