14 research outputs found

    Spectral correlation density estimation via minimum variance distortion-less response filterbanks

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    Characterization of Information Channels for Asymptotic Mean Stationarity and Stochastic Stability of Non-stationary/Unstable Linear Systems

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    Stabilization of non-stationary linear systems over noisy communication channels is considered. Stochastically stable sources, and unstable but noise-free or bounded-noise systems have been extensively studied in information theory and control theory literature since 1970s, with a renewed interest in the past decade. There have also been studies on non-causal and causal coding of unstable/non-stationary linear Gaussian sources. In this paper, tight necessary and sufficient conditions for stochastic stabilizability of unstable (non-stationary) possibly multi-dimensional linear systems driven by Gaussian noise over discrete channels (possibly with memory and feedback) are presented. Stochastic stability notions include recurrence, asymptotic mean stationarity and sample path ergodicity, and the existence of finite second moments. Our constructive proof uses random-time state-dependent stochastic drift criteria for stabilization of Markov chains. For asymptotic mean stationarity (and thus sample path ergodicity), it is sufficient that the capacity of a channel is (strictly) greater than the sum of the logarithms of the unstable pole magnitudes for memoryless channels and a class of channels with memory. This condition is also necessary under a mild technical condition. Sufficient conditions for the existence of finite average second moments for such systems driven by unbounded noise are provided.Comment: To appear in IEEE Transactions on Information Theor

    Time-frequency representations of generalized almost-cyclostationary signals

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    Nous proposons dans cet article une contribution à la théorie récemment introduite des signaux quasi-cyclostationnaires généralisés. Cette classe de signaux étend la classe des signaux quasi-cyclostationnaires au cas de signaux dont les fréquences cycliques dépendent du temps. Des représentations temps-fréquence de ces signaux sont données en fonction des statistiques cycliques généralisées. Notamment, la distribution de Wigner-Ville et la fonction d'ambiguïté sont examinées en détail. Le problème de l'extraction des caractéristiques des signaux quasi-cyclostationnaires généralisés, basée sur l'estimation d'un seul enregistrement, est également traité

    Non Co-Operative Detection of LPI/LPD Signals Via Cyclic Spectral Analysis

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    This research proposes and evaluates a novel technique for detecting LPI/LPD communication signals using a digital receiver primarily designed to detect radar signals, such as a Radar Warning Receiver (RWR) or an Electronic Support Measures (ESM) receiver. The proposed Cyclic Spectrum Analysis (CSA) receiver is a robust detector that takes advantage of the spectral correlation properties of second-order cyclostationary signals. A computationally efficient algorithm is used to estimate the Spectral Correlation Function (SCF). Using state-of-the-art FFT processing, it is expected that the proposed CSA receiver architecture could estimate the entire cyclic spectrum m approximately 0.6 ms. The estimate is then reduced to an energy related test statistic that is valid for all cycle frequencies within the receiver bandwidth. By producing an estimate of the cyclic spectrum, the CSA receiver also benefits post-detection tasks such as signal classification and exploitation. As modeled, the ideal CSA receiver detection performance is within 1.0 dB of the radiometer in benign signal environments and consistently outperforms the radiometer in adverse signal environments. The effect on detection performance when the CSA receiver is implemented with channelized and quadrature digital receiver architectures is also examined

    The Wold isomorphism for cyclostationary sequences

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    In 1948 H.Wold introduced an isometric isomorphism between a Hilbert (linear) space formed from the weighted shifts of a numerical sequence and a suitable Hilbert space of values of a second order stochastic sequence. Motivated by a recent resurrection of the idea in the context of cyclostationary sequences and processes, we present the details of the Wold isomorphism between cyclostationary stochastic sequences and cyclostationary numerical sequences. We show how Hilbert-space representations of cyclostationary sequences are interpreted in the case of numerical CS sequences

    Statistical signal processing of nonstationary tensor-valued data

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    Real-world signals, such as the evolution of three-dimensional vector fields over time, can exhibit highly structured probabilistic interactions across their multiple constitutive dimensions. This calls for analysis tools capable of directly capturing the inherent multi-way couplings present in such data. Yet, current analyses typically employ multivariate matrix models and their associated linear algebras which are agnostic to the global data structure and can only describe local linear pairwise relationships between data entries. To address this issue, this thesis uses the property of linear separability -- a notion intrinsic to multi-dimensional data structures called tensors -- as a linchpin to consider the probabilistic, statistical and spectral separability under one umbrella. This helps to both enhance physical meaning in the analysis and reduce the dimensionality of tensor-valued problems. We first introduce a new identifiable probability distribution which appropriately models the interactions between random tensors, whereby linear relationships are considered between tensor fibres as opposed to between individual entries as in standard matrix analysis. Unlike existing models, the proposed tensor probability distribution formulation is shown to yield a unique maximum likelihood estimator which is demonstrated to be statistically efficient. Both matrices and vectors are lower-order tensors, and this gives us a unique opportunity to consider some matrix signal processing models under the more powerful framework of multilinear tensor algebra. By introducing a model for the joint distribution of multiple random tensors, it is also possible to treat random tensor regression analyses and subspace methods within a unified separability framework. Practical utility of the proposed analysis is demonstrated through case studies over synthetic and real-world tensor-valued data, including the evolution over time of global atmospheric temperatures and international interest rates. Another overarching theme in this thesis is the nonstationarity inherent to real-world signals, which typically consist of both deterministic and stochastic components. This thesis aims to help bridge the gap between formal probabilistic theory of stochastic processes and empirical signal processing methods for deterministic signals by providing a spectral model for a class of nonstationary signals, whereby the deterministic and stochastic time-domain signal properties are designated respectively by the first- and second-order moments of the signal in the frequency domain. By virtue of the assumed probabilistic model, novel tests for nonstationarity detection are devised and demonstrated to be effective in low-SNR environments. The proposed spectral analysis framework, which is intrinsically complex-valued, is facilitated by augmented complex algebra in order to fully capture the joint distribution of the real and imaginary parts of complex random variables, using a compact formulation. Finally, motivated by the need for signal processing algorithms which naturally cater for the nonstationarity inherent to real-world tensors, the above contributions are employed simultaneously to derive a general statistical signal processing framework for nonstationary tensors. This is achieved by introducing a new augmented complex multilinear algebra which allows for a concise description of the multilinear interactions between the real and imaginary parts of complex tensors. These contributions are further supported by new physically meaningful empirical results on the statistical analysis of nonstationary global atmospheric temperatures.Open Acces
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