Related papers: Unbiased two-windows approach for Welch's method
Welch's method provides an estimator of the power spectral density that is statistically consistent. This is achieved by averaging over periodograms calculated from overlapping segments of a time series. For a finite length time series,…
We present a statistical analysis of a variant of the periodogram method that forms power spectral density estimates by cross-correlating the discrete Fourier transforms of adjacent time windows. The proposed estimator is closely related to…
We present and analyze an alternative, more robust approach to the Welch's overlapped segment averaging (WOSA) spectral estimator. Our method computes sample percentiles instead of averaging over multiple periodograms to estimate power…
The periodogram is a widely used tool to analyze second order stationary time series. An attractive feature of the periodogram is that the expectation of the periodogram is approximately equal to the underlying spectral density of the time…
During the inversion of discrete linear systems noise in data can be amplified and result in meaningless solutions. To combat this effect, characteristics of solutions that are considered desirable are mathematically implemented during…
The usual nonparametric approach to spectral analysis is revisited within the regularization framework. Both usual and windowed periodograms are obtained as the squared modulus of the minimizer of regularized least squares criteria. Then,…
Spectrum estimation is a fundamental methodology in the analysis of time-series data, with applications including medicine, speech analysis, and control design. The asymptotic theory of spectrum estimation is well-understood, but the theory…
Power spectrum estimation is an important tool in many applications, such as the whitening of noise. The popular multitaper method enjoys significant success, but fails for short signals with few samples. We propose a statistical model…
This article discusses a generalization of the 1-dimensional multi-reference alignment problem. The goal is to recover a hidden signal from many noisy observations, where each noisy observation includes a random translation and random…
We review the methodology for measurements of two point functions of the cosmological observables, both power spectra and correlation functions. For pseudo-$C_\ell$ estimators, we will argue that the window weighted overdensity field can…
Processing of speech and audio signals with time-frequency representations require windowing methods which allow perfect reconstruction of the original signal and where processing artifacts have a predictable behavior. The most common…
The three cardinal, statistically consistent, families of non-parametric estimators to the power spectral density of a time series are lag-window, multitaper and Welch estimators. However, when estimating power spectral densities from a…
Smooth window functions are often applied to strain data when inferring the parameters describing the astrophysical sources of gravitational-wave transients. Within the LIGO-Virgo-KAGRA collaboration, it is conventional to include a term to…
The analysis of gravitational wave interferometer data requires estimates for the noise covariance matrix. For stationary noise, this amounts to estimating the power spectrum. Classical methods such as Welch averaging are used in many…
We propose a time-varying optimal window width (TVOWW) selection scheme to optimize the performance of several nonlinear-type time-frequency analyses, including the reassignment method, and the synchrosqueezing transform (SST) and its…
In this paper three different scenarios in wide band spectrum sensing have been studied. While the signal and noise statistics are supposed to be unspecified, random matrixes have been utilized in order to estimate the noise variance. These…
Integrated Sensing and Communication (ISAC) with Orthogonal Frequency Division Multiplexing (OFDM) waveforms is a key enabler for next-generation wireless systems. Recent studies show that Convolutional Neural Networks (CNNs) can estimate…
This paper presents a new methodology for the solution of problems of two- and three-dimensional acoustic scattering (and, in particular, two-dimensional electromagnetic scattering) by obstacles and defects in presence an arbitrary number…
A new method is proposed for variable screening, variable selection and prediction in linear regression problems where the number of predictors can be much larger than the number of observations. The method involves minimizing a penalized…
Spectral analysis using overlapping sliding windows is among the most widely used techniques in analyzing non-stationary time series. Although sliding window analysis is convenient to implement, the resulting estimates are sensitive to the…