Application of Non-Harmonic Analysis for Gravitational Wave Detection

Transcription

1 Application of Non-Harmonic Analysis for Gravitational Wave Detection Masaya Nakano University 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 7 th Korea-Japan workshop on KAGRA Univ. Toyama

2 Background Gravitational 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. Using the NHA of high-precision analysis Frequency analysis method of the current highest accuracy 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.

3 Conventional Frequency Analysis Technique Fourier 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 26 Instantaneous Frequency Take the differential value of the phase, the analysis of detailed harmonic structure -Alexander Stoeer,et al. Physical Rev. D 79, 29 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

4 Non-Harmonic Analysis (NHA) NHA estimates the Fourier coefficient by solving a non-linear equation. (least square method) N 1 1 ˆ ( ˆ, ˆ, ˆ) ( ) ˆ f F A f x n Acos 2 n ˆ N n f s 1 Original spectrum N : 窓長 2 DFT(zero-padding) 2 NHA shows near original spectrum without undesired side-lobes. NHA

5 Advantages of NHA We compared the accuracy of frequency analysis achieved by two approaches. The accuracy of DFT analysis is relatively low when the objective signal is not a multiple of the fundamental frequency. Method DFT Accuracy 1 order of magnitude The square error of each estimated parameter. NHA 1 or more orders of magnitude At normalized Better frequencies axail resolution below can expected 1 Hz, NHA when NHA is demonstrated is to have greater analysis used. accuracy than DFT. Accurate estimation at frequencies below Gravitational 1 Hz implies Wave that Detection object signals Using with Non-Harmonic periods longer Analysis than the window length can be analyzed accurately.

6 frequency [Hz] frequency [Hz] amplitude Comprison of simulation signal (a) waveform (b) source.5 1 time [s] (c) STFT (d) HSA (f) NHA time.5 [s] 1 time [s]

7 frequency [Hz] frequency [Hz] amplitude Comparison of BBH Analysis Mass: m 1 = m 2 = 1M ISCO Frequency: f isco = 22[Hz] 1 (a) waveform 2 (b) STFT (c) HSA (d) NHA 1 2 time [s]

8 Problems under Noisy Conditions DFT Source spectrum + Noise spectrum = Noise environment spectrum Source spectrum and noise spectrum may overlap in harmonic analysis based on DFT, in which the frequency resolution is generally low. NHA 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.

9 amplitude 1-1 (a) waveform Experiment Condition Under the noisy conditioni n the case of SN=1 1 2 time [s] Before Processing :f s = Hz After Processing:f s = 512 Hz Frequency Characterization To cut of wasted bandwidth, use the Low-pass filter :f c = 3[Hz] Matched filter S/N ρ 2 = 4 f h 2 S n (f) df isco f = 4 f h 2 df S n (f) f Line noise: Violin mode of KAGRA

10 frequency [Hz] Noisy Condition 2 NHA SN = 1 SN = time [s] 2

11 Conclusions Gravitational 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 = 1 and 1, it was visualized the frequency trajectory due to merger waveform. Feature Works 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.

12 That s all. Thank you for your attention!

13 Concept of NHA The spectrum parameter of NHA is obtained by the signal shape fitting. 1. Set the initial value of the spectrum parameters. initial phase 2. Adjust the frequency and the initial phase by expanding or contracting or translating. 3. Adjust the amplitude.

14 OCT Image Based on NHA 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 Fixed mirror Reference Arm L 1 L 2 High Coherence Source Probe Arm l Scan Δλ l Coupler c/ L Sampl e t f OCT signal FFT dz Depth OCT cross-sectional images of finger skin.