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Register a new userExponential Approximation of Band-limited Signals from Nonuniform Sampling
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Reconstructing a band-limited function from its finite sample data is a fundamental task in signal analysis. A simple Gaussian or hyper-Gaussian regularized Shannon sampling series has been proved to be able to achieve exponential convergence for uniform sampling. In this paper, we prove that exponential approximation can also be attained for general nonuniform sampling. The analysis is based on the the residue theorem to represent the truncated error by a contour integral. Several concrete examples of nonuniform sampling with exponential convergence will be presented.
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Correlation coefficient is usually used to measure the correlation degree between two time signals. However, its performance will drop or even fail if the signals are noised. Based on the time-frequency phase spectrum (TFPS) provided by normal time-frequency transform (NTFT), similarity coefficient is proposed to measure the similarity between two non-narrow-band time signals, even if the signals are noised. The basic idea of the similarity coefficient is to translate the interest part of signal f1(t)s TFPS along the time axis to couple with signal f2(t)s TFPS. Such coupling would generate a maximum if f1(t)and f2(t) are really similar to each other in time-frequency structure. The maximum, if normalized, is called similarity coefficient. The location of the maximum indicates the time delay between f1(t) and f2(t). Numerical results show that the similarity coefficient is better than the correlation coefficient in measuring the correlation degree between two noised signals. Precision and accuracy of the time delay estimation (TDE) based on the similarity analysis are much better than those based on cross-correlation (CC) method and generalized CC (GCC) method under low SNR.
The multipath radio channel is considered to have a non-bandlimited channel impulse response. Therefore, it is challenging to achieve high resolution time-delay (TD) estimation of multipath components (MPCs) from bandlimited observations of communication signals. It this paper, we consider the problem of multiband channel sampling and TD estimation of MPCs. We assume that the nonideal multibranch receiver is used for multiband sampling, where the noise is nonuniform across the receiver branches. The resulting data model of Hankel matrices formed from acquired samples has multiple shift-invariance structures, and we propose an algorithm for TD estimation using weighted subspace fitting. The subspace fitting is formulated as a separable nonlinear least squares (NLS) problem, and it is solved using a variable projection method. The proposed algorithm supports high resolution TD estimation from an arbitrary number of bands, and it allows for nonuniform noise across the bands. Numerical simulations show that the algorithm almost attains the Cramer Rao Lower Bound, and it outperforms previously proposed methods such as multiresolution TOA, MI-MUSIC, and ESPRIT.
A notion of band limited functions is considered in the case of the hyperbolic plane in its Poincare upper half-plane $mathbb{H}$ realization. The concept of band-limitedness is based on the existence of the Helgason-Fourier transform on $mathbb{H}$. An iterative algorithm is presented, which allows to reconstruct band-limited functions from some countable sets of their values. It is shown that for sufficiently dense metric lattices a geometric rate of convergence can be guaranteed as long as the sampling density is high enough compared to the band-width of the sampled function.
In this paper, we reconsider the problem of detecting a matrix-valued rank-one signal in unknown Gaussian noise, which was previously addressed for the case of sufficient training data. We relax the above assumption to the case of limited training data. We re-derive the corresponding generalized likelihood ratio test (GLRT) and two-step GLRT (2S--GLRT) based on certain unitary transformation on the test data. It is shown that the re-derived detectors can work with low sample support. Moreover, in sample-abundant environments the re-derived GLRT is the same as the previously proposed GLRT and the re-derived 2S--GLRT has better detection performance than the previously proposed 2S--GLRT. Numerical examples are provided to demonstrate the effectiveness of the re-derived detectors.
We present a joint SO(3)-spectral domain filtering framework using directional spatially localized spherical harmonic transform (DSLSHT), for the estimation and enhancement of random anisotropic signals on the sphere contaminated by random anisotropic noise. We design an optimal filter for filtering the DSLSHT representation of the noise-contaminated signal in the joint SO(3)-spectral domain. The filter is optimal in the sense that the filtered representation in the joint domain is the minimum mean square error estimate of the DSLSHT representation of the underlying (noise-free) source signal. We also derive a least-square solution for the estimate of the source signal from the filtered representation in the joint domain. We demonstrate the capability of the proposed filtering framework using the Earth topography map in the presence of anisotropic, zero-mean, uncorrelated Gaussian noise, and compare its performance with the joint spatial-spectral domain filtering framework.
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