hayama nao

Reducing the Binary Confusion Noise
)
(
kazuhiro.hayama@nao.ac.jp
– p.1/17
2000
(
)
– p.2/17
2000
(
)
(
)
– p.2/17
2000
(
)
(
)
– p.2/17
Wavelet
(Innocent, Torrésani)
BCN
+
(Binary Confusion Noise + (
))
– p.3/17
Binary Confusion Noise
h(t) = f (t) +
PN
i
g i (t)
Wavelet
X
X
X
dj,k ψj,k (t) =
αj,k ψj,k (t) +
β i j,k ψj,k (t)
j,k
j,k
i,j,k
ψj,k (t) = 2j/2 ψ(2j t − k)
– p.4/17
Binary Confusion Noise
h(t) = f (t) +
PN
i
g i (t)
Wavelet
X
X
X
dj,k ψj,k (t) =
αj,k ψj,k (t) +
β i j,k ψj,k (t)
j,k
j,k
i,j,k
Amplitude
ψj,k (t) = 2j/2 ψ(2j t − k)
Time
(c)
– p.4/17
Binary Confusion Noise
h(t) = f (t) +
PN
i
g i (t)
Wavelet
X
X
X
dj,k ψj,k (t) =
αj,k ψj,k (t) +
β i j,k ψj,k (t)
j,k
j,k
i,j,k
Power
Amplitude
ψj,k (t) = 2j/2 ψ(2j t − k)
(e)
Frequency
Time
(f)
– p.4/17
Wavelet
CN (Fourier
CN logN )
– p.5/17
BCN
Wavelet Spectrum
P P i 2
Ej := k αj,k + i βj,k Fourier Spectrum
E ∼ ω −7/6 ⇒ Ej ∼ 2−j/6
Ej =
P
2
k |αj,k | +
i −j/6
E
+ RNj
i j2
P
– p.6/17
BCN
P P i 2
Ej := k αj,k + i βj,k Wavelet Spectrum
Fourier Spectrum
E ∼ ω −7/6 ⇒ Ej ∼ 2−j/6
Ej =
2
k |αj,k | +
i −j/6
E
+ RNj
i j2
P
Wavelet
0.6
0.5
Number
BCN
P
0.4
0.3
0.2
0.1
0
-28 -27 -26 -25 -24 -23 -22 -21 -20 -19
Base-10 Logarithm of Alpha
– p.6/17
BCN
P P i 2
Ej := k αj,k + i βj,k Wavelet Spectrum
Fourier Spectrum
E ∼ ω −7/6 ⇒ Ej ∼ 2−j/6
Ej =
2
k |αj,k | +
i −j/6
E
+ RNj
i j2
P
Wavelet
0.6
0.5
P i −j/6
1/2
Bj := ( i Ej 2
+ RNj )/T
⇒ BCN
Number
BCN
P
0.4
0.3
0.2
0.1
0
-28 -27 -26 -25 -24 -23 -22 -21 -20 -19
Base-10 Logarithm of Alpha
– p.6/17
Binary Confusion Noise
∗
αj,k
Wavelet
∗
dj,k = αj,k
+ Bj
∗
αj,k
=
BCN
dj,k
Wavelet
Reduction Rule


 sgn(dj,k )(|dj,k | − Bj ) if |dj,k | − Bj > 0

0
if |dj,k | − Bj < 0
– p.7/17
Binary Confusion Noise
∗
αj,k
Wavelet
∗
dj,k = αj,k
+ Bj
BCN
dj,k
Wavelet
Reduction Rule


 sgn(dj,k )(|dj,k | − Bj ) if |dj,k | − Bj > 0
∗
αj,k
=

0
Bj
BCN
if |dj,k | − Bj < 0
– p.7/17
Binary Confusion Noise
∗
αj,k
Wavelet
∗
dj,k = αj,k
+ Bj


 sgn(dj,k )(|dj,k | − Bj ) if |dj,k | − Bj > 0

0
Bj
BCN
if |dj,k | − Bj < 0
∗
αj,k
=
BCN
dj,k
Wavelet
Reduction Rule
+
– p.7/17
–BCN
(
)
Amplitude
Time-Series Data of Embedded Ringdown
0
10000
20000
30000
Time (sec)
– p.8/17
–BCN
104
chirp
BCN
Time-Series Data Before our Algorithm
Amplitude
Amplitude
Time-Series Data of Embedded Ringdown
0
10000
20000
Time (sec)
30000
0
0
10000
20000
30000
Time (sec)
– p.8/17
–BCN
BCN
Time-Series Data Before our Algorithm
Amplitude
Amplitude
Time-Series Data of Embedded Ringdown
10000
20000
30000
0
10000
Time (sec)
20000
30000
Time (sec)
Time-Series Data After our Algorithm
Amplitude
0
0
0
10000
20000
30000
Time (sec)
– p.8/17
Wavelet
+
BCN
BCN
– p.9/17
– S/N
S/N
ρ=2
Z
H(f ) · T (f )∗
df
S(f )2
– p.10/17
– S/N
S/N
ρ=2
Z
H(f ) · T (f )∗
df
S(f )2
Log10 Signal to Ratio
7
6
5
4
3
2
1
0
2
4
6
8
10
12
Energy Ratio of BCN and Ringdown
(g) RBCN
S/N
– p.10/17
– S/N
S/N
ρ=2
H(f ) · T (f )∗
df
S(f )2
Z
ρ vs ρafter
7
base-10 log S/N after WS
Log10 Signal to Ratio
7
6
5
4
3
2
1
0
2
4
6
8
10
12
6
5
4
3
2
1
-0.5
0
Energy Ratio of BCN and Ringdown
(h) RBCN
S/N
0.5
1
1.5
2
base-10 log S/N
(i)
– p.10/17
– S/N
S/N
ρ=2
H(f ) · T (f )∗
df
S(f )2
Z
ρ vs ρafter
7
base-10 log S/N after WS
Log10 Signal to Ratio
7
6
5
4
3
2
1
0
2
4
6
8
10
12
6
5
4
3
2
1
-0.5
0
Energy Ratio of BCN and Ringdown
(j) RBCN
S/N
0.5
1
1.5
2
base-10 log S/N
(k)
– p.10/17
Amplitude
Amplitude
–
20000
30000
0
10000
30000
Time [sec]
(l)
Time [sec]
20000
(m) BCN
10000
0
– p.11/17
1
BCN
2
Binary Confusion Noise
BCN
– p.12/17
BCN
BCN
2
Binary Confusion Noise
1
Binary Confusion Noise
– p.12/17
BCN
BCN
2
Binary Confusion Noise
1
BCN
Binary Confusion Noise
– p.12/17
Amplitude
Amplitude
– BCN +
20000
30000
0
10000
30000
(o) BCN
Time [sec]
(n)
Time [sec]
20000
10000
0
– p.13/17
BCN
Unknown Signal
Binary Confusion Noise
– p.14/17
BCN
Confusion Noise
Wavelet
Unknown Signal
Binary Confusion Noise
– p.14/17
BCN
Confusion Noise
Wavelet
Unknown Signal
Binary Confusion Noise
Noise
Confusion
– p.14/17
Unknown Signal
Binary Confusion Noise
Wavelet
BCN
Confusion Noise
Noise
Confusion
BCN
10
Ringdown
12.1
S/N
– p.14/17
– TAMA
TAMA
52F76_5_1_0.dat
0.15
Amplitude
0.1
0.05
0
-0.05
-0.1
-0.15
0.25
0.26
0.27
0.28
Time (sec)
0.29
0.3
(q)
52F70_9_1_0.dat
0.02
0.015
0.01
0.005
0
-0.005
0.5
1
1.5
2
Time (sec)
2.5
3
3.5
(r)
0
Amplitude
(p)
-0.2
0.24
1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5
Time (sec)
1
Amplitude
52F82_5_1_0.dat
0.6
0.5
0.4
0.3
0.2
0.1
0
-0.1
-0.2
-0.3
-0.4
-0.5
– p.15/17
(Dimmelmeier et el. (2002))
Time-Series Data of Burst GW
4
Amplitude
2
0
-2
-4
-6
-8
-10
0
50 100 150 200 250 300 350 400 450
Time (milli sec)
– p.16/17
+Gaussian Noise
Time-Series Data of Burst GW
Time-Series Data Before our Algorithm
4
0
Amplitude
Amplitude
2
-2
-4
-6
-8
-10
0
50 100 150 200 250 300 350 400 450
Time (milli sec)
8
6
4
2
0
-2
-4
-6
-8
-10
-12
0
50 100 150 200 250 300 350 400 450
Time (milli sec)
– p.16/17
Time-Series Data of Burst GW
Time-Series Data Before our Algorithm
4
Amplitude
0
-2
-4
-6
-8
-10
0
50 100 150 200 250 300 350 400 450
0
50 100 150 200 250 300 350 400 450
Time (milli sec)
Time (milli sec)
Time-Series Data After our Algorithm
4
2
Amplitude
Amplitude
2
8
6
4
2
0
-2
-4
-6
-8
-10
-12
0
-2
-4
-6
-8
0
50 100 150 200 250 300 350 400 450
Time (milli sec)
– p.16/17
Time-Series Data of Burst GW
Time-Series Data Before our Algorithm
4
Amplitude
0
-2
-4
-6
-8
-10
0
50 100 150 200 250 300 350 400 450
0
50 100 150 200 250 300 350 400 450
Time (milli sec)
Time (milli sec)
Time-Series Data After our Algorithm
4
2
Amplitude
Amplitude
2
8
6
4
2
0
-2
-4
-6
-8
-10
-12
0
-2
-4
-6
-8
0
50 100 150 200 250 300 350 400 450
Time (milli sec)
– p.16/17
– p.17/17