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the line noise band for gravitational wave observation system by the. analysis of Non-Harmonic Analysis. DongBao Jia . University . of . Toyama. Kyohei. . Miyake, Kenta . Yanagisawa, . Shigeki . Hirobayashi. ID: 551076

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Slide1

Time frequency visualization of surroundingthe line noise band for gravitational wave observation system by theanalysis of Non-Harmonic Analysis

DongBao Jia University of ToyamaKyohei Miyake, Kenta Yanagisawa, Shigeki HirobayashiHideyuki Tagoshi, Tatsuya Narikawa, Nami Uchikata Hirotaka TakahashiUniversity of Toyama, Osaka City University, Nagaoka University of Technology2016-12-28, Kyoto

1

Annual Symposium 2016

on

"New

Developments

in Astrophysics

Through Multi-Messenger

Observations of

Gravitational Wave Sources".

Slide2Background

According to the theory of relativity, the existence of gravitational wave (GW) has been proven indirectly. In particular, the GW was observed for the first time in LIGO on September 14, 2015, the GW astronomy about the neutron binary star may developing greatly. And the neutron binary star is a promising target of laser interferometer GW detector, such as the LIGO, VIRGO, and KAGRA, etc.

2

Slide3Instrument noise for each detector nearthe time of the signal detection

About the real data of detector, the plural line noises such as the power supply noise are appearing bigger than the gravitational wave signal greatly. Narrow-band features include calibration lines (33–38, 330, and 1080 Hz), vibrational modes of suspension fibers (500 Hz and harmonics), and 60 Hz electric power grid harmonics.

Observation of Gravitational Waves from a Binary Black Hole

Merger PHYSICAL REVIEW LETTERS12 FEBRUARY 2016

3

Slide4Influence of notch filter

If the notch filter is performed in the frequency band where the line noise exists, the gravitational wave signal which near the line noises will be removed too, the original characteristics of gravitational wave will lose. Therefore, without the notch filter to analyze and observe the gravitational wave signal in detail becomes necessary. Namely, the analysis method with a high frequency resolution is necessary.

The signal, GW151226, was observed by the twin detectors of the Laser Interferometer Gravitational-Wave Observatory (LIGO) on December 26, 2015 at 03:38:53 UTC.

4

Slide5Non-Harmonic Analysis (NHA)

NHA estimates the Fourier coefficient by solving a non-linear equation. (least square technique)

sinusoidal wave model

N

: frame length

We applied NHA as a frequency analysis method in order to solve the

problem of

spectrum degradation

of FFT

.

The influence of the analytical window length is minimal, allowing accurate estimation of the frequency and other parameters.

input signal

5

Slide61. 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.

frequency

initial phase

The spectrum parameter of

NHA

is obtained by the signal

shape fitting

.

Non-Harmonic Analysis (NHA)

6

Slide7Advantages of NHA

Among the various techniques, we proposed and tried to use the Non-Harmonic Analysis (NHA) which improved the frequency resolution dramatically to analyze the gravitational wave.

original

FFT (Zero-padding)

NHA

7

Slide8Advantages of NHA

NHA

can extract the information of frequency and amplitude individually, and corresponding the frequency and amplitude of time signal formula. NHA can make the time resolution compatible with the frequency resolution.

FFT can analyzed accurately at a frequency that is an integer multiple, but the side lobe occurs under the influence of the window. Impact of the analysis window is small for NHA, it can be analyzed accurately even in waveform having a frequency which is not an integer multiple.

8

Slide9Precision verification and comparison with other methods

The observed GW has a rapid frequency variations and includes many noises.

Further, for capturing the frequency change in the process of the time, it is necessary to compatible the high frequency resolution and high time resolution. In the actual GW measurement, plural line noises are crossing and covering the parts of GW, and existing in the band of the GW. They are influencing the analysis of GW especially, and reduce the effects of line noise becomes necessary. For assuming and simulating the line noise cross the gravity wave just as the actual GW measurement, we made two signals which assume the gravity wave and the line noise respectively, and make them cross.

9

Slide10Analyzation based on data of LIGO

The data of LIGO (L-L1_LOSC_4_V1-843272192-4096-0.txt)

Model waveform of neutron binary star coalescence

waveform

inspiral

merger

The

=

40Hz is the cut frequency which be used to analyze the data of

LIGO.

A

s

for 1600Hz, when

for the mass of neutron binary star, after merged, the highest frequency

10

Slide11Data flow

Gravity waveform with noise. (a+b=c)

Pre Processing

Frequency analysis

Input Signal(

GW

model+Noise

)

whitening

Band-Pass Filter(40-1600Hz)

NHA

FFT

Visualization of the Time-Frequency Domain

LIGO

data S5

Band in which

GW

exist

11

Slide12Window function

For the sampling frequency =4096Hz, the analysis was under the short time window of 512points (0.125s) in this time. There is an advantage that NHA can analyze correctly than FFT at the short window. Especially, the window function was used in FFT generally, but according to the characteristics of signal and noise, which window function should be used becomes important. But the influence of window length is small for NHA.

The frequency characteristics of LIGO data using window function and the chirp wave

12

Slide13Results

SN=10

(c) SN=30

Time-frequency analysis of FFT (Hanning window) and NHA,

window length is 512points,

fs=4096Hz, t=15sec.

SN=30

SN=20

13

Slide14Enlarged view

NHA(window125ms)

There are line noises

in the

60Hz

and 120Hz.

The frequency variation

of GW is from

60Hz

to

250Hz

NHA Result (SN=30)

14

Slide15FFT and NHA results (SN=20)

NHA(window125ms)

Relatively, it is also possible to capture the variation in either Method

FFT(

Hanning

window125ms)

In the case of FFT, the signal

buried under the influence of the main lobe and the side lobe,

but NHA can capture

the change

in the case of SN=20.

15

Slide16Summary

We analyzed the measured LIGO data at SN=10, 20, 30. Under the influence of window function, FFT cannot capture the parts of frequency change of GW signal which be covered by the large line spectrum of power supply noise. But the influence of analysis window is small to NHA, it can visualize the waveform delicately to the limit and capture the imperceptible changes even enlarge.In addition, if perform the notch filter, the original characteristics of GW which near the line noise will lose. But NHA can detailed analyze and visualize the GW signal which near the line noise without doing the notch filter since the influence of analysis window length is small.Thus, NHA provides a higher-resolution analysis than other methods. And in the future, we proposed to use NHA to analyze the GW which be detected by the observation system such as LIGO, KAGRA and so on.

16

Slide17Thank you for your attention.

17

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