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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: It is hoped that this implementation and fixed-point error analysis will lead to a better understanding of the issues involved in finite register length implementation of the discrete fractional Fourier transform and will help the signal processing community make better use of the transform.

128 citations

Proceedings ArticleDOI
01 Oct 2013
TL;DR: A new algorithm to estimate a signal from its short-time Fourier transform modulus (STFTM) shows not only significant improvement in speed of convergence but it does as well recover the signals with a smaller error than the traditional GLA.
Abstract: In this paper, we present a new algorithm to estimate a signal from its short-time Fourier transform modulus (STFTM). This algorithm is computationally simple and is obtained by an acceleration of the well-known Griffin-Lim algorithm (GLA). Before deriving the algorithm, we will give a new interpretation of the GLA and formulate the phase recovery problem in an optimization form. We then present some experimental results where the new algorithm is tested on various signals. It shows not only significant improvement in speed of convergence but it does as well recover the signals with a smaller error than the traditional GLA.

128 citations

Journal ArticleDOI
TL;DR: In this paper, the best fit wavelet is defined as the ratio of the cross spectrum between the synthetic spike sequence and the seismic trace to the power spectrum of the synthetic wavelet, and the statistics of the match are related to the ordinary coherence function.
Abstract: A crucial step in the use of synthetic seismograms is the estimation of the filtering needed to convert the synthetic reflection spike sequence into a clearly recognizable approximation of a given seismic trace. In the past the filtering has been effected by a single wavelet, usually found by trial and error, and evaluated by eye. Matching can be made more precise than this by using spectral estimation procedures to determine the contribution of primaries and other reflection components to the seismic trace. The wavelet or wavelets that give the least squares best fit to the trace can be found, the errors of fit estimated, and statistics developed for testing whether a valid match can be made. If the composition of the seismogram is assumed to be known (e.g. that it consists solely of primaries and internal multiples) the frequency response of the best fit wavelet is simply the ratio of the cross spectrum between the synthetic spike sequence and the seismic trace to the power spectrum of the synthetic spike sequence, and the statistics of the match are related to the ordinary coherence function. Usually the composition cannot be assumed to be known (e.g. multiples of unknown relative amplitude may be present), and the synthetic sequence has to be split into components that contribute in different ways to the seismic trace. The matching problem is then to determine what filters should be applied to these components, regarded as inputs to a multichannel filter, in order to best fit the seismic trace, regarded as a noisy output. Partial coherence analysis is intended for just this problem. It provides fundamental statistics for the match, and it cannot be properly applied without interpreting these statistics. A useful and concise statistic is the ratio of the power in the total filtered synthetic trace to the power in the errors of fit. This measures the overall goodness-of-fit of the least squares match. It corresponds to a coherent (signal) to incoherent (noise) power ratio. Two limits can be set on it: an upper one equal to the signal-to-noise ratio estimated from the seismic data themselves, and a lower one defined from the distribution of the goodness-of-fit ratios yielded by matching with random noise of the same bandwidth and duration as the seismic trace segment. A match can be considered completely successful if its goodness-of-fit reaches the upper limit; it is rejected if the goodness-of-fit falls below the lower one.

128 citations

Proceedings ArticleDOI
04 Oct 2012
TL;DR: This paper defines generalized translation and modulation operators for signals on graphs, and uses these operators to adapt the classical windowed Fourier transform to the graph setting, enabling vertex-frequency analysis.
Abstract: The prevalence of signals on weighted graphs is increasing; however, because of the irregular structure of weighted graphs, classical signal processing techniques cannot be directly applied to signals on graphs. In this paper, we define generalized translation and modulation operators for signals on graphs, and use these operators to adapt the classical windowed Fourier transform to the graph setting, enabling vertex-frequency analysis. When we apply this transform to a signal with frequency components that vary along a path graph, the resulting spectrogram matches our intuition from classical discrete-time signal processing. Yet, our construction is fully generalized and can be applied to analyze signals on any undirected, connected, weighted graph.

128 citations

Journal ArticleDOI
TL;DR: In order to reduce the influence of Heisenberg' s uncertainty, it is proposed that different signal components are windowed by different Gaussian windows, which brings better adaption and flexibility.
Abstract: This paper proposes a real-time power quality disturbances (PQDs) classification by using a hybrid method (HM) based on S-transform (ST) and dynamics (Dyn). Classification accuracy and run time are mainly considered in our work. The HM firstly uses Dyn to identify the location of the signal components in the frequency spectrum yielded by Fourier transform, and uses inverse Fourier transform to only some of the signal components. Then features from Fourier transform, ST, and Dyn are selected, and a decision tree is used to classify the types of PQD. In order to reduce the influence of Heisenberg' s uncertainty, we proposed that different signal components are windowed by different Gaussian windows, which brings better adaption and flexibility. By the HM, run time of the application has been greatly reduced with satisfactory classification accuracy. Finally, a DSP-FPGA based hardware platform is adopted to test the run time and correctness of the proposed method under real standard signals. Field signal tests have also presented. Both simulations and experiments validate the feasibility of the new method.

128 citations


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