Detection of gravitational-wave bursts with chirplet-like template families

Gravitational Wave (GW) burst detection algorithms typically rely on the hypothesis that the burst signal is "locally stationary", that is it changes slowly with frequency. Under this assumption, the signal can be decomposed into a small number of wavelets with constant frequency. This justifies the use of a family of sine-Gaussian templates in the Omega pipeline, one of the algorithms used in LIGO-Virgo burst searches. However there are plausible scenarios where the burst frequency evolves rapidly, such as in the merger phase of a binary black hole and/or neutron star coalescence. In those cases, the local stationarity of sine-Gaussians induces performance losses, due to the mismatch between the template and the actual signal. We propose an extension of the Omega pipeline based on chirplet-like templates. Chirplets incorporate an additional parameter, the chirp rate, to control the frequency variation. In this paper, we show that the Omega pipeline can easily be extended to include a chirplet template bank. We illustrate the method on a simulated data set, with a family of phenomenological binary black-hole coalescence waveforms embedded into Gaussian LIGO/Virgo-like noise. Chirplet-like templates result in an enhancement of the measured signal-to-noise ratio.Comment: 8 pages, 6 figures. Submitted to Class. Quantum Grav. Special issue: Proceedings of GWDAW-14, Rome (Italy), 2010; fixed several minor issue

Best chirplet chain: near-optimal detection of gravitational wave chirps

The list of putative sources of gravitational waves possibly detected by the ongoing worldwide network of large scale interferometers has been continuously growing in the last years. For some of them, the detection is made difficult by the lack of a complete information about the expected signal. We concentrate on the case where the expected GW is a quasi-periodic frequency modulated signal i.e., a chirp. In this article, we address the question of detecting an a priori unknown GW chirp. We introduce a general chirp model and claim that it includes all physically realistic GW chirps. We produce a finite grid of template waveforms which samples the resulting set of possible chirps. If we follow the classical approach (used for the detection of inspiralling binary chirps, for instance), we would build a bank of quadrature matched filters comparing the data to each of the templates of this grid. The detection would then be achieved by thresholding the output, the maximum giving the individual which best fits the data. In the present case, this exhaustive search is not tractable because of the very large number of templates in the grid. We show that the exhaustive search can be reformulated (using approximations) as a pattern search in the time-frequency plane. This motivates an approximate but feasible alternative solution which is clearly linked to the optimal one. [abridged version of the abstract]Comment: 23 pages, 9 figures. Accepted for publication in Phys. Rev D Some typos corrected and changes made according to referee's comment

Time-frequency representation of earthquake accelerograms and inelastic structural response records using the adaptive chirplet decomposition and empirical mode decomposition

In this paper, the adaptive chirplet decomposition combined with the Wigner-Ville transform and the empirical mode decomposition combined with the Hilbert transform are employed to process various non-stationary signals (strong ground motions and structural responses). The efficacy of these two adaptive techniques for capturing the temporal evolution of the frequency content of specific seismic signals is assessed. In this respect, two near-field and two far-field seismic accelerograms are analyzed. Further, a similar analysis is performed for records pertaining to the response of a 20-story steel frame benchmark building excited by one of the four accelerograms scaled by appropriate factors to simulate undamaged and severely damaged conditions for the structure. It is shown that the derived joint time–frequency representations of the response time histories capture quite effectively the influence of non-linearity on the variation of the effective natural frequencies of a structural system during the evolution of a seismic event; in this context, tracing the mean instantaneous frequency of records of critical structural responses is adopted. The study suggests, overall, that the aforementioned techniques are quite viable tools for detecting and monitoring damage to constructed facilities exposed to seismic excitations

Chirplet approximation of band-limited, real signals made easy

In this paper we present algorithms for approximating real band-limited signals by multiple Gaussian Chirps. These algorithms do not rely on matching pursuit ideas. They are hierarchial and, at each stage, the number of terms in a given approximation depends only on the number of positive-valued maxima and negative-valued minima of a signed amplitude function characterizing part of the signal. Like the algorithms used in \cite{gre2} and unlike previous methods, our chirplet approximations require neither a complete dictionary of chirps nor complicated multi-dimensional searches to obtain suitable choices of chirp parameters

evolutionary frequency response function of linear systems subjected to earthquake accelerograms using the adaptive chirplet decomposition

Abstract In seismic engineering, in order to reproduce the typical characteristics of real earthquakes ground-motion time history, several approaches has been proposed in literature. In this study the adaptive chirplet signal decomposition is adopted to analyze recorded accelerograms in order of defining appropriately evolutionary power spectra [1]. The present study focuses on a method to evaluate in closed-form the evolutionary frequency response function, that is required to evaluate the statistics of the response of linear structural systems [2], once the adaptive chirplet signal decomposition is adopted

Guided-wave signal processing using chirplet matching pursuits and mode correlation for structural health monitoring

Signal processing algorithms for guided wave pulse echo-based structural health monitoring (SHM) must be capable of isolating individual reflections from defects in the structure, if any, which could be overlapping and multimodal. In addition, they should be able to estimate the time–frequency centers, the modes and individual energies of the reflections, which would be used to locate and characterize defects. Finally, they should be computationally efficient and amenable to automated processing. This work addresses these issues with a new algorithm employing chirplet matching pursuits followed by a mode correlation check for single point sensors. Its theoretical advantages over conventional time–frequency representations for SHM are elaborated. Results from numerical simulations and experiments in isotropic plate structures are presented, which show the capability of the proposed algorithm. Finally, the issue of in-plane triangulation is discussed and experimental work done to explore this issue is presented.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/58147/2/sms7_2_014.pd

Best network chirplet-chain: Near-optimal coherent detection of unmodeled gravitation wave chirps with a network of detectors

The searches of impulsive gravitational waves (GW) in the data of the ground-based interferometers focus essentially on two types of waveforms: short unmodeled bursts and chirps from inspiralling compact binaries. There is room for other types of searches based on different models. Our objective is to fill this gap. More specifically, we are interested in GW chirps with an arbitrary phase/frequency vs. time evolution. These unmodeled GW chirps may be considered as the generic signature of orbiting/spinning sources. We expect quasi-periodic nature of the waveform to be preserved independent of the physics which governs the source motion. Several methods have been introduced to address the detection of unmodeled chirps using the data of a single detector. Those include the best chirplet chain (BCC) algorithm introduced by the authors. In the next years, several detectors will be in operation. The joint coherent analysis of GW by multiple detectors can improve the sight horizon, the estimation of the source location and the wave polarization angles. Here, we extend the BCC search to the multiple detector case. The method amounts to searching for salient paths in the combined time-frequency representation of two synthetic streams. The latter are time-series which combine the data from each detector linearly in such a way that all the GW signatures received are added constructively. We give a proof of principle for the full sky blind search in a simplified situation which shows that the joint estimation of the source sky location and chirp frequency is possible.Comment: 22 pages, revtex4, 6 figure

Frequency Estimation Using Time-Frequency Based Methods

Any periodic signal can be decomposed into a sum of oscillating functions. Traditionally, cosine and sine segments have been used to represent a single period of the periodic signal (Fourier Series). In more general cases, each of these functions can be represented by a set of spectral parameters such as its amplitude, frequency, phase, and the variability of its instantaneous spectral components. The accuracy of these parameters depends on several processing variables such as resolution, noise level, and bias of the algorithm used. This thesis presents some background of existing frequency estimation techniques and proposes a new technique for estimating the instantaneous frequency of signals using short sinusoid-like basis functions. Furthermore, it also shows that the proposed algorithm can be implemented in a popular embedded DSPmicroprocessor for practical use. This algorithm can also be implemented using more complex features on more resourceful processing processors in order to improve estimation accurac