Search for bursts with the Frequency Domain Adaptive Filter FDAF

1
Search for bursts with the Frequency Domain
Adaptive Filter (FDAF )

• Sabrina DAntonio Roma II Tor Vergata
• Sergio Frasca, Pia Astone Roma 1

• Outlines
• FDAF description
• Project1a data application
• Filters performances comparison
• WSR7 seg. 27 data application

2
Overview on the filter and cluster generation
procedure

• Three STEPS
• 1. Filtering procedure
• An Adaptive Wiener Filter (AWF), in frequency
  domain, followed by a series (N) of band-pass
  filters with a Gaussian shape (phase zero)
  -(N1) filtered output
• 2. Event extraction
• An Adaptive threshold algorithm for the selection
  of the events applied at each filtered channel CH
  (N1).
• 3. Cluster generation
• Events coming from different CH in
  coincidence in a given time window W are put
  together this is one CLUSTER

3
Filtering procedure
back in time-domain
Hp
FFT
1 2 ... .. 4 ... .. .. ..
. .. N1
Wiener Filter WF
RAW DATA
Power Spectrum SP estimation
IFFT
Hp
N1 filtered output channels In the time domain
Filters bank (N) With Gaussian shape
Frequency domain
IFFT
Hp
4
Power spectra estimation
PS is the estimated Power Spectrum of
the noise, evaluated with a first order
Auto-Regressive (AR) sum of the
periodograms, Pi from
PSi W PSi-1 Pi and
ni 1 W ni-1
PSPS/n in our case
Wexp(-T/tau)0.9991 T3.2768 s (time
duration of one data chunk used to obtain the
Periodogram)
tau3600 s (Memory time Simulated data-
stationary noise)
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Event extraction adaptive threshold technique
for the events selection (event search procedure
applied at each filtered channel y(i))
Let y(i) the filtered data samples in time
domain, we estimate mi yi
Wmi-1 qi y²i Wqi-1
ni 1 Wni-1
with W exp(-dt/tau)
0.9999900 (corresponding to dt 1/20000
s tau 5 s) and
Mi mi /n I
Qi qi/ni
Si sqrt(Qi-(Mi)2) From these we define
the Critical Ratio (CRi) of y(i)
CRi(yi-Mi)/Si
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Event extraction

• We define a dead time, td, as the minimum time
  between two events, and we put the threshold, ?,
  on the CR.
• A two-state ( 0 and 1 ) mechanism event
  machine has been used
• The machine starts with state 0
• When CR ?, it changes to state 1 and an event
  begins
• The state changes to 0 after CR remains below ?
  for a time td (the
  event finishes)
• T0 starting time
• CRmax Max value of CR
• A amplitude
• The event is characterized
  Tmax time of max CR
• by L length (in seconds)
  (duration of state 1)
• CH frequency channel
• ?3.9
• td0.2 s

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Event cluster
EVENT LIST of all frequency Channel (N1) Ch1
Time CR Ch4 Time CR
Ch7 Time CR
. Ch1 Time CR
All Events coming from different frequency
channel Ch in coincidences into a given time
window W are put together this is one
CLUSTER. The time corresponding to the higher CR
is the CLUSTER time .
CLUSTER list Time CR1 CR2 CR3 . CRN1 Time
CR1 CRN1 . . Time
CR1 CRN1
CRi0 if the frequency channel Chi not in time
coincidence with other.
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Event cluster example (Preliminary Procedure!)
Event list Freq. Channel Time cr Ampl
length .. 1 (40 Hz) tim1 6.13
.. .. .. .. 2 (90Hz) tim2 6.75
.. .. .. 3 (200Hz) tim3
6.0 .. .. .. .. 10(0-2000Hz)
tim10 4.8 6
tim2 is the time corresponding to the maximum CR
-time2CLUSTER time
CR value
CR
Time distances tim10-tim1 They are put together- one CLUSTER
cluster ordering number
Cluster list Time CR1 CR2 CR3 CR4 ..
.. .. .. CR10 Time2 6.13 6.75 6.0 0
0 0 0 0 4.8
40 90 200 600 1000 1400
0-2000 Hz
Frequency channels Mean values of the Gaussian
filters
WF channel 0-2000 Hz
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Project1a preliminary results
gr-qc/0701026 A comparison of methods for
gravitational wave burst searches from LIGO and
Virgo
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3 hours of Virgo simulated noise
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Injected signals
INPUT 3 hours of Virgo (vs20 kHz) simulated
noise Signals injected with SNR7, 10 Gaussian
signals with s 1ms 2 kinds of supernovae
signals (from Dimmelmeier-Font-Muller
simulations) _at_ 8.5 kpc A1B2G1,A2B4G1) Sine-Gaussi
an signals with Q 5 and ? 235 Hz or ? 820
Hz Sine-Gaussian signals with Q 15 and ?
820 Hz Wiener filter (WF) Band-Pass filters
with Gaussian shape The frequency range 0-2000
Hz is linearly divided into 9 bands (step 200
Hz, Sigma100 Hz) . -- 10 different filters
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Waveform families of burst sources used in this
study time domain
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Waveform families of burst sources used in this
study frequency domain
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SGQ15f820 clusters in time coincidences with the
injected signals (163) at SNR7 (frequency
domain characteristic)
SNR7 number of event detected from each channel
SNR7 CR
Event number
cluster ordering number
90 200 600 1000 1400 0-2000 Hz
90 200 600 1000 1400 0-2000 Hz
Due to the noise! Not in the expected channel
and they dont change with the SNR of injected
signals
15
SGQ15f820 clusters in time coincidences with the
injected signals (163) at SNR10 (frequency
domain characteristic)
SNR10 number of event detected from each channel
SNR10 CR
Event number
cluster ordering number
N
90 200 600 1000 1400 0-2000
Hz
90 200 600 1000 1400
0-2000 Hz
Due to the noise! Not in the expected channel
and they dont change with the SNR of injected
signals
16
SGQ5f820 clusterin time coincidences with the
injected signals (178) at SNR7 (frequency domain
characteristic)
SNR7 number of event detected from each channel
SNR7 CR
Event number
cluster ordering number
90 200 600 1000 1400 0-2000 Hz
90 200 600 1000 1400
0-2000 Hz
17
SGQ5f820 cluster in time coincidences with the
injected signals (178) at SNR10 (frequency
domain characteristic)
SNR10 number of event detected from each channel
SNR10 CR
Event number
cluster ordering number
90 200 600 1000 1400
0-2000 Hz
90 200 600 1000 1400
0-2000 Hz
18
SGQ5f235 clusters in time coincidences with the
injected signals (190) at SNR7 (frequency domain
characteristic)
SNR7 number of event detected from each channel
SNR7 CR
Event number
cluster ordering number
90 200 600 1000 1400
0-2000 Hz
90 200 600 1000 1400 0-2000 Hz
19
SGQ5f235 clusters in time coincidences with the
injected signals (190) at SNR10 (frequency
domain characteristic)
SNR10 number of event detected from each channel
SNR10 CR
Event number
cluster ordering number
90 200 600 1000 1400
0-2000 Hz
90 200 600 1000 1400
0-2000 Hz
20
A1B2G1 clusters in time coincidences with the
injected signals (165) at SNR7 (frequency domain
characteristic)
SNR7 number of event detected from each channel
SNR7 CR
Event number
cluster ordering number
90 200 600 1000 1400 0-2000 Hz
90 200 600 1000 1400
0-2000 Hz
21
A1B2G1 clusters in time coincidences with the
injected signals (165) at SNR10 (frequency
domain characteristic)
SNR10 CR
SNR10 number of event detected from each channel
Event number
cluster ordering number
90 200 600 1000 1400
0-2000 Hz
90 200 600 1000 1400
0-2000 Hz
22
A2B4G1 clusters in time coincidences with the
injected signals (170) at SNR7 (frequency domain
characteristic)
SNR7 number of event detected from each channel
SNR7 CR
Event number
cluster ordering number
90 200 600 1000 1400
0-2000 Hz
90 200 600 1000 1400 0-2000 Hz
23
A2B4G1 clusters in time coincidences with the
injected signals (170) at SNR10 (frequency
domain characteristic)
SNR10 number of event detected from each channel
SNR10 CR
Event number
cluster ordering number
90 200 600 1000 1400
0-2000 Hz
90 200 600 1000 1400
0-2000 Hz
24
To see better the lower frequency region (A2B4G1
GAUSS1ms)Ive added another channel at 40 Hz
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A2B4G1 clusters in time coincidences with the
injected signals (170) at SNR7 (frequency domain
characteristic)
SNR7 number of event detected from each channel
SNR7 CR
Event number
cluster ordering number
40 90 200 600 1000
0-2000 Hz
40 90 200 600 1000
0-2000 Hz
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A2B4G1 clusters in time coincidences with the
injected signals (170) at SNR10 (frequency
domain characteristic)
SNR10 number of event detected from each channel
SNR10 CR
Event number
cluster ordering number
40 90 200 600 1000
0-2000 Hz
40 90 200 600 1000
0-2000 Hz
27
GAU1ms clusters in time coincidences with the
injected signals (178) at SNR7 (frequency domain
characteristic)
SNR7 CR
SNR7 number of event detected from each channel
cluster ordering number
Event number
40 90 200 600 1000
0-2000 Hz
40 90 200 600 1000 0-2000
Hz
28
GAU1ms clusters in time coincidences with the
injected signals (178) at SNR10 (frequency
domain characteristic)
SNR10 number of event detected from each channel
SNR10 CR
Event number
cluster ordering number
40 90 200 600 1000 0-2000
Hz
40 90 200 600 1000
0-2000 Hz
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Trigger due to the noise (no signal injection!)
NOISE number of event in each channel
NOISE CR
cluster ordering number
Event number
90 200 600 1000 1400
0-2000 Hz
90 200 600 1000 1400
0-2000 Hz
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percentage of CLUSTERS detected at the exact
sample (DT0.0) _at_ obtained over all CLUSTERS
(due to the noise due to the signals)
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percentage of CLUSTERS detected at the exact
sample (DT0.0) The red values are obtained
adding the lower frequency channel at 40 Hz
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Filters performances comparison
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Efficiency vs False Alarm Rate SNR7
(Comparison with Power filter (Red))
sgQ15f820
GAU1ms
A1B2G1
A2B4G1
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Efficiency vs False Alarm Rate SNR7
sgQ5f235
sgQ5f820
Signals injected with SNR10 give efficiency1
with FAR10-4
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Time error comparison stdms
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Time error comparison bias ms
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WSR7 Preliminary Results seg.27
GPS time start852852866 GPS time stop
852858889 Hardware Injections
(SNR7.5,15,25) Injected signals
N SGf1000Q5/Q15 34/34 SGf1300Q5/Q15 34/34
SGf1600Q5/Q15 34/33 271 inj. GAUSSIAN
34/34 A2B4G1 34/34
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Pre HP filter with freq. cutoff at 80 Hz Power
Spectra Estimation tau1800 s T3.2768 s CR
?4.0
Wiener filter (WF) Band-Pass filters with
Gaussian shape The frequency range 0-2000 Hz is
linearly divided into 10 bands (step 150 Hz,
Sigma100 Hz) . -- 11 different filters
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GAUSSIAN/A2B4G1 all signals detected
150 550 800 1150 1450 0-2000 Hz
150 550 800 1150 1450
0-2000 Hz
150 550 800 1150 1450 0-2000 Hz
150 550 800 1150 1450 0-2000 Hz
40
SGf1000Q15/Q5 all signals detected
150 550 800 1150 1450 0-2000 Hz
150 550 800 1150 1450 0-2000 Hz
150 550 800 1150 1450 0-2000
Hz
150 550 800 1150 1450 0-2000 Hz
41
SGf1300Q15/Q5 all signals detected
150 550 800 1150 1450 0-2000 Hz
150 550 800 1150 1450 0-2000 Hz
150 550 800 1150 1450 0-2000 Hz
150 550 800 1150 1450 0-2000 Hz
42
SGf1600Q15/Q5 all events detected
150 550 800 1150 1450 0-2000 Hz
150 550 800 1150 1450 0-2000 Hz
150 550 800 1150 1450 0-2000 Hz
150 550 800 1150 1450 0-2000 Hz
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CR
clusters in time coincidence with the injected
signals
all clusters-271 clusters in time coincidence
with the injected signals
15.22 Std(CR)7.27
4.44 Std(CR)0.61
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4 BIG events not due to the injected
signals (first injection time852852651.45370)
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Without 4 big events
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