Related papers: A guide on spectral methods applied to discrete da…
Frequency-domain analysis has emerged as a powerful paradigm for time series analysis, offering unique advantages over traditional time-domain approaches while introducing new theoretical and practical challenges. This survey provides a…
Spectrograms are fundamental tools in time-frequency analysis, being the squared magnitude of the so-called short time Fourier transform (STFT). Signal analysis via spectrograms has traditionally explored their peaks, i.e. their maxima.…
Many estimation problems in astrophysics are highly complex, with high-dimensional, non-standard data objects (e.g., images, spectra, entire distributions, etc.) that are not amenable to formal statistical analysis. To utilize such data and…
The estimation of power spectra from LDA data provides signal processing challenges for fluid dynamicists for several reasons: acquisition is dictated by randomly arriving particles, the registered particle velocities tend to be biased…
Signal scaling is a fundamental operation of practical importance in which a signal is enlarged or shrunk in the coordinate direction(s). Scaling or magnification is not trivial for signals of a discrete variable since the signal values may…
Signal decomposition and multiscale signal analysis provide many useful tools for time-frequency analysis. We proposed a random feature method for analyzing time-series data by constructing a sparse approximation to the spectrogram. The…
Fourier Transforms is a first in a series of monographs we present on harmonic analysis. Harmonic analysis is one of the most fascinating areas of research in mathematics. Its centrality in the development of many areas of mathematics such…
The spectrogram is a classical DSP tool used to view signals in both time and frequency. Unfortunately, the Heisenberg Uncertainty Principal limits our ability to use them for detecting and measuring narrowband signal modulation in wideband…
An algorithm is presented which generates pairs of oscillatory random time series which have identical periodograms but differ in the number of oscillations. This result indicate the intrinsic limitations of spectral methods when it comes…
Context. Recently our ability to study stars using asteroseismic techniques has increased dramatically, largely through the use of space based photometric observations. Work has also been done using ground based spectroscopic observations…
The covariance function and the variogram play very important roles in modelling and in prediction of spatial and spatio-temporal data. The assumption of second order stationarity, in space and time, is often made in the analysis of spatial…
This proceeding is intended to be a first introduction to spectral methods. It is written around some simple problems that are solved explicitly and in details and that aim at demonstrating the power of those methods. The mathematical…
In his monograph Chebyshev and Fourier Spectral Methods, John Boyd claimed that, regarding Fourier spectral methods for solving differential equations, ``[t]he virtues of the Fast Fourier Transform will continue to improve as the relentless…
The problem of recovering a signal from its phaseless Fourier transform measurements, called Fourier phase retrieval, arises in many applications in engineering and science. Fourier phase retrieval poses fundamental theoretical and…
The Lomb-Scargle periodogram is a well-known algorithm for detecting and characterizing periodic signals in unevenly-sampled data. This paper presents a conceptual introduction to the Lomb-Scargle periodogram and important practical…
This algorithm is designed to perform numerical transforms to convert data from the temporal domain into the spectral domain. This algorithm obtains the spectral magnitude and phase by studying the Coefficient of Determination of a series…
Intrinsic spectrum that results from the coupling of spontaneous emission in a laser cavity, can determine the energy concentration and coherence of lasers, which is crucial for the optical high-precision measurement. Up to now, it is hard…
This paper addresses the problem of expressing a signal as a sum of frequency components (sinusoids) wherein each sinusoid may exhibit abrupt changes in its amplitude and/or phase. The Fourier transform of a narrow-band signal, with a…
We present two methods for reducing multidimensional information to one dimension for ease of understand or analysis while maintaining statistical power. While not new, dimensional reduction is not greatly used in high-energy physics and…
We analyze signal recovery when samples are taken concomitantly from a signal and its Fourier transform. This two-sided sampling framework extends classical one-sided reconstruction and is particularly useful when measurements in either…