Search for bursts with the Frequency Domain Adaptive Filter (FDAF ) Sabrina D’Antonio Roma II Tor Vergata Sergio Frasca, Pia Astone Roma 1 Outlines: FDAF description FDAF description Project1a data application Project1a data application Filters performances comparison Filters performances comparison WSR7 seg. 27 data application WSR7 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 …... ….. N+1 filtered output channels In the time domain Filtering procedure IFFT Hp Frequency domain back in time-domain 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, P i : from PS i ’ = W ∙ PS’ i-1 + P i and n i = 1 + W ∙ n i-1 PS=PS’/n in our case: W=exp(-T/tau)= T= 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 m i = y i + W∙m i-1 q i = y² i + W∙q i-1 n i = 1 + W∙n i-1 with W = exp(-dt/tau) = (corresponding to dt= 1/20000 s & tau = 5 s) and M i = m i /n I Q i = q i /n i S i = sqrt(Q i -(M i ) 2 ) From these we define the Critical Ratio (CR i ) of y(i) CR i =|(y i -M i )/S i |

Event extraction We define a “dead time’’, t d, 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 0 2. 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 > t d (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 ϑ =3.9 td=0.2 s

Event cluster EVENT LIST of all frequency Channel (N+1) 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 …. CRN+1 Time CR1 … … … CRN+1 …………………. Time CR1 … … … CRN+1 CR i =0 if the frequency channel Ch i not in time coincidence with other.

Event cluster example (Preliminary Procedure!) Frequency channels: Mean values of the Gaussian filters CR value WF channel Hz Event list: Freq. Channel Time cr Ampl length.. 1 (40 Hz) tim … ….... … (90Hz) tim … ….... ….. 3 (200Hz) tim3 6.0 … ….... … (0-2000Hz) tim … … Time distances tim10-tim1 < W=10ms They are put together-> one CLUSTER Cluster list Time CR1 CR2 CR3 CR CR10 Time cluster ordering number CR Hz tim2 is the time corresponding to the maximum CR ->time2=CLUSTER time

Project1a preliminary results gr-qc/ A comparison of methods for gravitational wave burst searches from LIGO and Virgo

3 hours of Virgo simulated noise

Injected signals INPUT: 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 8.5 kpc: A1B2G1,A2B4G1) Sine-Gaussian signals with Q = 5 and ν = 235 Hz or ν = 820 Hz Sine-Gaussian signals with Q = 15 and ν = 820 Hz Wiener filter (WF) +Band-Pass filters with Gaussian shape: The frequency range 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: CR SNR=7: number of event detected from each channel cluster ordering number Event number Hz

SGQ15f820: clusters in time coincidences with the injected signals (163) at SNR=10 (frequency domain 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 cluster ordering number Hz SNR=10: number of event detected from each channel Event number Hz

SGQ5f820: clusterin time coincidences with the injected signals (178) at SNR=7 (frequency domain characteristic) SNR=7: CR cluster ordering number Hz SNR=7: number of event detected from each channel Event number Hz

SGQ5f820: cluster in time coincidences with the injected signals (178) at SNR=10 (frequency domain characteristic) SNR=10: CR cluster ordering number Hz SNR=10: number of event detected from each channel Event number Hz

SGQ5f235: clusters in time coincidences with the injected signals (190) at SNR=7 (frequency domain characteristic) SNR=7: CR cluster ordering number Hz SNR=7: number of event detected from each channel Event number Hz

SGQ5f235: clusters in time coincidences with the injected signals (190) at SNR=10 (frequency domain characteristic) SNR=10: CR cluster ordering number Hz SNR=10: number of event detected from each channel Event number Hz

A1B2G1: clusters in time coincidences with the injected signals (165) at SNR=7 (frequency domain characteristic) SNR=7: CR cluster ordering number Hz SNR=7: number of event detected from each channel Event number Hz

A1B2G1: clusters in time coincidences with the injected signals (165) at SNR=10 (frequency domain characteristic) SNR=10: CR cluster ordering number Hz SNR=10: number of event detected from each channel Event number Hz

A2B4G1: clusters in time coincidences with the injected signals (170) at SNR=7 (frequency domain characteristic) SNR=7: CR cluster ordering number Hz SNR=7: number of event detected from each channel Event number Hz

A2B4G1: clusters in time coincidences with the injected signals (170) at SNR=10 (frequency domain characteristic) SNR=10: CR cluster ordering number Hz SNR=10: number of event detected from each channel Event number Hz

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

A2B4G1: clusters in time coincidences with the injected signals (170) at SNR=7 (frequency domain characteristic) SNR=7: CR cluster ordering number Hz SNR=7: number of event detected from each channel Event number Hz

A2B4G1: clusters in time coincidences with the injected signals (170) at SNR=10 (frequency domain characteristic) SNR=10: CR cluster ordering number SNR=10: number of event detected from each channel Event number Hz

GAU1ms: clusters in time coincidences with the injected signals (178) at SNR=7 (frequency domain characteristic) SNR=7: CR cluster ordering number Hz SNR=7: number of event detected from each channel Event number Hz

GAU1ms: clusters in time coincidences with the injected signals (178) at SNR=10 (frequency domain characteristic) SNR=10: CR cluster ordering number Hz SNR=10: number of event detected from each channel Event number Hz

Trigger due to the noise (no signal injection!) NOISE: CR cluster ordering number NOISE: number of event in each channel Event number Hz

SignalSNR Std(CR)bias [ms] Std(DT) [ms] Eff % *35.6% (4.2) 0.94 (0.3) *20.86% A1B2G (4.2) 1.0 (0.4) *43% (4.2) 0.9 (0.3) *32.5% SGQ5f (4.2) 1.0 (0.4) *55% (4.2) 0.9 (0.3) 0.0 *34.3% * : percentage of CLUSTERS detected at the exact sample obtained over all CLUSTERS (due to the noise+ due to the signals)

SignalSNR Std(CR)bias [ms] Std(DT) [ms] Eff % SGQ5f (4.2) 1.0 (0.4) 0.1 *24.21% (4.2) 1.0 (0.3) *15.22% A2B4G (4.2) 0.9 (0.4) (4.2) (0.3) GAUSS1ms108.9 (4.2) 1.0 (0.5) *18% (4.2) 0.9 (0.3) *11.3% *: 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] QTPFKWPCEGCMFALFAFDF A1B2G A2B4G GAUSS SG235Q SG820Q SG820Q

Time error comparison bias [ms] bias[ms] QTPFKWPCEGCMFALFAFDF A1B2G A2B4G GAUSS SG235Q SG820Q SG820Q

WSR7 Preliminary Results seg.27 GPS time start= GPS time stop = 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= s CR: ϑ =4.0 Wiener filter (WF) +Band-Pass filters with Gaussian shape: The frequency range Hz is linearly divided into 10 bands (step = 150 Hz, Sigma=100 Hz). --> 11 different filters

GAUSSIAN/A2B4G1: all signals detected Hz

SGf1000Q15/Q5: all signals detected Hz

SGf1300Q15/Q5: all signals detected Hz

SGf1600Q15/Q5: all events detected Hz

Signal Std(CR/SNR)Bias [ms] Std(DT) [ms] Eff % SGf1000Q SGf1000Q SGf1300Q SGf1300Q SGf1600Q SGf1600Q A2B4G GAUSSIAN

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

4 BIG events not due to the injected signals (first injection time= )

Without 4 big events

Signal Dt=1/20000 [s] Std(CR/SNR)Bias [ms] Std(DT) [ms] Eff % SGf1000Q SGf1000Q SGf1300Q SGf1300Q SGf1600Q SGf1600Q A2B4G GAUSSIAN