scholarly journals Trend filtering – I. A modern statistical tool for time-domain astronomy and astronomical spectroscopy

2020 ◽  
Vol 492 (3) ◽  
pp. 4005-4018 ◽  
Author(s):  
Collin A Politsch ◽  
Jessi Cisewski-Kehe ◽  
Rupert A C Croft ◽  
Larry Wasserman
Keyword(s):  
Time Domain ◽  
Gaussian Process Regression ◽  
Smoothing Splines ◽  
Companion Paper ◽  
Statistical Tool ◽  
Observational Astronomy ◽  
Astronomical Object ◽  
Frequency Components ◽  
The Time Domain ◽  
Kernel Smoothers

ABSTRACT The problem of denoising a 1D signal possessing varying degrees of smoothness is ubiquitous in time-domain astronomy and astronomical spectroscopy. For example, in the time domain, an astronomical object may exhibit a smoothly varying intensity that is occasionally interrupted by abrupt dips or spikes. Likewise, in the spectroscopic setting, a noiseless spectrum typically contains intervals of relative smoothness mixed with localized higher frequency components such as emission peaks and absorption lines. In this work, we present trend filtering, a modern non-parametric statistical tool that yields significant improvements in this broad problem space of denoising spatially heterogeneous signals. When the underlying signal is spatially heterogeneous, trend filtering is superior to any statistical estimator that is a linear combination of the observed data – including kernel smoothers, LOESS, smoothing splines, Gaussian process regression, and many other popular methods. Furthermore, the trend filtering estimate can be computed with practical and scalable efficiency via a specialized convex optimization algorithm, e.g. handling sample sizes of n ≳ 107 within a few minutes. In a companion paper, we explicitly demonstrate the broad utility of trend filtering to observational astronomy by carrying out a diverse set of spectroscopic and time-domain analyses.

Time domain waveform inversion—A frequency domain view: How well we need to match waveforms?

1991 ◽  
Vol 81 (6) ◽  
pp. 2351-2370
Author(s):  
Zoltan A. Der ◽  
Robert H. Shumway ◽  
Michael R. Hirano
Keyword(s):  
Time Domain ◽  
High Frequency ◽  
Waveform Inversion ◽  
Quantitative Measure ◽  
Domain Modeling ◽  
Low Frequencies ◽  
Waveform Modeling ◽  
Time Domain Modeling ◽  
Frequency Components ◽  
The Time Domain

Abstract Waveform modeling in the time domain matches the various frequency components of seismic signals unevenly; the agreement is better at low frequencies and becomes progressively worse towards higher frequencies. The net effect of this kind of time-domain modeling is that the resolution in the spatial details of the source is less than optimal since the high-frequency components of the signal with their short wavelengths to resolve finer details do not fit the data. These problems are demonstrated by numerical simulations and by the reanalysis of some aspects of the El Golfo earthquake in using a new seismic imaging technique based on a generalization of an f-k algorithm. This procedure computes a statistic that can be used to derive confidence limits of the parameters sought in the inversion, thus providing a quantitative measure of the uncertainties in the results.

Frequency‐domain elastic wave modeling by finite differences: A tool for crosshole seismic imaging

Geophysics ◽  
1990 ◽  
Vol 55 (5) ◽  
pp. 626-632 ◽  
Author(s):  
R. Gerhard Pratt
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Equations Of Motion ◽  
Domain Modeling ◽  
Multiple Sources ◽  
State Equations ◽  
Migration Imaging ◽  
Time Domain Modeling ◽  
Frequency Components ◽  
The Time Domain

The migration, imaging, or inversion of wide‐aperture cross‐hole data depends on the ability to model wave propagation in complex media for multiple source positions. Computational costs can be considerably reduced in frequency‐domain imaging by modeling the frequency‐domain steady‐state equations, rather than the time‐domain equations of motion. I develop a frequency‐domain approach in this note that is competitive with time‐domain modeling when solutions for multiple sources are required or when only a limited number of frequency components of the solution are required.

scholarly journals Trend filtering – II. Denoising astronomical signals with varying degrees of smoothness

2020 ◽  
Vol 492 (3) ◽  
pp. 4019-4032 ◽  
Author(s):  
Collin A Politsch ◽  
Jessi Cisewski-Kehe ◽  
Rupert A C Croft ◽  
Larry Wasserman
Keyword(s):  
Light Curve ◽  
Time Domain ◽  
Data Reduction ◽  
Large Scale ◽  
State Of The Art ◽  
Large Scale Structure ◽  
Light Curves ◽  
Statistical Tool ◽  
Observational Astronomy ◽  
Quasar Spectra

ABSTRACT Trend filtering – first introduced into the astronomical literature in Paper I of this series – is a state-of-the-art statistical tool for denoising 1D signals that possess varying degrees of smoothness. In this work, we demonstrate the broad utility of trend filtering to observational astronomy by discussing how it can contribute to a variety of spectroscopic and time-domain studies. The observations we discuss are (1) the Lyman-α (Lyα) forest of quasar spectra; (2) more general spectroscopy of quasars, galaxies, and stars; (3) stellar light curves with planetary transits; (4) eclipsing binary light curves; and (5) supernova light curves. We study the Lyα forest in the greatest detail – using trend filtering to map the large-scale structure of the intergalactic medium along quasar-observer lines of sight. The remaining studies share broad themes of: (1) estimating observable parameters of light curves and spectra; and (2) constructing observational spectral/light-curve templates. We also briefly discuss the utility of trend filtering as a tool for 1D data reduction and compression.

NUMERICAL ANALYSIS OF SAFETY ZONE OF A LARGE FLAT-PLATE BOUNDED-WAVE EMP SIMULATOR

2019 ◽  
Vol 188 (2) ◽  
pp. 205-212
Author(s):  
Liuhong Huang ◽  
Cui Meng ◽  
Yuebo Li ◽  
Jie Yang ◽  
Jiuliang Xiong ◽  
...  
Keyword(s):  
Electric Field ◽  
Flat Plate ◽  
Time Domain ◽  
Simulation Software ◽  
Safety Zone ◽  
Exposure Limits ◽  
Leakage Field ◽  
Frequency Components ◽  
The Time Domain ◽  
Double Limit

Abstract The safety zone of a large flat-plate bounded-wave electromagnetic pulse simulator was analyzed using the 3D electromagnetic simulation software Computer Simulation Technology. First, the double-limit requirement cited from the GB 8702 for an instantaneous pulse was clarified compared with the International Commission on Non-Ionizing Radiation Protection guidelines. This means that both the amplitude of the time-domain waveforms and all frequency components should be satisfied with the respective exposure limits. Then, the leakage field of a large flat-plate bounded-wave simulator was simulated. After analyzing the peak amplitude of an instantaneous electric field in a certain area, the observation points along six directions were specified, and the corresponding amplitudes were given. Furthermore, it was verified that the time-domain electric field of the critical points was satisfied with the frequency-domain exposure limits. Finally, the safety distances lower than the reference levels were given, and the safety zones corresponding to the three common exposure limits were obtained.

Can impedance characterize the heart?

1976 ◽  
Vol 40 (2) ◽  
pp. 250-252 ◽  
Author(s):  
W. Hunter ◽  
A. Noordergraaf
Keyword(s):  
Mechanical Properties ◽  
Fourier Series ◽  
Fourier Analysis ◽  
Frequency Analysis ◽  
Time Domain ◽  
Arterial Tree ◽  
Heart Cycle ◽  
Frequency Components ◽  
Flow Oscillations ◽  
The Time Domain

When considering the use of Fourier series in hemodynamics, the question is whether one can relate the frequency components of the flow oscillations to the corresponding ones of pressure using impedance concepts. For the arteries, this method provided the basis for great advances in understanding. However, it is precisely because the arterial tree acts almost linearly while its properties do not change markedly within one beat that frequency analysis achieved such success. For the ventricle, in which the mechanical properties vary widely over the course of one heart cycle, Fourier analysis loses its usefulness. Consequently, we must return to the time domain for formulating a description of the heart as a pump. A time-domain method, the impulse response, is suggested as a possible alternative to impedance.

The Improved Method for Solving Permutation Problem in Frequency Domain Blind Source Separation of Speech Signals

2012 ◽  
Vol 433-440 ◽  
pp. 7029-7034
Author(s):  
De Xiang Zhang ◽  
Xiao Pei Wu ◽  
Zhao Lv ◽  
Xiao Jing Guo
Keyword(s):  
Frequency Domain ◽  
Blind Source Separation ◽  
Time Domain ◽  
Source Separation ◽  
Speech Signals ◽  
Source Signal ◽  
Frequency Components ◽  
Permutation Problem ◽  
The Time Domain ◽  
Permutation Ambiguity

The signals of convolutive mixture in time-domain can be transformed to instantaneous mixtures in frequency-domain and complex-valued independent component analysis (CICA) can separate efficiently the signals of instantaneous mixture in each frequency bin. However, since CICA is calculated in each frequency bin independently, the permutation ambiguity becomes a serious problem. The permutation ambiguity of CICA in each frequency bin should be aligned so that a separated signal in the time-domain contains frequency components of the same source signal. The paper presents a novel and efficient approach for solving the permutation problem in frequency domain blind source separation of speech signals. The new algorithm models the frequency-domain separated signals by means of Teager energy correlation between neighboring bins for the detection of correct permutations. Experimental results show that the proposed algorithm can efficiently solve the permutation ambiguity problem in each frequency bin.

Apodisation in the time domain

1992 ◽  
Vol 2 (4) ◽  
pp. 615-620
Author(s):  
G. W. Series
Keyword(s):  
Time Domain ◽  
The Time Domain

JOINT INTERPRETATION OF AIRBORNE ELECTROMAGNETIC DATA IN THE TIME DOMAIN AND FREQUENCY DOMAIN

2018 ◽  
Vol 12 (7-8) ◽  
pp. 76-83
Author(s):  
E. V. KARSHAKOV ◽  
J. MOILANEN
Keyword(s):  
Fourier Transform ◽  
Frequency Domain ◽  
Time Domain ◽  
Frequency Interval ◽  
Single Spectrum ◽  
Simultaneous Inversion ◽  
Homogeneous Half Space ◽  
Time Domain Data ◽  
The Time Domain

Тhe advantage of combine processing of frequency domain and time domain data provided by the EQUATOR system is discussed. The heliborne complex has a towed transmitter, and, raised above it on the same cable a towed receiver. The excitation signal contains both pulsed and harmonic components. In fact, there are two independent transmitters operate in the system: one of them is a normal pulsed domain transmitter, with a half-sinusoidal pulse and a small "cut" on the falling edge, and the other one is a classical frequency domain transmitter at several specially selected frequencies. The received signal is first processed to a direct Fourier transform with high Q-factor detection at all significant frequencies. After that, in the spectral region, operations of converting the spectra of two sounding signals to a single spectrum of an ideal transmitter are performed. Than we do an inverse Fourier transform and return to the time domain. The detection of spectral components is done at a frequency band of several Hz, the receiver has the ability to perfectly suppress all sorts of extra-band noise. The detection bandwidth is several dozen times less the frequency interval between the harmonics, it turns out thatto achieve the same measurement quality of ground response without using out-of-band suppression you need several dozen times higher moment of airborne transmitting system. The data obtained from the model of a homogeneous half-space, a two-layered model, and a model of a horizontally layered medium is considered. A time-domain data makes it easier to detect a conductor in a relative insulator at greater depths. The data in the frequency domain gives more detailed information about subsurface. These conclusions are illustrated by the example of processing the survey data of the Republic of Rwanda in 2017. The simultaneous inversion of data in frequency domain and time domain can significantly improve the quality of interpretation.

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