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.

High precision fourier transform spectrometry: The critical role of phase corrections

Abstract: In high precision Fourier transform spectrometry, proper handling of the phase correction is essential if the full potential wave number accuracy of the data is to be preserved. One-sided interferograms are shown to be especially sensitive to phase error, and this sensitivity is quantitatively related to the signal-to-noise ratio. The role of the truncation/apodization function used to obtain the phase correction is also discussed, as is the special problem of emission spectra.

A unified view of multitaper multivariate spectral estimation

Abstract: SUMMARY The orthogonal multitaper framework for cross-spectral estimators provides a simple unifying structure for determining the corresponding statistical properties. Here crossspectral estimators are represented by a weighted average of orthogonally-tapered crossperiodograms, with the weights corresponding to a set of rescaled eigenvalues. Such a structure not only encompasses the Thomson estimators, using Slepian and sine tapers, but also Welch's weighted overlapped segment averaging estimator and lag window estimators including frequency-averaged cross-periodograms. The means, smoothing and leakage biases, variances and asymptotic distributions of such estimators can all be formulated in a common way; comparisons are made for a fixed number of degrees of freedom. The common structure of the estimators also provides a necessary condition for the invertibility of an estimated cross-spectral matrix, namely that the weight matrix of the estimator written in bilinear form must have rank greater than or equal to the dimension of the cross-spectral matrix. An example is given showing the importance of small leakage and thus illustrating that the various estimators need not be equivalent in practice.

A unified approach to sparse signal processing

Abstract: A unified view of the area of sparse signal processing is presented in tutorial form by bringing together various fields in which the property of sparsity has been successfully exploited. For each of these fields, various algorithms and techniques, which have been developed to leverage sparsity, are described succinctly. The common potential benefits of significant reduction in sampling rate and processing manipulations through sparse signal processing are revealed. The key application domains of sparse signal processing are sampling, coding, spectral estimation, array processing, component analysis, and multipath channel estimation. In terms of the sampling process and reconstruction algorithms, linkages are made with random sampling, compressed sensing, and rate of innovation. The redundancy introduced by channel coding in finite and real Galois fields is then related to over-sampling with similar reconstruction algorithms. The error locator polynomial (ELP) and iterative methods are shown to work quite effectively for both sampling and coding applications. The methods of Prony, Pisarenko, and MUltiple SIgnal Classification (MUSIC) are next shown to be targeted at analyzing signals with sparse frequency domain representations. Specifically, the relations of the approach of Prony to an annihilating filter in rate of innovation and ELP in coding are emphasized; the Pisarenko and MUSIC methods are further improvements of the Prony method under noisy environments. The iterative methods developed for sampling and coding applications are shown to be powerful tools in spectral estimation. Such narrowband spectral estimation is then related to multi-source location and direction of arrival estimation in array processing. Sparsity in unobservable source signals is also shown to facilitate source separation in sparse component analysis; the algorithms developed in this area such as linear programming and matching pursuit are also widely used in compressed sensing. Finally, the multipath channel estimation problem is shown to have a sparse formulation; algorithms similar to sampling and coding are used to estimate typical multicarrier communication channels.

The SLEX model of a non-stationary random process

Abstract: We propose a new model for non-stationary random processes to represent time series with a time-varying spectral structure. Our SLEX model can be considered as a discrete time-dependent Cramer spectral representation. It is based on the so-called Smooth Localized complex EXponential basis functions which are orthogonal and localized in both time and frequency domains. Our model delivers a finite sample size representation of a SLEX process having a SLEX spectrum which is piecewise constant over time segments. In addition, we embed it into a sequence of models with a limit spectrum, a smoothly in time varying “evolutionary” spectrum. Hence, we develop the SLEX model parallel to the Dahlhaus (1997, Ann. Statist., 25, 1–37) model of local stationarity, and we show that the two models are asymptotically mean square equivalent. Moreover, to define both the growing complexity of our model sequence and the regularity of the SLEX spectrum we use a wavelet expansion of the spectrum over time. Finally, we develop theory on how to estimate the spectral quantities, and we briefly discuss how to form inference based on resampling (bootstrapping) made possible by the special structure of the SLEX model which allows for simple synthesis of non-stationary processes.

A comparative study and assessment of Doppler ultrasound spectral estimation techniques. Part I: Estimation methods.

Abstract: When compared to the classical Discrete Fourier Transform (DFT) or Fast Fourier Transform (FFT) approach, modern estimation methods offer the potential for achieving significant improvements in estimating the power density spectrum of Doppler ultrasound signals. Such improvements, for example, might enable minor flow disturbances to be detected, thereby improving the sensitivity in arterial disease assessment. Specifically, reduction in the variance and bias can be achieved, and this may enable disturbed flow to be detected in a more sensitive manner. The approach taken here, is to consider spectral estimation methods as a problem of fitting an assumed model to the Doppler signal. The models described assume that the signal is stationary. Since the Doppler signal is generally nonstationary, it is assumed that a short enough time window interval can be chosen over which the signal can be considered stationary. We shall review the various methods and when appropriate, relate them to the nature of the Doppler signal.