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Spectral density estimation

About: Spectral density estimation is a research topic. Over the lifetime, 5391 publications have been published within this topic receiving 123105 citations.


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Journal ArticleDOI
TL;DR: Numerical results demonstrate that the performance of the proposed frequency estimator has lower SNR threshold to closely reach the Cramer-Rao bound (CRB) in the low SNR region and its performance also outperforms previous estimators in the highSNR region.
Abstract: Frequency estimation of a single complex exponential waveform is an important problem in many fields. In this letter, a new frequency estimator for a complex exponential sine waveform observed under the additive white Gaussian noise (AWGN) is proposed. The proposed estimator is obtained by solving the nonlinear functions. The new estimator has an analytical expression based on interpolation method with three DFT samples. Numerical results demonstrate that the performance of the proposed estimator has lower SNR threshold to closely reach the Cramer-Rao bound (CRB) in the low SNR region and its performance also outperforms previous estimators in the high SNR region.

35 citations

Journal ArticleDOI
TL;DR: In this article, a sieve was proposed for the estimation of the spectral density of a Gaussian stationary stochastic process, where the sieve exploits the full Gaussian nature of the process.
Abstract: We suggest a sieve for the estimation of the spectral density of a Gaussian stationary stochastic process. In contrast to the standard periodogram-based estimates this one aims at exploiting the full Gaussian nature of the process.

34 citations

Journal ArticleDOI
TL;DR: A new spectral estimation algorithm based on signal reconstruction in a shift-invariant signal space, where a direct spectral estimation procedure is developed using the B-spline basis that is superior to the Lomb-Scargle algorithm and the classical Fourier periodogram based method in detecting periodically expressed genes.
Abstract: Periodogram analysis of time-series is widespread in biology. A new challenge for analyzing the microarray time series data is to identify genes that are periodically expressed. Such challenge occurs due to the fact that the observed time series usually exhibit non-idealities, such as noise, short length, and unevenly sampled time points. Most methods used in the literature operate on evenly sampled time series and are not suitable for unevenly sampled time series. For evenly sampled data, methods based on the classical Fourier periodogram are often used to detect periodically expressed gene. Recently, the Lomb-Scargle algorithm has been applied to unevenly sampled gene expression data for spectral estimation. However, since the Lomb-Scargle method assumes that there is a single stationary sinusoid wave with infinite support, it introduces spurious periodic components in the periodogram for data with a finite length. In this paper, we propose a new spectral estimation algorithm for unevenly sampled gene expression data. The new method is based on signal reconstruction in a shift-invariant signal space, where a direct spectral estimation procedure is developed using the B-spline basis. Experiments on simulated noisy gene expression profiles show that our algorithm is superior to the Lomb-Scargle algorithm and the classical Fourier periodogram based method in detecting periodically expressed genes. We have applied our algorithm to the Plasmodium falciparum and Yeast gene expression data and the results show that the algorithm is able to detect biologically meaningful periodically expressed genes. We have proposed an effective method for identifying periodic genes in unevenly sampled space of microarray time series gene expression data. The method can also be used as an effective tool for gene expression time series interpolation or resampling.

34 citations

Journal ArticleDOI
TL;DR: Higherorder spectral estimations, bispectrum and third-order cumulants, are evaluated, saved, and pre-trained using convolutional neural networks (CNN) algorithm to implement a reliable and applicable deep learning classification technique.
Abstract: Electrocardiogram (ECG) is one of the most important and effective tools in clinical routine to assess the cardiac arrhythmias. In this research higherorder spectral estimations, bispectrum and third-order cumulants, are evaluated, saved, and pre-trained using convolutional neural networks (CNN) algorithm. CNN is transferred in this study to carry out automatic ECG arrhythmia diagnostics after employing the higher-order spectral algorithms. Transfer learning strategies are applied on pre-trained convolutional neural network, namely AlexNet and GoogleNet, to carry out the final classification. Five different arrhythmias of ECG waveform are chosen from the MIT-BIH arrhythmia database to evaluate the proposed approach. The main contribution of this study is to utilize the pre-trained convolutional neural networks with a combination of higher-order spectral estimations of arrhythmias ECG signal to implement a reliable and applicable deep learning classification technique. The Highest average accuracy obtained is 97.8 % when using third cumulants and GoogleNet. As is evident from these results, the proposed approach is an efficient automatic cardiac arrhythmia classification method and provides a reliable recognition system based on well-established CNN architectures instead of training a deep CNN from scratch.

34 citations

Journal ArticleDOI
TL;DR: The pointwise behavior of the Fourier transform of the spectral measure for discrete one-dimensional Schrodinger operators with sparse potentials has been studied in this article, and a resonance structure which admits a physical interpretation in terms of a simple quasiclassical model has been found.
Abstract: We study the pointwise behavior of the Fourier transform of the spectral measure for discrete one-dimensional Schrodinger operators with sparse potentials. We find a resonance structure which admits a physical interpretation in terms of a simple quasiclassical model. We also present an improved version of known results on the spectrum of such operators.

34 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202316
202248
202159
2020101
201994
201895