Super-Resolution in Phase Space

This work considers the problem of super-resolution. The goal is to resolve a Dirac distribution from knowledge of its discrete, low-pass, Fourier measurements. Classically, such problems have been dealt with parameter estimation methods. Recently, it has been shown that convex-optimization based formulations facilitate a continuous time solution to the super-resolution problem. Here we treat super-resolution from low-pass measurements in Phase Space. The Phase Space transformation parametrically generalizes a number of well known unitary mappings such as the Fractional Fourier, Fresnel, Laplace and Fourier transforms. Consequently, our work provides a general super- resolution strategy which is backward compatible with the usual Fourier domain result. We consider low-pass measurements of Dirac distributions in Phase Space and show that the super-resolution problem can be cast as Total Variation minimization. Remarkably, even though are setting is quite general, the bounds on the minimum separation distance of Dirac distributions is comparable to existing methods.Comment: 10 Pages, short paper in part accepted to ICASSP 201

SAR-Based Vibration Estimation Using the Discrete Fractional Fourier Transform

A vibration estimation method for synthetic aperture radar (SAR) is presented based on a novel application of the discrete fractional Fourier transform (DFRFT). Small vibrations of ground targets introduce phase modulation in the SAR returned signals. With standard preprocessing of the returned signals, followed by the application of the DFRFT, the time-varying accelerations, frequencies, and displacements associated with vibrating objects can be extracted by successively estimating the quasi-instantaneous chirp rate in the phase-modulated signal in each subaperture. The performance of the proposed method is investigated quantitatively, and the measurable vibration frequencies and displacements are determined. Simulation results show that the proposed method can successfully estimate a two-component vibration at practical signal-to-noise levels. Two airborne experiments were also conducted using the Lynx SAR system in conjunction with vibrating ground test targets. The experiments demonstrated the correct estimation of a 1-Hz vibration with an amplitude of 1.5 cm and a 5-Hz vibration with an amplitude of 1.5 mm

Iterative Time-Varying Filter Algorithm Based on Discrete Linear Chirp Transform

Denoising of broadband non--stationary signals is a challenging problem in communication systems. In this paper, we introduce a time-varying filter algorithm based on the discrete linear chirp transform (DLCT), which provides local signal decomposition in terms of linear chirps. The method relies on the ability of the DLCT for providing a sparse representation to a wide class of broadband signals. The performance of the proposed algorithm is compared with the discrete fractional Fourier transform (DFrFT) filtering algorithm. Simulation results show that the DLCT algorithm provides better performance than the DFrFT algorithm and consequently achieves high quality filtering.Comment: 6 pages, conference pape

Wavelet entropy of stochastic processes

We compare two different definitions for the wavelet entropy associated to stochastic processes. The first one, the Normalized Total Wavelet Entropy (NTWS) family [Phys. Rev. E 57 (1998) 932; J. Neuroscience Method 105 (2001) 65; Physica A (2005) in press] and a second introduced by Tavares and Lucena [Physica A 357 (2005)~71]. In order to understand their advantages and disadvantages, exact results obtained for fractional Gaussian noise (-1<alpha< 1) and the fractional Brownian motion (1 < alpha < 3) are assessed. We find out that NTWS family performs better as a characterization method for these stochastic processes.Comment: 12 pages, 4 figures, submitted to Physica

Quasi-periodic pulse amplitude modulation in the accreting millisecond pulsar IGR J00291+5934

We introduce a new method for analysing the aperiodic variability of coherent pulsations in accreting millisecond X-ray pulsars. Our method involves applying a complex frequency correction to the time-domain light curve, allowing for the aperiodic modulation of the pulse amplitude to be robustly extracted in the frequency domain. We discuss the statistical properties of the resulting modulation spectrum and show how it can be correlated with the non-pulsed emission to determine if the periodic and aperiodic variability are coupled processes. Using this method, we study the 598.88 Hz coherent pulsations of the accreting millisecond X-ray pulsar IGR J00291+5934 as observed with the Rossi X-ray Timing Explorer and XMM-Newton. We demonstrate that our method easily confirms the known coupling between the pulsations and a strong 8 mHz QPO in XMM-Newton observations. Applying our method to the RXTE observations, we further show, for the first time, that the much weaker 20 mHz QPO and its harmonic are also coupled the pulsations. We discuss the implications of this coupling and indicate how it may be used to extract new information on the underlying accretion process.Comment: 12 pages, 7 figures, 1 table. Accepted for publication in Ap