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

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

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

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

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 10110010 awg psinject sbaniso.c pg. 23

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.

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

Original Time Series strain time(s)

Original time series strain time(s)

FFT of time series fft frequency(Hz)

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)

Pendulum Transfer Function P(f) frequency(Hz)

FFT multiplied by tfH Time series frequency(Hz)

ifft back to time series

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)

Ratio of two time series 1.07 1 time(s)

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

Windowed time series segment counts time(s)

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

Final time series counts time (s)

No modulation of the envelope Rms value of the pre-windowed time series = 2.2348 Rms value of the combined time series = 2.2334 The close rms values of the two time series shows apparent agreement

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)

Set with “LHO” Set with “LLO” LHO LLO 2.148124 -1.29882 -0.082698 1.384901 -0.611360 2.570094 0.864168 2.751956 1.978097 2.107497

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

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.