Topic
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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Book•
01 Dec 1993
TL;DR: In this paper, the authors introduce the idea of joint probability distributions and average for linear systems and their response to random vibrational signals. But they do not discuss the relationship between these distributions and the average.
Abstract: 1. Introduction To Probability Distributions And Averages. 2. Joint Probability Distributions, Ensemble Averages. 3. Correlation. 4. Fourier Analysis. 5. Spectral Density. 6. Excitation - Response Relations For Linear Systems. 7. Transmission Of Random Vibration. 8. Statistics Of Narrow Band Processes. 9. Accuracy Of Measurements. 10. Digital Spectral Analysis I: Discrete Fourier Transforms. 11. Digital Spectral Analysis II: Windows And Smoothing. 12. The Fast Fourier Transform. 14. Application Notes. 15. Multi-Dimensional Spectral Analysis. 16. Response Of Continuous Linear Systems To Stationary Random Excitation. 17. Discrete Wavelet Analysis.
855 citations
24 Mar 2011
TL;DR: In this paper, a new approach to super resolution line spectrum estimation in both temporal and spatial domain using a coprime pair of samplers is proposed, where the difference set of this pair of sample spacings (which arise naturally in computation of second order moments) can be generated using only O(M + N) physical samples.
Abstract: A new approach to super resolution line spectrum estimation in both temporal and spatial domain using a coprime pair of samplers is proposed. Two uniform samplers with sample spacings MT and NT are used where M and N are coprime and T has the dimension of space or time. By considering the difference set of this pair of sample spacings (which arise naturally in computation of second order moments), sample locations which are O(MN) consecutive multiples of T can be generated using only O(M + N) physical samples. In order to efficiently use these O(MN) virtual samples for super resolution spectral estimation, a novel algorithm based on the idea of spatial smoothing is proposed, which can be used for estimating frequencies of sinusoids buried in noise as well as for estimating Directions-of-Arrival (DOA) of impinging signals on a sensor array. This technique allows us to construct a suitable positive semidefinite matrix on which subspace based algorithms like MUSIC can be applied to detect O(MN) spectral lines using only O(M + N) physical samples.
706 citations
TL;DR: In this article, a discrete Fourier transform for arbitrary data spacing is defined, and the pathology of the data spacing, including aliasing and related effects, is shown to be contained in the spectral window.
Abstract: The general problems of Fourier and spectral analysis are discussed. A discrete Fourier transformF
N
(v) of a functionf(t) is presented which (i) is defined for arbitrary data spacing; (ii) is equal to the convolution of the true Fourier transform off(t) with a spectral window. It is shown that the ‘pathology’ of the data spacing, including aliasing and related effects, is all contained in the spectral window, and the properties of the spectral windows are examined for various kinds of data spacing. The results are applicable to power spectrum analysis of stochastic functions as well as to ordinary Fourier analysis of periodic or quasiperiodic functions.
623 citations
Book•
01 Jan 1988
TL;DR: In this article, a single stationary sinusoid plus noise was used to estimate the parameters of a prior probability prior to the student t-distribution of the student distribution.
Abstract: 1 Introduction.- 2 Single Stationary Sinusoid Plus Noise.- 3 The General Model Equation Plus Noise.- 4 Estimating the Parameters.- 5 Model Selection.- 6 Spectral Estimation.- 7 Applications.- 8 Summary and Conclusions.- A Choosing a Prior Probability.- B Improper Priors as Limits.- C Removing Nuisance Parameters.- D Uninformative Prior Probabilities.- E Computing the "Student t-Distribution".
601 citations
TL;DR: The Fourier transform is a function that describes the amplitude and phase of each sinusoid, which corresponds to a specific frequency, which has become a powerful tool in diverse fields of science.
Abstract: To calculate a transform, just listen. The ear automatically performs the calculation, which the intellect can execute only after years of mathematical education. The ear formulates a transform by converting sound-the waves of pressure traveling through time and the atmosphere-into a spectrum, a description of the sound as a series of volumes at distinct pitches. The brain turns this information into perceived sound. Similar operations can be done by mathematical methods on sound waves or virtually any other fluctuating phenomenon, from light waves to ocean tides to solar cycles. These mathematical tools can decompose functions representing such fluctuations into a set of sinusoidal components-undulating curves that vary from a maximum to a minimum and back, much like the heights of ocean waves. The Fourier transform is a function that describes the amplitude and phase of each sinusoid, which corresponds to a specific frequency. The Fourier transform has become a powerful tool in diverse fields of science. In some cases, the Fourier transform can provide a means of solving unwieldy equations that describe dynamic response to electricity, hear or light. In other cases, it can identify the regular contributions to a fluctuating signal, thereby helping to make sense of observations inmore » astronomy, medicine and chemistry.« less
588 citations