Regularized sampling of multiband signals

This paper presents a regularized sampling method for multiband signals, that makes it possible to approach the Landau limit, while keeping the sensitivity to noise at a low level. The method is based on band-limited windowing, followed by trigonometric approximation in consecutive time intervals. The key point is that the trigonometric approximation "inherits" the multiband property, that is, its coefficients are formed by bursts of non-zero elements corresponding to the multiband components. It is shown that this method can be well combined with the recently proposed synchronous multi-rate sampling (SMRS) scheme, given that the resulting linear system is sparse and formed by ones and zeroes. The proposed method allows one to trade sampling efficiency for noise sensitivity, and is specially well suited for bounded signals with unbounded energy like those in communications, navigation, audio systems, etc. Besides, it is also applicable to finite energy signals and periodic band-limited signals (trigonometric polynomials). The paper includes a subspace method for blindly estimating the support of the multiband signal as well as its components, and the results are validated through several numerical examples.Comment: The title and introduction have changed. Submitted to the IEEE Transactions on Signal Processin

Efficient Sampling of Band-limited Signals from Sine Wave Crossings

This correspondence presents an efficient method for reconstructing a band-limited signal in the discrete domain from its crossings with a sine wave. The method makes it possible to design A/D converters that only deliver the crossing timings, which are then used to interpolate the input signal at arbitrary instants. Potentially, it may allow for reductions in power consumption and complexity in these converters. The reconstruction in the discrete domain is based on a recently-proposed modification of the Lagrange interpolator, which is readily implementable with linear complexity and efficiently, given that it re-uses known schemes for variable fractional-delay (VFD) filters. As a spin-off, the method allows one to perform spectral analysis from sine wave crossings with the complexity of the FFT. Finally, the results in the correspondence are validated in several numerical examples.Comment: To appear in the IEEE Transactions on Signal Processin

FFT Interpolation from Nonuniform Samples Lying in a Regular Grid

This paper presents a method to interpolate a periodic band-limited signal from its samples lying at nonuniform positions in a regular grid, which is based on the FFT and has the same complexity order as this last algorithm. This kind of interpolation is usually termed "the missing samples problem" in the literature, and there exists a wide variety of iterative and direct methods for its solution. The one presented in this paper is a direct method that exploits the properties of the so-called erasure polynomial, and it provides a significant improvement on the most efficient method in the literature, which seems to be the burst error recovery (BER) technique of Marvasti's et al. The numerical stability and complexity of the method are evaluated numerically and compared with the pseudo-inverse and BER solutions.Comment: Submitted to the IEEE Transactions on Signal Processin

Dialogue \u27On The Ground\u27: The Complicated Identities and the Complex Negotiations of Catholics and Hindus in South India

Interreligious dialogue is a vital theological concern for the Catholic Church in India. Over the past three decades, church leaders, progressive theologians, and maverick monastics have experimented with various models and forms of interreligious dialogue. Quite distinct from these contrived institutional initiatives is the dynamic of intimate, subtle, and spontaneous ritual exchange and dialogue between ordinary Hindus and Catholics occurring in the arena of popular piety and rituals at the grassroots level - often in opposition to institutional norms and directives - that may be described as dialogue on the ground. In light of ethnographic research at the shrine of St. Anthony at Uvari in Tamil Nadu - that serves as a representative sample of regional shrines in rural south India - this essay focuses on the logic and grammar of a specific public ritual locally known as asanam as an illustrative case-study of the \u27dialogue on the ground,\u27 delineates the social and religious themes embedded in this ritual, and reflects on its implications for interreligious dialogue

Long-term multi-risk assessment: statistical treatment of interaction among risks

Multi-risk approaches have been recently proposed to assess and compare different risks in the same target area. The key points of multi-risk assessment are the development of homogeneous risk definitions and the treatment of risk interaction. The lack of treatment of interaction may lead to significant biases and thus to erroneous risk hierarchization, which is one of primary output of risk assessments for decision makers. In this paper, a formal statistical model is developed to treat interaction between two different hazardous phenomena in long-term multi-risk assessments, accounting for possible effects of interaction at hazard, vulnerability and exposure levels. The applicability of the methodology is demonstrated through two illustrative examples, dealing with the influence of (1) volcanic ash in seismic risk and (2) local earthquakes in tsunami risk. In these applications, the bias in single-risk estimation induced by the assumption of independence among risks is explicitly assessed. An extensive application of this methodology at regional and sub-regional scale would allow to identify when and where a given interaction has significant effects in long-term risk assessments, and thus, it should be considered in multi-risk analyses and risks hierarchization