Compressive Sensing of Analog Signals Using Discrete Prolate Spheroidal Sequences

Compressive sensing (CS) has recently emerged as a framework for efficiently capturing signals that are sparse or compressible in an appropriate basis. While often motivated as an alternative to Nyquist-rate sampling, there remains a gap between the discrete, finite-dimensional CS framework and the problem of acquiring a continuous-time signal. In this paper, we attempt to bridge this gap by exploiting the Discrete Prolate Spheroidal Sequences (DPSS's), a collection of functions that trace back to the seminal work by Slepian, Landau, and Pollack on the effects of time-limiting and bandlimiting operations. DPSS's form a highly efficient basis for sampled bandlimited functions; by modulating and merging DPSS bases, we obtain a dictionary that offers high-quality sparse approximations for most sampled multiband signals. This multiband modulated DPSS dictionary can be readily incorporated into the CS framework. We provide theoretical guarantees and practical insight into the use of this dictionary for recovery of sampled multiband signals from compressive measurements

Efficient time-domain modeling and simulation of passive bandpass systems

In communication systems, the signals of interest are often amplitude and/or phase modulated ones. In this framework, the baseband equivalent signals and systems representation is usually adopted to simulate the digital parts of communication systems in an efficient manner. This contribution extends the applicability of such representation to RF/analog devices, leading to a common and efficient modeling and simulation framework. In particular, the proposed method can build half-size models compared to existing approaches, and allows one to choose the simulation time step according to the bandwidth of the modulating signals rather than the carrier frequency, thereby significantly speeding up the simulation procedure. The novel proposed method is validated via a suitable application example

The Robustness of Least-Squares Frequency Switching (LSFS)

Least-squares frequency switching (LSFS) is a new method to reconstruct signal and gain function (known as bandpass or baseline) from spectral line observations using the frequency switching method. LSFS utilizes not only two but a set of three or more local oscillator (LO) frequencies. The reconstruction is based on a least squares fitting scheme. Here we present a detailed investigation on the stability of the LSFS method in a statistical sense and test the robustness against radio frequency interference (RFI), receiver gain instabilities and continuum sources. It turns out, that the LSFS method is indeed a very powerful method and is robust against most of these problems. Nevertheless, LSFS fails in presence of RFI signals or strong line emission. We present solutions to overcome these limitations using a flagging mechanism or remapping of measured signals, respectively.Comment: 17 pages, 21 figures, 1 table, accepted for publication in ApJS (November 2007, v173n1

A new family of high-resolution multivariate spectral estimators

In this paper, we extend the Beta divergence family to multivariate power spectral densities. Similarly to the scalar case, we show that it smoothly connects the multivariate Kullback-Leibler divergence with the multivariate Itakura-Saito distance. We successively study a spectrum approximation problem, based on the Beta divergence family, which is related to a multivariate extension of the THREE spectral estimation technique. It is then possible to characterize a family of solutions to the problem. An upper bound on the complexity of these solutions will also be provided. Simulations suggest that the most suitable solution of this family depends on the specific features required from the estimation problem

A nonlinear detection algorithm for periodic signals in gravitational wave detectors

We present an algorithm for the detection of periodic sources of gravitational waves with interferometric detectors that is based on a special symmetry of the problem: the contributions to the phase modulation of the signal from the earth rotation are exactly equal and opposite at any two instants of time separated by half a sidereal day; the corresponding is true for the contributions from the earth orbital motion for half a sidereal year, assuming a circular orbit. The addition of phases through multiplications of the shifted time series gives a demodulated signal; specific attention is given to the reduction of noise mixing resulting from these multiplications. We discuss the statistics of this algorithm for all-sky searches (which include a parameterization of the source spin-down), in particular its optimal sensitivity as a function of required computational power. Two specific examples of all-sky searches (broad-band and narrow-band) are explored numerically, and their performances are compared with the stack-slide technique (P. R. Brady, T. Creighton, Phys. Rev. D, 61, 082001).Comment: 9 pages, 3 figures, to appear in Phys. Rev.

Circular polarization measurement in millimeter-wavelength spectral-line VLBI observations

This paper considers the problem of accurate measurement of circular polarization in imaging spectral-line VLBI observations in the lambda=7 mm and lambda=3 mm wavelength bands. This capability is especially valuable for the full observational study of compact, polarized SiO maser components in the near-circumstellar environment of late-type, evolved stars. Circular VLBI polarimetry provides important constraints on SiO maser astrophysics, including the theory of polarized maser emission transport, and on the strength and distribution of the stellar magnetic field and its dynamical role in this critical circumstellar region. We perform an analysis here of the data model containing the instrumental factors that limit the accuracy of circular polarization measurements in such observations, and present a corresponding data reduction algorithm for their correction. The algorithm is an enhancement of existing spectral line VLBI polarimetry methods using autocorrelation data for calibration, but with innovations in bandpass determination, autocorrelation polarization self-calibration, and general optimizations for the case of low SNR, as applicable at these wavelengths. We present an example data reduction at $\lambda=7$ mm and derive an estimate of the predicted accuracy of the method of m_c < 0.5% or better at lambda=7 mm and m_c < 0.5-1% or better at lambda=3 mm. Both the strengths and weaknesses of the proposed algorithm are discussed, along with suggestions for future work.Comment: 23 pages, 13 figure