Matched Filter Analysis with S5 Hardware Injections

• H1
• H2
• L1

• In order to decide if the injection is good, two conditions below has been used;
  
  ε_h < 0.3    and    Δ(δt) < 45 ms where ε_h is the fractional difference; ε_h ≡ (hrss_injected-hrss_measured)/hrss_injected
  and Δ(δt) is the time difference between the offset time of the injection and the peak time measured by the matched filter. The condition for hrss seems to be too tough for several waveforms like Gaussians with 1 ms width;
  
  
  
  In the top plot above, which is the GPS time dependence of ε_h from L1 injections, two red lines are the condition used so far. This condition was relaxed with ε_h < 0.6 for all waveforms, which are shown with two green lines in the plots above.


• Fitting for some waveforms with small statistics for H1 and H2 (an example) was failed because of a couple of bad injections in the beginning. With those bad injections excluded (the H2 example) , fitting was improved;


• H1 (with and without bad injections)
  
      


• H2 (with and without bad injections)
  
      


• Central values from fitting of time differences depend on the shape of injected waveform. The value increase as the width of Gaussian as shown below (H1 with bad injections excluded)
  
  
  Here the first four points are from Gaussians and the following 12 are from sine-Gaussians.


• Comments on each waveform;



Waveform	On hrss	On Time Difference
Gaussian σ=0.3 ms	Measured values of hrss are consistently below injected values, especially for H1 and L1. With the new criteria for εh, they will not be bad calibrations any more, but still needed to be studied. Saturation with higher hrss in early injections can be noticeable, especially with L1.	Time difference plots of L1 are interesting.
Gaussian σ=1 ms	New condition for εh should work for this waveform better. From H2 plots, it is shown that something happened with low hrss injections around 834500000.	H2 plots shows that something happened with low hrss injections around 834500000.
Gaussian σ=3 ms	Even if these injections have been good with old criteria, shifts in εh - once (H1 and L1) or twice (H2) during the S5, which is reason of double-peaked distributions for H1 and L1. (Calibration??)	The time difference plots of H1 show that most injections are close to L1 while a few of early injections have the same value as H2.
Gaussian &sigma=10 ms	Good	Good
Sine Gaussian f=50Hz Q=9	A couple of bad injections early on H1 and H2 injections.	A couple of bad injections early on H1 and H2 injections.
Sine Gaussian f=70Hz Q=9	H2 shows the similar problem with Gaussian with σ=1ms around 834500000.	H2 shows the similar problem with Gaussian with σ=1ms around 834500000.
Sine Gaussian f=100Hz Q=9	Small shifts are noticeable in H1 and H2 like Gaussian with σ=3ms (above). A couple of bad injections early on H1 and H2.	Good
Sine Gaussian f=153Hz Q=9	A couple of bad injections early on H1 and H2. A small, but noticeable, shift on H1.	Good
Sine Gaussian f=235Hz Q=9	New condition for εh should work for this waveform better. H2 shows problem around 824500000.	Most bad injections with time measurement are with low hrss injections for all IFOs. H2 problem around 824500000.
Sine Gaussian f=393Hz Q=9	Good	A couple of bad injections early on H1 and H2 - The condition for time difference (30ms) too big??
Sine Gaussian f=554Hz Q=9	A couple of bad injections early on H1 and H2.	A couple of bad injections early on H1 and H2
Sine Gaussian f=850Hz Q=9	A couple of bad injections early on H1 and H2	A couple of bad injections early on H1 and H2.
Sine Gaussian f=914Hz Q=9	New condition for εh should work for this waveform better. H2 has bad injections occasionally including the one around 824500000 - Need to relax the condition for this??	Some outliers with H2.
Sine Gaussian f=1304Hz Q=9	A couple of bad injections early on H1 and H2	A couple of bad injections early on H1 and H2
Sine Gaussian f=2000Hz Q=9	New condition for εh should work for this waveform better. H2 shows problem around 824500000.	Noisy with low hrss injections for all IFOs. H2 shows problem around 824500000.
Sine Gaussian f=3068Hz Q=9	New condition for εh should work for this waveform better. Early injections with higher hrss(H1, H2, L1) had saturation. A couple of bad injection early on H1 and H2.	A couple of bad injections early on H1 and H2.
Zwerger-Mueller (A3B3G1)	New condition for εh should work for this waveform better. H2 shows problem around 824500000.	Peak time measured is 10 ms after the injected offset time consistently for all IFOs. H2 shows problem around 824500000.
Cosmic string cusp fcutoff= 220 Hz	Strength of injections may be too small (Bustset 23), as shown in here for H1 and the same plots from other IFOs are similar.	Noisy - Need to check!
Band-Limited White Noise Burst f=250hz δf=100hz σ=30ms	Double peaked distribution of hrss difference as shown in here for H1 and other ifos show the similar distributions too.	Noisy - Need to check!!
Ringdown f=2600Hz δt=30ms	H2 shows problem around 824500000.	Noisy with low hrss injections.