Average sampling of band-limited stochastic processes

We consider the problem of reconstructing a wide sense stationary band-limited process from its local averages taken either at the Nyquist rate or above. As a result, we obtain a sufficient condition under which average sampling expansions hold in mean square and for almost all sample functions. Truncation and aliasing errors of the expansion are also discussed

Evaluation of several reconstruction methods of bandlimited signals

In this paper we evaluate several methods of reconstructing signals from finite sets of their samples. A class of band-limited signals is considered. Both, noise-free and noisy cases are studied. The evaluation is performed by extensive simulations where different shapes and bandwidths of the reconstructing filters are examined. We demonstrate that if a fixed number of signal samples are used in the reconstruction, then the signal to noise ratio becomes the main factor limiting the quality of the reconstruction

Choice of Sampling Interval and Extent for Finite-Energy Fields

We focus on the problem of representing a nonstationary finite-energy random field, with finitely many samples. We do not require the field to be of finite extent or to be bandlimited. We propose an optimizable procedure for obtaining a finite-sample representation of the given field. We estimate the reconstruction error of the procedure, showing that it is the sum of the truncation errors in the space and frequency domains. We also optimize the truncation parameters analytically and present the resultant Pareto-optimal tradeoff curves involving the error in reconstruction and the sample count, for several examples. These tradeoff curves can be used to determine the optimal sampling strategy in a practical situation based on the relative importance of error and sample count for that application. © 2016 IEEE

Applications of nonuniform sampling in wideband multichannel communication systems

This research is an investigation into utilising randomised sampling in communication systems to ease the sampling rate requirements of digitally processing narrowband signals residing within a wide range of overseen frequencies. By harnessing the aliasing suppression capabilities of such sampling schemes, it is shown that certain processing tasks, namely spectrum sensing, can be performed at significantly low sampling rates compared to those demanded by uniform-sampling-based digital signal processing. The latter imposes sampling frequencies of at least twice the monitored bandwidth regardless of the spectral activity within. Aliasing can otherwise result in irresolvable processing problems, as the spectral support of the present signal is a priori unknown. Lower sampling rates exploit the processing module(s) resources (such as power) more efficiently and avoid the possible need for premium specialised high-cost DSP, especially if the handled bandwidth is considerably wide. A number of randomised sampling schemes are examined and appropriate spectral analysis tools are used to furnish their salient features. The adopted periodogram-type estimators are tailored to each of the schemes and their statistical characteristics are assessed for stationary, and cyclostationary signals. Their ability to alleviate the bandwidth limitation of uniform sampling is demonstrated and the smeared-aliasing defect that accompanies randomised sampling is also quantified. In employing the aforementioned analysis tools a novel wideband spectrum sensing approach is introduced. It permits the simultaneous sensing of a number of nonoverlapping spectral subbands constituting a wide range of monitored frequencies. The operational sampling rates of the sensing procedure are not limited or dictated by the overseen bandwidth antithetical to uniform-sampling-based techniques. Prescriptive guidelines are developed to ensure that the proposed technique satisfies certain detection probabilities predefined by the user. These recommendations address the trade-off between the required sampling rate and the length of the signal observation window (sensing time) in a given scenario. Various aspects of the introduced multiband spectrum sensing approach are investigated and its applicability highlighted