On the Analytic Wavelet Transform

An exact and general expression for the analytic wavelet transform of a real-valued signal is constructed, resolving the time-dependent effects of non-negligible amplitude and frequency modulation. The analytic signal is first locally represented as a modulated oscillation, demodulated by its own instantaneous frequency, and then Taylor-expanded at each point in time. The terms in this expansion, called the instantaneous modulation functions, are time-varying functions which quantify, at increasingly higher orders, the local departures of the signal from a uniform sinusoidal oscillation. Closed-form expressions for these functions are found in terms of Bell polynomials and derivatives of the signal's instantaneous frequency and bandwidth. The analytic wavelet transform is shown to depend upon the interaction between the signal's instantaneous modulation functions and frequency-domain derivatives of the wavelet, inducing a hierarchy of departures of the transform away from a perfect representation of the signal. The form of these deviation terms suggests a set of conditions for matching the wavelet properties to suit the variability of the signal, in which case our expressions simplify considerably. One may then quantify the time-varying bias associated with signal estimation via wavelet ridge analysis, and choose wavelets to minimize this bias

Analysis of Modulated Multivariate Oscillations

The concept of a common modulated oscillation spanning multiple time series is formalized, a method for the recovery of such a signal from potentially noisy observations is proposed, and the time-varying bias properties of the recovery method are derived. The method, an extension of wavelet ridge analysis to the multivariate case, identifies the common oscillation by seeking, at each point in time, a frequency for which a bandpassed version of the signal obtains a local maximum in power. The lowest-order bias is shown to involve a quantity, termed the instantaneous curvature, which measures the strength of local quadratic modulation of the signal after demodulation by the common oscillation frequency. The bias can be made to be small if the analysis filter, or wavelet, can be chosen such that the signal's instantaneous curvature changes little over the filter time scale. An application is presented to the detection of vortex motions in a set of freely-drifting oceanographic instruments tracking the ocean currents

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

Frequency-domain P-approximant filters for time-truncated inspiral gravitational wave signals from compact binaries

Frequency-domain filters for time-windowed gravitational waves from inspiralling compact binaries are constructed which combine the excellent performance of our previously developed time-domain P-approximants with the analytic convenience of the stationary phase approximation without a serious loss in event rate. These Fourier-domain representations incorporate the ``edge oscillations'' due to the (assumed) abrupt shut-off of the time-domain signal caused by the relativistic plunge at the last stable orbit. These new analytic approximations, the SPP-approximants, are not only `effectual' for detection and `faithful' for parameter estimation, but are also computationally inexpensive to generate (and are `faster' by factors up to 10, as compared to the corresponding time-domain templates). The SPP approximants should provide data analysts the Fourier-domain templates for massive black hole binaries of total mass m less than about 40 solar mases, the most likely sources for LIGO and VIRGO.Comment: 50 Pages, 10 Postscript figures, 7 Tables, Revtex, Typos corrected, References updated, Additions on pages 25, 26 and 3

The Expanded Very Large Array

In almost 30 years of operation, the Very Large Array (VLA) has proved to be a remarkably flexible and productive radio telescope. However, the basic capabilities of the VLA have changed little since it was designed. A major expansion utilizing modern technology is currently underway to improve the capabilities of the VLA by at least an order of magnitude in both sensitivity and in frequency coverage. The primary elements of the Expanded Very Large Array (EVLA) project include new or upgraded receivers for continuous frequency coverage from 1 to 50 GHz, new local oscillator, intermediate frequency, and wide bandwidth data transmission systems to carry signals with 16 GHz total bandwidth from each antenna, and a new digital correlator with the capability to process this bandwidth with an unprecedented number of frequency channels for an imaging array. Also included are a new monitor and control system and new software that will provide telescope ease of use. Scheduled for completion in 2012, the EVLA will provide the world research community with a flexible, powerful, general-purpose telescope to address current and future astronomical issues.Comment: Added journal reference: published in Proceedings of the IEEE, Special Issue on Advances in Radio Astronomy, August 2009, vol. 97, No. 8, 1448-1462 Six figures, one tabl

IIR Adaptive Filters for Detection of Gravitational Waves from Coalescing Binaries

In this paper we propose a new strategy for gravitational waves detection from coalescing binaries, using IIR Adaptive Line Enhancer (ALE) filters. This strategy is a classical hierarchical strategy in which the ALE filters have the role of triggers, used to select data chunks which may contain gravitational events, to be further analyzed with more refined optimal techniques, like the the classical Matched Filter Technique. After a direct comparison of the performances of ALE filters with the Wiener-Komolgoroff optimum filters (matched filters), necessary to discuss their performance and to evaluate the statistical limitation in their use as triggers, we performed a series of tests, demonstrating that these filters are quite promising both for the relatively small computational power needed and for the robustness of the algorithms used. The performed tests have shown a weak point of ALE filters, that we fixed by introducing a further strategy, based on a dynamic bank of ALE filters, running simultaneously, but started after fixed delay times. The results of this global trigger strategy seems to be very promising, and can be already used in the present interferometers, since it has the great advantage of requiring a quite small computational power and can easily run in real-time, in parallel with other data analysis algorithms.Comment: Accepted at SPIE: "Astronomical Telescopes and Instrumentation". 9 pages, 3 figure

Retrieval of phase relation and emission profile of quantum cascade laser frequency combs

The major development recently undergone by quantum cascade lasers has effectively extended frequency comb emission to longer-wavelength spectral regions, i.e. the mid and far infrared. Unlike classical pulsed frequency combs, their mode-locking mechanism relies on four-wave mixing nonlinear processes, with a temporal intensity profile different from conventional short-pulses trains. Measuring the absolute phase pattern of the modes in these combs enables a thorough characterization of the onset of mode-locking in absence of short-pulses emission, as well as of the coherence properties. Here, by combining dual-comb multi-heterodyne detection with Fourier-transform analysis, we show how to simultaneously acquire and monitor over a wide range of timescales the phase pattern of a generic frequency comb. The technique is applied to characterize a mid-infrared and a terahertz quantum cascade laser frequency comb, conclusively proving the high degree of coherence and the remarkable long-term stability of these sources. Moreover, the technique allows also the reconstruction of electric field, intensity profile and instantaneous frequency of the emission.Comment: 20 pages. Submitted to Nature Photonic

Space-based Aperture Array For Ultra-Long Wavelength Radio Astronomy

The past decade has seen the rise of various radio astronomy arrays, particularly for low-frequency observations below 100MHz. These developments have been primarily driven by interesting and fundamental scientific questions, such as studying the dark ages and epoch of re-ionization, by detecting the highly red-shifted 21cm line emission. However, Earth-based radio astronomy below frequencies of 30MHz is severely restricted due to man-made interference, ionospheric distortion and almost complete non-transparency of the ionosphere below 10MHz. Therefore, this narrow spectral band remains possibly the last unexplored frequency range in radio astronomy. A straightforward solution to study the universe at these frequencies is to deploy a space-based antenna array far away from Earths' ionosphere. Various studies in the past were principally limited by technology and computing resources, however current processing and communication trends indicate otherwise. We briefly present the achievable science cases, and discuss the system design for selected scenarios, such as extra-galactic surveys. An extensive discussion is presented on various sub-systems of the potential satellite array, such as radio astronomical antenna design, the on-board signal processing, communication architectures and joint space-time estimation of the satellite network. In light of a scalable array and to avert single point of failure, we propose both centralized and distributed solutions for the ULW space-based array. We highlight the benefits of various deployment locations and summarize the technological challenges for future space-based radio arrays.Comment: Submitte