Electrical - Electronic Engineering / Elektrik - Elektronik Mühendisliği

Permanent URI for this collectionhttps://hdl.handle.net/11147/11

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End date: 2009Publisher: search.filters.publisher.Elsevier Ltd.

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  • Article
    Citation - WoS: 4
    Citation - Scopus: 4
    Phase Dependence Mitigation for Autocorrelation-Based Frequency Estimation
    (Elsevier Ltd., 2008) Altınkaya, Mustafa Aziz; Anarım, Emin; Sankur, Bülent
    The sinusoidal frequency estimation from short data records based on Toeplitz autocorrelation (AC) matrix estimates suffer from the dependence on the initial phases of the sinusoid(s). This effect becomes prominent when the impact of additive noise vanishes, that is at high signal-to-noise ratios (SNR). Based on both analytic derivation of the AC lag terms and simulation experiments we show that data windowing can mitigate the limitations caused by the phase dependence. Thus with proper windowing, the variance of the frequency estimate is no more eclipsed by phase dependence, but it continues to decrease linearly with increasing SNR. The study covers both the cases of a single sinusoid and two sinusoids closely spaced in the frequency with the Pisarenko frequency estimator, MUSIC and principal component autoregressive frequency estimators. The trade-offs between the spectral broadening and the achieved minimum variance level due to the data window are analyzed in detail.
  • Article
    Citation - WoS: 2
    Citation - Scopus: 2
    Determination of the Stationary State Densities of the Stochastic Nonlinear Dynamical Systems
    (Elsevier Ltd., 2006) Günel, Serkan; Savacı, Ferit Acar
    The stationary state probability densities appear not only in the study of dynamical systems with random vector fields, but also in the deterministic dynamical systems exhibiting chaotic behavior when the uncertainties in the initial conditions are represented with the probability densities. But since it is very hard problem to determine these densities, in this paper the new efficient method to obtain an approximate solution of Fokker-Planck-Kolmogorov equation which arises in the determination of the stationary state probability densities has been given by representing the densities with compactly supported functions. With specific choice of the compactly supported functions as piecewise multivariable polynomials which are supported on the ellipsoidal regions, the parameters to be calculated for determining the densities can be considerably decreased compared to Multi-Gaussian Closure scheme, in which the stationary densities are assumed to be the weighted average of the Gaussian densities. The main motivation to choose the compactly supported functions is that, in the chaotic dynamics the states are trapped in a specific compact subspace of the state space. The stationary state densities of two basic examples commonly considered in the literature have been estimated using the Parzen's estimator, and the densities obtained using the newly proposed method have been compared with these estimated densities and the densities obtained with the Multi-Gaussian Closure scheme. The results indicate that the presented compactly supported piecewise polynomial scheme can be successful compared to Multi-Gaussian scheme, when the system is highly nonlinear.
  • Article
    Citation - WoS: 9
    Citation - Scopus: 15
    Subspace-Based Frequency Estimation of Sinusoidal Signals in Alpha-Stable Noise
    (Elsevier Ltd., 2002) Altınkaya, Mustafa Aziz; Deliç, Hakan; Sankur, Bülent; Anarım, Emin
    In the frequency estimation of sinusoidal signals observed in impulsive noise environments, techniques based on Gaussian noise assumption are unsuccessful. One possible way to find better estimates is to model the noise as an alpha-stable process and to use the fractional lower order statistics (FLOS) of the data to estimate the signal parameters. In this work, we propose a FLOS-based statistical average, the generalized covariation coefficient (GCC). The GCCs of multiple sinusoids for unity moment order in SαS noise attain the same form as the covariance expressions of multiple sinusoids in white Gaussian noise. The subspace-based frequency estimators FLOS-multiple signal classification (MUSIC) and FLOS-Bartlett are applied to the GCC matrix of the data. On the other hand, we show that the multiple sinusoids in SαS noise can also be modeled as a stable autoregressive moving average process approximated by a higher order stable autoregressive (AR) process. Using the GCCs of the data, we obtain FLOS versions of Tufts-Kumaresan (TK) and minimum norm (MN) estimators, which are based on the AR model. The simulation results show that techniques employing lower order statistics are superior to their second-order statistics (SOS)-based counterparts, especially when the noise exhibits a strong impulsive attitude. Among the estimators, FLOS-MUSIC shows a robust performance. It behaves comparably to MUSIC in non-impulsive noise environments, and both in impulsive and non-impulsive high-resolution scenarios. Furthermore, it offers a significant advantage at relatively high levels of impulsive noise contamination for distantly located sinusoidal frequencies.