search for bursts with the frequency domain adaptive filter ( fdaf )

Search for bursts with the Search for bursts with the Frequency Domain Adaptive Filter (Frequency Domain Adaptive Filter (FDAFFDAF ) )

Sabrina D’Antonio Roma II Tor Vergata Sergio Frasca, Pia Astone Roma 1

Outlines:Outlines:

FDAF descriptionFDAF description

Project1a data application Project1a data application

Filters performances comparisonFilters performances comparison

WSR7 seg. 27 data applicationWSR7 seg. 27 data application

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) ->(N+1) filtered output

2. Event extraction• An Adaptive threshold algorithm for the selection of

the events applied at each filtered channel CH (N+1).

3. Cluster generation

Events coming from different CH in coincidence in a given time window W are put together: this is one CLUSTER

RAW DATA

Wiener Filter

WF

Power Spectrum SP estimation

Filters bank (N)

With

Gaussian

shape

FFT

1

2 ... ..

4 ... ..

.. … ..

. … ..

N+1

N+1

filtered

output

channels

In the time domain

Filtering procedure

IFFT

IFFT

Hp

Frequency domain

back in

time-domain

Hp

Hp

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 ∙ PS’i-1 + Pi

and ni = 1 + W ∙ ni-1

PS=PS’/n in our case:

W=exp(-T/tau)=0.9991

T=3.2768 s (time duration of one data chunk used to obtain the Periodogram) tau=3600 s (Memory time: Simulated data-> stationary noise)

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 + W∙mi-1 qi = y²i + W∙qi-1

ni = 1 + W∙ni-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|

Event extractionWe define a “dead time’’, td, as the minimum time between two events, and

we put the threshold, ϑ, on the CR. A two-state ( 0 and 1 ) mechanism “event machine’’ has been used: 1. The “machine’’ starts with state 02. When CR > ϑ, it changes to state 1 and an event begins

3. The state changes to 0 after CR remains below ϑ for a time > td (the event finishes)

T0 = starting time CRmax = Max value of CR

A = amplitudeThe ‘event’ is characterized Tmax = time of max CR

by: L = length (in seconds) (duration of state 1) CH = frequency channel

ϑ=3.9 td=0.2 s

Event cluster

EVENT LIST

of all frequency Channel (N+1)

Ch1 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 …. CRN+1

Time CR1 … … … CRN+1

………………….

………………….

Time CR1 … … … CRN+1

CRi=0 if the frequency channel Chi not in time coincidence with other.

Event cluster example (Preliminary Procedure!)

Frequency channels: Mean values of the Gaussian filters

CR value

WF channel

0-2000 Hz

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 …

… Time distances tim10-tim1 < W=10ms

They are put together-> one CLUSTER

Cluster list

Time CR1 CR2 CR3 CR4 .. .. .. .. CR10

Time2 6.13 6.75 6.0 0 0 0 0 0 4.8

clust

er

ord

eri

ng n

um

ber

CR

40 90 200 600 1000 1400 0-2000 Hz

tim2 is the time corresponding to the maximum CR ->time2=CLUSTER time

Project1a preliminary results

gr-qc/0701026 A comparison of methods for gravitational wave burst searches

from LIGO and Virgo

3 hours of Virgo simulated noise

Injected signalsINPUT:

3 hours of Virgo (vs=20 kHz) simulated noise

Signals injected with SNR=7, 10

Gaussian signals with σ = 1ms

2 kinds of supernovae signals (from Dimmelmeier-Font-Muller simulations) @ 8.5 kpc: A1B2G1,A2B4G1)

Sine-Gaussian signals with Q = 5 and ν = 235 Hz or ν = 820 HzSine-Gaussian signals with Q = 15 and ν = 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, Sigma=100 Hz) .--> 10 different filters

Waveform families of burst sources used in this study: time domain

Waveform families of burst sources used in this study: frequency domain

SGQ15f820: clusters in time coincidences with the injected signals (163) at SNR=7 (frequency domain

characteristic)

Due to the noise!

Not in the expected channel and they don’t change with the SNR of injected signals

SNR=7: CRSNR=7: number of event detected from each channel

clust

er

ord

eri

ng n

um

ber

Event

num

ber

90 200 600 1000 1400 0-2000 Hz

90 200 600 1000 1400 0-2000 Hz


characteristic)

Due to the noise!

Not in the expected channel and they don’t change with the SNR of injected signals

N

SNR=10: CR

clust

er

ord

eri

ng n

um

ber

90 200 600 1000 1400 0-2000 Hz

SNR=10: number of event detected from each channel

Event

nu

mber

90 200 600 1000 1400 0-2000 Hz

SGQ5f820: clusterin time coincidences with the injected signals (178) at SNR=7 (frequency domain

characteristic) SNR=7: CR

clust

er

ord

eri

ng n

um

ber

90 200 600 1000 1400 0-2000 Hz


Event

nu

mber

90 200 600 1000 1400 0-2000 Hz

SGQ5f820: cluster in time coincidences with the injected signals (178) at SNR=10 (frequency domain


clust

er

ord

eri

ng n

um

ber

90 200 600 1000 1400 0-2000 Hz


Event

nu

mber

90 200 600 1000 1400 0-2000 Hz



clust

er

ord

eri

ng n

um

ber

90 200 600 1000 1400 0-2000 Hz


Event

nu

mber

90 200 600 1000 1400 0-2000 Hz

SGQ5f235: clusters in time coincidences with the injected signals (190) at SNR=10 (frequency

domain characteristic) SNR=10: CR

clust

er

ord

eri

ng n

um

ber

90 200 600 1000 1400 0-2000 Hz


Event

nu

mber

90 200 600 1000 1400 0-2000 Hz

A1B2G1: clusters in time coincidences with the injected signals (165) at SNR=7 (frequency domain


clust

er

ord

eri

ng n

um

ber

90 200 600 1000 1400 0-2000 Hz


Event

nu

mber

90 200 600 1000 1400 0-2000 Hz



clust

er

ord

eri

ng n

um

ber

90 200 600 1000 1400 0-2000 Hz


Event

nu

mber

90 200 600 1000 1400 0-2000 Hz

To see better the lower frequency region (A2B4G1 & GAUSS1ms)I’ve added another channel at 40 Hz



clust

er

ord

eri

ng n

um

ber

40 90 200 600 1000 0-2000 Hz


Event

nu

mber

40 90 200 600 1000 0-2000 Hz



clust

er

ord

eri

ng n

um

ber


Event

nu

mber

40 90 200 600 1000 0-2000 Hz 40 90 200 600 1000 0-2000 Hz

GAU1ms: clusters in time coincidences with the injected signals (178) at SNR=7 (frequency domain


clust

er

ord

eri

ng n

um

ber

40 90 200 600 1000 0-2000 Hz


Event

nu

mber

40 90 200 600 1000 0-2000 Hz

GAU1ms: clusters in time coincidences with the injected signals (178) at SNR=10 (frequency domain


clust

er

ord

eri

ng n

um

ber

40 90 200 600 1000 0-2000 Hz


Event

nu

mber

40 90 200 600 1000 0-2000 Hz

Trigger due to the noise (no signal injection!)

NOISE: CR

clust

er

ord

eri

ng n

um

ber

NOISE: number of event in each channel

Event

nu

mber

90 200 600 1000 1400 0-2000 Hz

90 200 600 1000 1400 0-2000 Hz

Signal SNR <CR> Std(CR) bias[ms]

Std(DT)[ms]

Eff %

SGQ15f820 10 8.98@(4.2)

1.0@(0.46)

-0.031*35.6%

0.55 100

7 6.42(4.2)

0.94(0.3)

-0.06*20.86%

0.8 100

A1B2G1 10 8.28(4.2)

1.0(0.4)

-0.008*43%

0.05 100

7 5.92(4.2)

0.9(0.3)

-0.0024*32.5%

0.1 98.2

SGQ5f820 10 8.3(4.2)

1.0(0.4)

-0.008*55%

0.26 100

7 5.99(4.2)

0.9(0.3)

0.0*34.3%

0.39 97.8

*: percentage of CLUSTERS detected at the exact sample (DT=0.0)

@: obtained over all CLUSTERS (due to the noise+ due to the signals)

Signal SNR <CR> Std(CR) bias[ms]

Std(DT)[ms]

Eff %

SGQ5f235 10 8.24(4.2)

1.0(0.4)

0.1*24.21%

0.8 10099.4

7 5.99(4.2)

1.0(0.3)

0.006*15.22%

1.2 96.84

A2B4G1 10 6.47.47(4.2)

0.90.9(0.4)

0.8 1.0

0.960.28

100100

7 4.865.36(4.2)

0.640.8(0.3)

0.85 1.0

1.50.9

78.897.05

GAUSS1ms 10 8.9(4.2)

1.0(0.5)

-0.007*18%

0.11 100

7 6.3(4.2)

0.9(0.3)

-0.015*11.3%

0.17 99.4

*: percentage of CLUSTERS detected at the exact sample (DT=0.0)

The red values are obtained adding the lower frequency channel at 40 Hz

Filters performances comparison

Efficiency vs False Alarm Rate SNR=7 (Comparison with Power filter (Red))

sgQ15f820

A1B2G1

GAU1ms

A2B4G1

sgQ5f235

sgQ5f820

Signals injected with SNR=10

give efficiency=1 with FAR=10-4

Efficiency vs False Alarm Rate SNR=7

Time error comparison std[ms]

Std[ms] QT PF KW PC EGC MF ALF AFDFA1B2G1 0.2 0.05 0.5 0.04 0.03 0.05 0.3 0.05A2B4G1 1.4 0.7 2.6 0.2 0.4 0.5 2.2 0.28GAUSS1 0.8 1.2 1.4 0.1 0.2 0.8 1.5 0.11SG235Q5 0.9 1.4 0.9 1.3 0.5 1.3 1.1 0.8SG820Q5 0.2 0.2 0.3 - 0.2 0.3 0.3 0.26SG820Q15 0.7 0.6 1.1 - 0.5 1.3 1.1 0.55

Time error comparison bias [ms]

bias[ms] QT PF KW PC EGC MF ALF AFDF

A1B2G1 -0.1 0.2 0.3 -0.05 -0.06 0.03 0.1 -0.008A2B4G1 -1.7 1.9 4.9 -1.3 -1.4 2.1 0.7 1.0GAUSS1 -0.05 1.7 3.4 -0.01 0.01 2.3 1.7 -0.007SG235Q5 -0.07 0.6 1.3 0.02 0.02 0.7 0.7 0.1SG820Q5 -0.01 0.2 0.2 - 0.01 0.1 0.1 -0.008SG820Q15 -0.04 0.2 0.3 - 0.03 0.3 0.2 -0.031

WSR7 Preliminary Results seg.27GPS time start=852852866

GPS time stop =852858889

Hardware Injections: (SNR=7.5,15,25)

Injected signals N

SGf1000Q5/Q15 34/34

SGf1300Q5/Q15 34/34

SGf1600Q5/Q15 34/33 = 271 inj.

GAUSSIAN 34/34

A2B4G1 34/34

Pre HP filter with freq. cutoff at 80 Hz

Power Spectra Estimation:

tau=1800 s

T=3.2768 s

CR: ϑ=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, Sigma=100 Hz) .--> 11 different filters

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

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

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

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

Signal <CR/SNR>

Std(CR/SNR)

Bias[ms]<Ts-Tc>

Std(DT)[ms]

Eff %

SGf1000Q15 0.99 0.11 -0.67 0.38 100

SGf1000Q5 0.97 0.11 -0.54 0.22 100

SGf1300Q15 1.15 0.11 -0.89 0.41 100

SGf1300Q5 0.9 0.10 -0.7 0.39 100

SGf1600Q15 1.22 0.10 -0.5 0.38 100

SGf1600Q5 0.9 0.12 -0.54 0.38 100

A2B4G1 0.7 0.1 -2.3 0.8 100

GAUSSIAN 0.92 0.088 -0.45 0.1 100

CR: clusters in time coincidence with the injected signals

all clusters-271 clusters in time coincidence with the injected signals

<CR>=15.22

Std(CR)=7.27

<CR>=4.44

Std(CR)=0.61

4 BIG events not due to the injected signals

(first injection time=852852651.45370)

Without 4 big events

Signal Dt=1/20000 [s]

<CR/SNR> Std(CR/SNR) Bias[ms]<Ts-Tc>

Std(DT)[ms]

Eff %

SGf1000Q15 0.996 0.116 -0.56 0.31 100

SGf1000Q5 0.97 0.11 -0.57 0.15 100

SGf1300Q15 1.15 0.11 -0.97 0.32 100

SGf1300Q5 0.9 0.10 -0.62 0.15 100

SGf1600Q15 1.22 0.10 -0.55 0.15 100

SGf1600Q5 0.9 0.12 -0.54 0.17 100

A2B4G1 0.7 0.1 -2.3 0.8 100

GAUSSIAN 0.92 0.09 -0.45 0.0065 100

search for bursts with the frequency domain adaptive filter ( fdaf )

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