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Some output from the optimal program

Some output from the optimal program follows:
...
max snr: 3.11 offset: 23623 data start: 180.00 sec. variance: 0.94044
max snr: 2.91 offset: 3311 data start: 185.17 sec. variance: 0.84484
...
max snr: 2.53 offset: 19041 data start: 309.26 sec. variance: 0.70333
max snr: 2.98 offset: 35711 data start: 314.43 sec. variance: 0.67523

Max SNR: 8.71 (offset 42109) variance 0.805030
If impulsive event, offset 55624 or time 325.23
If inspiral, template start offset 42109 (time 323.86) coalescence time 325.23
Normalization: S/N=1 at 116.75 kpc
Linear combination of max SNR: 0.9315 x phase_0 + 0.3638 x phase_pi/2
Less than 1% probability that this is a chirp (p=0.000000).
Distribution: s= 23, N>3s= 12 (expect 176), N>5s= 0 (expect 0)
Distribution does not appear to have outliers...

max snr: 2.51 offset: 31183 data start: 324.77 sec. variance: 0.63028
max snr: 2.56 offset: 49909 data start: 329.94 sec. variance: 0.66853
...
max snr: 2.82 offset: 35080 data start: 3002.03 sec. variance: 0.77306
max snr: 2.61 offset: 33141 data start: 3007.20 sec. variance: 0.74268

Max SNR: 89.75 (offset 16678) variance 82.547005
If impulsive event, offset 30193 or time 3015.43
If inspiral, template start offset 16678 (time 3014.06) coalescence time 3015.43
Normalization: S/N=1 at 128.49 kpc
Linear combination of max SNR: -0.3955 x phase_0 + 0.9185 x phase_pi/2
Less than 1% probability that this is a chirp (p=0.000000).
Distribution: s= 29, N>3s= 157 (expect 176), N>5s= 30 (expect 0)
Distribution has outliers! Reject

max snr: 3.24 offset: 22412 data start: 3017.54 sec. variance: 0.99474
max snr: 2.73 offset: 37777 data start: 3022.71 sec. variance: 0.75325
...
max snr: 2.80 offset: 5893 data start: 4140.89 sec. variance: 0.73240
max snr: 2.75 offset: 46932 data start: 4146.06 sec. variance: 0.69654

Max SNR: 6.08 (offset 30002) variance 0.883380
If impulsive event, offset 43517 or time 4155.64
If inspiral, template start offset 30002 (time 4154.27) coalescence time 4155.64
Normalization: S/N=1 at 113.04 kpc
Linear combination of max SNR: -0.4773 x phase_0 + 0.8787 x phase_pi/2
POSSIBLE CHIRP!  with > 1% probability (p=0.024142).
Distribution: s= 31, N>3s= 399 (expect 176), N>5s= 53 (expect 0)
Distribution has outliers! Reject

max snr: 2.77 offset: 15985 data start: 4156.40 sec. variance: 0.72095
max snr: 2.69 offset: 47338 data start: 4161.57 sec. variance: 0.69708
...

This output shows three events that triggered an optimal filtering routine. The first and second of these events were rejected for different reasons. The first was rejected because if failed the frequency-distribution test. The second was rejected because it had 30 outlier points. The third failed for the same reason: it had 53 outlier points.

Next, we show some output when a fake chirp signal is injected into the data stream. This can be done for example by modifying optimal to read:

invMpc_inject=100.0;   /* To inject a signal at 10 kpc, set this to 100.0 */
time_inject_chirp(1.0,0.0,12345,invMpc_inject,chirp0,chirp90,data,response,output0,npoint);

This produces the following output:
...
Max SNR: 9.96 (offset 12345) variance 0.872624
If impulsive event, offset 25860 or time 187.79
If inspiral, template start offset 12345 (time 186.42) coalescence time 187.79
Normalization: S/N=1 at 152.17 kpc
Linear combination of max SNR: 0.9995 x phase_0 + -0.0304 x phase_pi/2
POSSIBLE CHIRP!  with > 1% probability (p=0.421294).
Distribution: s= 23, N>3s= 12 (expect 176), N>5s= 0 (expect 0)
Distribution does not appear to have outliers...

Max SNR: 12.84 (offset 12345) variance 0.834527
If impulsive event, offset 25860 or time 192.96
If inspiral, template start offset 12345 (time 191.59) coalescence time 192.96
Normalization: S/N=1 at 132.47 kpc
Linear combination of max SNR: 0.9953 x phase_0 + 0.0973 x phase_pi/2
POSSIBLE CHIRP!  with > 1% probability (p=0.949737).
Distribution: s= 22, N>3s= 28 (expect 176), N>5s= 0 (expect 0)
Distribution does not appear to have outliers...

Max SNR: 14.86 (offset 12345) variance 0.801640
If impulsive event, offset 25860 or time 198.13
If inspiral, template start offset 12345 (time 196.76) coalescence time 198.13
Normalization: S/N=1 at 127.90 kpc
Linear combination of max SNR: 0.9993 x phase_0 + -0.0372 x phase_pi/2
POSSIBLE CHIRP!  with > 1% probability (p=0.999236).
Distribution: s= 22, N>3s= 35 (expect 176), N>5s= 0 (expect 0)
Distribution does not appear to have outliers...
...

The code is correctly finding the chirps, getting the distance and phase and time location of the chirps about as accurately as one would expect given the level of the IFO noise.

There are several interesting lessons that one can learn from this optimal filtering experience. The first is that (roughly speaking) the events that trigger an optimal filter (driving the output to a value much larger than would be expected for a colored-noise Gaussian input) can be broken into two classes: those which can be seen in the raw data stream, and those which can not. Here, by seen in the raw data stream", we mean visible to the naked eye upon examination of a graph". Shown in the following two figures are examples of each type of spurious event.

Next: The effective distance to Up: GRASP Routines: Gravitational Radiation Previous: Example: optimal program   Contents
Bruce Allen 2000-11-19