1. Plans for stochastic hardware injection
Eric Thrane, Mandy Pihlaja and Vuk Mandic

2. Overview Motivation Injection flow chart Relationship to reviewed code
Testing and validation

3. Summary of injection
spherical harmonic coefficients and spectrum specified
User sets parameters of GPS, random seed, injection duration
Parent routine, SphMapToTimeSeries, calls simulateSkyMapTimeDomain, which returns time series [d1, d2] and overlapping time series [Ovrlp1, Ovrlp2] for {LHO,LLO}.
simulateSkyMapTimeDomain = reviewed stochastic code

4. Summary cont. Then… Write combined h(t) to text file
FFT both time series
Apply frequency pendulum transfer function
Window time series using sin function
Combine time series and overlapping time series
Write combined h(t) to text file
sbaniso.c (based on standard injection code, sb.c) reads in text file and converts to binary
Sent to psinject
Sent to awg

5. Injection flowchart *new SpHMapToTimeSeries* simulateSkyMapTimeDomain
user-specified params: random seeds, seg dur, etc.
SpH map file: l, m, Plm
spectrum file: f, H(f)
gets time series
gets overlapping time series
FFT time series
Apply pendulum T(f)
IFFT
Window
Combine overlapping series
Write combined h(t) to files.
SpHMapToTimeSeries*
d1,d2
simulateSkyMapTimeDomain
(reviewed)
pg. 6
binary out
awg
psinject
sbaniso.c
pg. 23

6. simulateSkyMapTimeSeries.m
Returns [d1(t),d2(t)] for LHO, LLO given user-specified P() and H(f).
Written by Stefan Balmer and Joe Romano
Reviewed during SpH review.

7. Validation and testing- fft
The next four slides show the process of applying FFT, the pendulum transfer function, and the iFFT to the time series.
Then there is a consistency check to make sure this process could be reversed

8. Original Time Series
strain
time(s)

9. Original time series
strain
time(s)

10. FFT of time series
fft
frequency(Hz)

11. Next slide is the frequency domain Pendulum transfer function is given by sb.c
tfH=ffrequency^2/constants
Constants = (2.05e-13)(0.764)(0.764)

12. Pendulum Transfer Function
P(f)
frequency(Hz)

13. FFT multiplied by tfH
Time series
frequency(Hz)

14. ifft back to time series

15. In order to check that the pendulum transfer function was applied correctly, the transformed time series had the following inverse process applied
FFT, inverse pendulum transfer function, iFFT
The plot of the ratio of the ‘inverted’ time series to the original time series is on the next slide.
Within very small rounding, the original time series is recovered (~1.0)

16. Ratio of two time series
1.07 1
time(s)

17. Windowing
Each time series segment is multiplied by the sine function in order for beginning and end to scale to zero.

18. Windowed time series segment
counts
time(s)

19. Overlapping and combination
The overlapping time series lags the original time series by half of segment duration.
The second half of the current overlapping time series and the first half of the previous overlapping time series are concatenated to make the combined overlapping time series
The combined series is added to the original time series to form the final time series

20. Final time series
counts
time (s)

21. No modulation of the envelope
Rms value of the pre-windowed time series =
Rms value of the combined time series =
The close rms values of the two time series shows apparent agreement

22. Checking code at LHO and LLO
The code was run at LLO and LHO given the same random seed to check that the time series were the same
Data in Xcel sheet (next page)

23. Set with “LHO”
Set with “LLO”
LHO
LLO

24. sb.c
Originally generates time series, applies transfer function, overlaps segments and sends to AWG
Modified to read in text files created by SphMapToTimeSeries.m, send to AWG, and delete file after use (sbaniso.c)
Already used for S5 (w/o Vuk’s hacks) and reviewed

25. Handshake Day long injection generated in one minute segments
In order to not create a 1TB injection file, SphMapToTimeSeries.m only generates three files at a time and waits for sbaniso.c to delete a file before continuing.