Igor Pro has been used as a tool to analyze PDV data. The routine is demonstrated here, and the results are compared with other faster techniques. The advantage of the Igor tool is the use of the Wigner Transform which allows for inspection of short time scale features.

1. Lawrence Livermore National Laboratory
PDV Analysis using Igor Pro
Damon D Jackson
Lawrence Livermore National Laboratory, P. O. Box 808, Livermore, CA 94551
This work performed under the auspices of the U.S. Department of Energy by UCRL-PRES-233496
Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344

2. Igor Pro
 According to the WaveMetrics web page:
• Igor Pro is an extraordinarily powerful and extensible
scientific graphing, data analysis, image processing and
programming software tool for scientists and engineers.
 Runs on both a Mac and PC
 Both command line and/or menu driven
 Great for:
• Data Analysis
• Loading huge files
• Automating common procedures
Lawrence Livermore National Laboratory

3. What this tool does
Read in a file of PDV
data (voltage vs time)
Go through the steps to
perform a Wigner Transform
For each time step, find the
location of the max WT
intensity (velocity)
Export time, velocity, and
velocity error data to a new
file
Lawrence Livermore National Laboratory

4. What this tool does
Read in a file of PDV
data (voltage vs time)
Go through the steps to
perform a Wigner Transform
For each time step, find the
location of the max WT
intensity (velocity)
Export time, velocity, and
velocity error data to a new
file
Lawrence Livermore National Laboratory

5. What this tool does
Read in a file of PDV
data (voltage vs time)
Go through the steps to
perform a Wigner Transform
For each time step, find the
location of the max WT
intensity (velocity)
Export time, velocity, and
velocity error data to a new
file
Lawrence Livermore National Laboratory

6. What this tool does
Read in a file of PDV
data (voltage vs time)
Go through the steps to
perform a Wigner Transform
For each time step, find the
location of the max WT
intensity (velocity)
Export time, velocity, and
velocity error data to a new
file
Lawrence Livermore National Laboratory

7. What this tool does
Read in a file of PDV
data (voltage vs time)
Go through the steps to
perform a Wigner Transform
For each time step, find the
location of the max WT
intensity (velocity)
Export time, velocity, and
velocity error data to a new
file
Lawrence Livermore National Laboratory

8. Quick Guide Through the Program
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9. Load the PDV data and place the cursor at the
start
Lawrence Livermore National Laboratory
ata from Ted Strand

10. Load the PDV data and place the cursor at
the start
Lawrence Livermore National Laboratory
ata from Ted Strand

11. Load the PDV data and place the cursor at
the start
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ata from Ted Strand

12. Click ‘Begin Wigner Transform’ to bring up
a zoomed in window
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ata from Ted Strand

13. Click ‘Begin Wigner Transform’ to bring up
a zoomed in window
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ata from Ted Strand

14. Perform a Wigner transform over this time
window
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ata from Ted Strand

15. Wigner Transform
Data from Ralph
Hodgin
 Graph shows velocity vs time
• Red regions show large amplitude
• Black regions show low amplitude
− Can be scaled from the left and will be ignored
 Analyze ROI button creates velocity vs time data
Lawrence Livermore National Laboratory

16. Two alternative tools are the Wigner transform and the Continuous W
(CWT).
Wigner Transform Wigner Transform
Chapter III-9 — Signal Processing
The Wigner transform (also known as the Wigner Distribution Functio
signal[250,]+=sin(2*pi*x*100/500)
WignerTransform /Gaus=100 signal
// spectrum for1D time signal U(t) into a 2D time-frequency representation. Conceptu
DSPPeriodogram signal comparison
analogous to a musical score where the time axis is horizontal and the
1.5
are plotted on a vertical axis. The WDF is defined by the equation
1.0
∞
– i2πxν
dxU ( t + x ⁄ 2 )U∗ ( t – x ⁄ 2 )e
0.5
W ( t, ν ) = ∫
0.0
–∞
-0.5
Note that the WDF W(t,ν) is real (this can be seen from the fact that it is a
-1.0
an Hermitian quantity). The WDF is also a 2D Fourier transform of the A
 Is analogous to creating
-1.5
The localized spectrum can be derived from the WDF by integrating it
a musical score
0 100 200 300 400
s
dtdn. Using Gaussian weight functions in both t and n, and choosing t
The signal used in this example consists of two “pure” frequencies that have small amount
tainty condition dtdn=1, we obtain an estimateat a given
• Input sound for the local spectrum
of temporal overlap.
ˆ ( t, ν ;δt ) ∝frequency2π  ---------  exp ( – i2πνt' )
vst time
– t' 2
0.5
∫ U ( t' ) exp –  δt -
W
• Create an image of
0.4
To illustrate an applicationthe frequency
of the WignerTransform operation (see pa
0.3
the two-frequency signal:
(velocity) vs time
0.2
Make/N=500 signal
signal[0,350]=sin(2*pi*x*50/500)
0.1
0.0
0 100 200 300 400 500
s
The temporal dependence is clearly seen in the Wigner transform. Note that the horizontal
(time) transitions are not sharp.National Laboratory the application of the minimum
Lawrence Livermore This is mostly due to
uncertainty relation dtdn=1 but it is also due to computational edge effects. By comparison,
the spectrum of the signal while clearly showing the presence of two frequencies it pro-
vides no indication of the temporal variation of the signal’s frequency content. Further-

17. Wigner Transform
Data from Ralph
Hodgin
 Graph shows velocity vs time
• Red regions show large amplitude
• Black regions show low amplitude
− Can be scaled from the left and will be ignored
 Analyze ROI button creates velocity vs time data
Lawrence Livermore National Laboratory

18. Wigner Transform
Select a ROI. Areas
outside of these boxes will
be ignored.
Data from Ralph
Hodgin
 Graph shows velocity vs time
• Red regions show large amplitude
• Black regions show low amplitude
− Can be scaled from the left and will be ignored
 Analyze ROI button creates velocity vs time data
Lawrence Livermore National Laboratory

19. Wigner Transform
Data from Ralph
Hodgin
 Graph shows velocity vs time
• Red regions show large amplitude
• Black regions show low amplitude
− Can be scaled from the left and will be ignored
 Analyze ROI button creates velocity vs time data
Lawrence Livermore National Laboratory

20. Wigner Transform
Data from Ralph
Hodgin
 Graph shows velocity vs time
• Red regions show large amplitude
• Black regions show low amplitude
− Can be scaled from the left and will be ignored
 Analyze ROI button creates velocity vs time data
Lawrence Livermore National Laboratory

21. Wigner Transform
Data from Ralph
Hodgin
 Graph shows velocity vs time
• Red regions show large amplitude
• Black regions show low amplitude
− Can be scaled from the left and will be ignored
 Analyze ROI button creates velocity vs time data
Lawrence Livermore National Laboratory

22. Wigner Transform
Data from Ralph
Hodgin
 Graph shows velocity vs time
• Red regions show large amplitude
• Black regions show low amplitude
− Can be scaled from the left and will be ignored
 Analyze ROI button creates velocity vs time data
Lawrence Livermore National Laboratory

23. Velocity vs Time
 Each column (time slice) of the
Wigner Trans. is analyzed for
the maximum intensity
• velocity is found by the
location of gaussian peak
 Final output saves:
• Time
• Velocity
• Velocity Error (Gaussian
peak error)
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24. Perform a Wigner transform over this time
window
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ata from Ted Strand

25. Perform a Wigner transform over this time
window
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ata from Ted Strand

26. Record of Velocity vs Time
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ata from Ted Strand

27. Go to next section of PDV data and Repeat
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ata from Ted Strand

28. Continue making Velocity vs Time graph
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ata from Ted Strand

29. Continue making Velocity vs Time graph
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ata from Ted Strand

30. Continue making Velocity vs Time graph
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ata from Ted Strand

31. Continue making Velocity vs Time graph
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ata from Ted Strand

32. Continue making Velocity vs Time graph
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ata from Ted Strand

33. Continue making Velocity vs Time graph
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ata from Ted Strand

34. Continue making Velocity vs Time graph
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ata from Ted Strand

35. Save data to a new file when finished
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ata from Ted Strand

36. Comparison of Methods
26 ns window 6.25 ns window
Analyzed via MatLab Analyzed via Igor Pro
 MatLab reduces data points depending on sampling rate and
FFT window size (1:260 in this example)
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37. Comparison of Methods
 “Sliding” FFT, 3.2 ns
window, 1.6 ns step
size
• half-window
overlap
 Quick - 17 seconds
 Pixelated
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ata/Analysis by Ralph Hodgin and Chadd May

38. Comparison of Methods
 “Sliding” FFT, 12.8 ns
window, 1.6 ns step
size
• 1/8-window
overlap
 65 seconds to
complete calculation
 Pixelated, but much
better
Lawrence Livermore National Laboratory
ata/Analysis by Ralph Hodgin and Chadd May

39. Comparison of Methods
 Wigner Transform,
12.8 ns window
 5 minutes to
complete calculation
 Very good resolution
• no loss in data
points along time-
axis
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40. Wigner Transform - another great tool for
fast time resolved PDV data
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41. Wigner Transform - another great tool for
fast time resolved PDV data
Plasma
Shock arrival at
behind kapton
front of kapton
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42. PDV Analysis using Igor Pro
 Routine reads in PDV data files
• Either Voltage vs time or just Voltage
 Goes through sections of the data to perform
a Wigner Transform
• results in an improved resolution over FFT
 Exports a velocity vs time history (csv file)
 Can also use to fit a sine wave to the data for
determining shock arrival times
Lawrence Livermore National Laboratory

43. Acknowledgments
Chadd May Ed Roos
Ashok Kumar John Weeks
(WaveMetrics)
Ted Strand
Reed
Dave Hare
Patterson
Ralph Hodgin
Lawrence Livermore National Laboratory