Plans for stochastic hardware injection

Eric Thrane, Mandy Pihlaja and Vuk Mandic

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Overview

• Motivation

• Injection flow chart

• Relationship to reviewed code

• Testing and validation

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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

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Summary cont.• Then…

– 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

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Injection flowchart

SpHMapToTimeSeries*

SpH map file: l, m, Plm spectrum file: f, H(f)user-specified params: random seeds, seg dur, etc.

simulateSkyMapTimeDomain

(reviewed)

d1,d2

gets time seriesgets overlapping time seriesFFT time seriesApply pendulum T(f)IFFTWindowCombine overlapping seriesWrite combined h(t) to files.

*new

sbaniso.cpsinjectawgbinary out 10110010 pg. 23

pg. 6

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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.

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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

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time(s)

strain

Original Time Series

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Original time series

strain

time(s)

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FFT of time series

frequency(Hz)

fft

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• 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)

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Pendulum Transfer Function

frequency(Hz)

P(f)

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FFT multiplied by tfH

frequency(Hz)

Time series

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ifft back to time series

time(s)

Time series

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• 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)

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Ratio of two time series

time(s)

1

ratio

1.07

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Windowing

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

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Windowed time series segment

time(s)

counts

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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

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Final time series

time (s)

counts

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• 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

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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)

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Set with “LHO”

Set with “LLO”

LHO LLO LHO LLO

2.148124 2.148124 -1.29882 -1.29882

-0.082698

-0.082698

1.384901 1.384901

-0.611360

-0.611360

2.570094 2.570094

0.864168 0.864168 2.751956 2.751956

1.978097 1.978097 2.107497 2.107497

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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

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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.