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Register a new userA Class of Doubly Stochastic Shift Operators for Random Graph Signals and their Boundedness
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A class of doubly stochastic graph shift operators (GSO) is proposed, which is shown to exhibit: (i) lower and upper $L_{2}$-boundedness for locally stationary random graph signals; (ii) $L_{2}$-isometry for textit{i.i.d.} random graph signals with the asymptotic increase in the incoming neighbourhood size of vertices; and (iii) preservation of the mean of any graph signal. These properties are obtained through a statistical consistency analysis of the graph shift, and by exploiting the dual role of the doubly stochastic GSO as a Markov (diffusion) matrix and as an unbiased expectation operator. Practical utility of the class of doubly stochastic GSOs is demonstrated in a real-world multi-sensor signal filtering setting.
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A unitary shift operator (GSO) for signals on a graph is introduced, which exhibits the desired property of energy preservation over both backward and forward graph shifts. For rigour, the graph differential operator is also derived in an analytical form. The commutativity relation of the shift operator with the Fourier transform is next explored in conjunction with the proposed GSO to introduce a graph discrete Fourier transform (GDFT) which, unlike existing approaches, ensures the orthogonality of GDFT bases and admits a natural frequency-domain interpretation. The proposed GDFT is shown to allow for a coherent definition of the graph discrete Hilbert transform (GDHT) and the graph analytic signal. The advantages of the proposed GSO are demonstrated through illustrative examples.
In this study, we propose an approach to constructing on-off keying (OOK) symbols for wake-up radios (WURs) by using sequences in the frequency domain. The proposed method enables orthogonal multiplexing of wake-up signals (WUSs) and orthogonal frequency division multiplexing (OFDM) waveforms. We optimize the sequences with a tractable algorithm by considering the reliability of WUSs in fading channels. The proposed algorithm relies on an alternating minimization technique, i.e. cyclic algorithm-new (CAN), which was originally proposed for obtaining a unimodular sequence with good aperiodic correlation properties. In this study, we extend CAN to generate OOK waveforms with Manchester coding. We demonstrate the performance of four optimized sequences and compare with state-of-the-art approaches. We show that the proposed scheme improves the wake-up radio receiver (WURx) performance by controlling the energy distribution in frequency domain while removing the interference-floor at the OFDM receiver.
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.
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.
In this article we demonstrate how graph theory can be used to identify those stations in the London underground network which have the greatest influence on the functionality of the traffic, and proceed, in an innovative way, to assess the impact of a station closure on service levels across the city. Such underground network vulnerability analysis offers the opportunity to analyse, optimize and enhance the connectivity of the London underground network in a mathematically tractable and physically meaningful manner.
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