Gravitational wave detection using Non-Harmonic Analysis...Background Gravitational Waves resulting...
Transcript of Gravitational wave detection using Non-Harmonic Analysis...Background Gravitational Waves resulting...
Application of Non-Harmonic Analysis for Gravitational Wave Detection
Masaya NakanoUniversity of Toyama
Collaborate with
S. Hirobayashi(Univ. Toyama), H. Tagoshi(Osaka Univ.),
K. Ueno(Osaka Univ.), T. Narikawa(Osaka Univ.),
K. Miyake(Univ. Toyama), N. Kanda(Osaka city Univ.),
K. Hayama(Osaka city Univ.)
The 7th Korea-Japan workshop on KAGRA
2014/12/19-20 @ Univ. Toyama
BackgroundGravitational Waves resulting from such neutron binary stars, binary black hole and early universe, is a means of a new space observation. Also, it is possible to clarify the physical behavior of the measured signal.
Gravitational wave that is shaking and fine frequency to time-frequency analysis, the amplitude change was visualized, sorting of noise and gravitational waves, detailed analysis of noise, it want to make a detailed analysis of the physical phenomena of gravitational wave sources.
Using the NHA of high-precision analysisFrequency analysis method of the current highest accuracy
Conventional Frequency Analysis TechniqueFourier Transform
The side-lobe suppression using Hamming and Hanning window, Interpolation of frequency resolution using the zero padding-Serge Droz, et al. Physical Rev. D, 1999
Wavelet Transform
Summing by scale basis functions. Time resolution is high.-B Abbott, et al. Classical and Quantum Gravity, 23, 8, S29 2006
Instantaneous Frequency
Take the differential value of the phase, the analysis of detailed harmonic structure-Alexander Stoeer,et al. Physical Rev. D 79, 2009
– Influence on analysis window
– Non-periodic signal is also regarded as a periodic signal analysis
・Lowering of the frequency resolution
・Discrete frequency decomposition width
– There is no completely independent of the mode decomposition
・It occurs Artifact
Fourier transform
Wavelet transform
Hilbert Spectrum analysis
Non-Harmonic Analysis (NHA)
N : 窓長
1
0
ˆ1ˆˆ ˆ ˆ ˆ( , , ) ( ) cos 2N
n s
fF A f x n A n
N f
2
2
DFT(zero-padding)
1 Original spectrum
NHA
NHA estimates the Fourier coefficient by solving a non-linear
equation. (least square method)
NHA shows near original spectrum
without undesired side-lobes.
Advantages of NHAWe compared the accuracy of frequency analysis achieved by two approaches.
Method Accuracy
DFT 1 order of magnitude
NHA10 or more orders of
magnitude
Better axail resolution can be expected when NHA is
used.
The accuracy of DFT analysis is
relatively low when the objective
signal is not a multiple of the
fundamental frequency.
Gravitational Wave Detection Using Non-Harmonic Analysis
At normalized frequencies below 1 Hz, NHA is demonstrated to have
greater analysis accuracy than DFT. Accurate estimation at frequencies
below 1 Hz implies that object signals with periods longer than the
window length can be analyzed accurately.
The square error of each estimated parameter.
¥
(c) STFT
(f) NHA
(d) HSA
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freq
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Hz]
time [s]
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(b) source
(a) waveform1
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-1
amp
litu
de
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cy [
Hz]
0 0.5 1time [s]
Comprison of simulation signal
0 0.5 1time [s]
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freq
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Hz]
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(d) NHA
(c) HSA
(b) STFT
0 1 2
(a) waveform1
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-1
amp
litu
de
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Comparison of BBH AnalysisMass:𝑚1 = 𝑚2 = 10𝑀⊙ 𝐼𝑆𝐶𝑂 𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦: 𝑓𝑖𝑠𝑐𝑜 = 220[𝐻𝑧]
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Problems under Noisy Conditions
Source spectrum and noise spectrum may overlap in harmonic
analysis based on DFT, in which the frequency resolution is
generally low.
Source spectrum + Noise spectrum = Noise environment spectrum
Source spectrum + Noise spectrum = Noise environment spectrum
Since NHA is affected very little by the frame length, the noise
and source spectra are less likely to overlap than with DFT.
Also, NHA can potentially preserve amplitude and initial phase.
NHA
DFT
(a) waveform
Experiment Condition
¥time [s]
0 1 2
1
0
-1ampli
tude
・To cut of wasted bandwidth, use the
Low-pass filter :𝑓𝑐 = 300[𝐻𝑧]
Before Processing :𝑓𝑠 = 16384 𝐻𝑧After Processing:𝑓𝑠 = 512 𝐻𝑧
・Matched filter S/N
𝜌2 = 4 0
∞ 𝑓 ℎ2
𝑆𝑛(𝑓)
𝑑𝑓
𝑓= 4
0
𝑖𝑠𝑐𝑜 𝑓 ℎ2
𝑆𝑛(𝑓)
𝑑𝑓
𝑓
Frequency Characterization
Under the noisy conditioni n the case of SN=100
Line noise: Violin mode of KAGRA
time [s]
freq
uen
cy [
Hz]
NHA
SN = 100
SN = 10
Noisy Condition
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ConclusionsGravitational wave have large frequency variation in a short time,
the reproducibility of the waveform is an important problem in gravitational wave observation.
In this report, for the binary black hole waveform, evaluated in time-frequency domain under the noisy condition.
Under the noisy condition of SN = 10 and 100, it was visualized the frequency trajectory due to merger waveform.
As challenges for the future, to conduct and review of GPU acceleration process, the analysis of detector data calculation can be expensive NHA. In addition, to perform accurate comparison with other frequency analysis methods.
Feature Works
That’s all.
Thank you for your attention!
Concept of NHA
1. Set the initial value
of the spectrum
parameters.
2. Adjust the frequency
and the initial phase by
expanding or contracting
or translating.
3. Adjust the amplitude.
initial phase
The spectrum parameter of NHA is obtained by the signal shape fitting.
High Coherence Source Probe Arm
lc/⊿L
t ➔ f
FFT
OCT
signaldz
Δλ
⊿L1 ⊿L2
l Scan
Depth
Reference Arm
Fixed mirror
Coupler
Sampl
e
OCT Image Based on NHA
OCT cross-sectional images of finger skin.
何か一言コメント OCTのNHAの応用性から重力波にも応用させる