Results 1001-1050 of 2311 (2268 ASCL, 43 submitted)
InitialConditions finds the initial series solutions for perturbations in our Universe. This includes all scalar (1 adiabatic, 4 isocurvature and 2 magnetic modes), vector (1 vorticity mode, 1 magnetic mode), and tensor (1 gravitational wave mode and 1 magnetic mode) perturbations including terms up to second order in the neutrino mass. It can handle the standard species (cdm, baryons, photons), and two neutrino mass eigenstates (1 light, 1 heavy).
intensitypower measures and models the auto- and cross-power spectrum multipoles of galaxy catalogs and radio intensity maps presented in spherical coordinates. It can also convert the multipoles to power spectrum wedges P(k,mu) and 2D power spectra P(k_perp,k_par). The code assumes the galaxy catalog is a set of discrete points and the radio intensity map is a pixelized continuous field which includes angular pixelization using healpix, binning in redshift channels, smoothing by a Gaussian telescope beam, and the addition of a Gaussian noise in each cell. The galaxy catalog and radio intensity map are transferred onto an FFT grid, and power spectrum multipoles are measured including curved-sky effects. Both maps include redshift-space distortions.
We describe a novel approach to accelerating Monte Carlo Markov Chains. Our focus is cosmological parameter estimation, but the algorithm is applicable to any problem for which the likelihood surface is a smooth function of the free parameters and computationally expensive to evaluate. We generate a high-order interpolating polynomial for the log-likelihood using the first points gathered by the Markov chains as a training set. This polynomial then accurately computes the majority of the likelihoods needed in the latter parts of the chains. We implement a simple version of this algorithm as a patch (InterpMC) to CosmoMC and show that it accelerates parameter estimatation by a factor of between two and four for well-converged chains. The current code is primarily intended as a "proof of concept", and we argue that there is considerable room for further performance gains. Unlike other approaches to accelerating parameter fits, we make no use of precomputed training sets or special choices of variables, and InterpMC is almost entirely transparent to the user.
The Beta Inverse code solves the inverse cumulative density function (CDF) of a Beta distribution, allowing one to sample from the Beta prior directly. The Beta distribution is well suited as a prior for the distribution of the orbital eccentricities of extrasolar planets; imposing a Beta prior on orbital eccentricity is valuable for any type of observation of an exoplanet where eccentricity can affect the model parameters (e.g. transits, radial velocities, microlensing, direct imaging). The Beta prior is an excellent description of the current, empirically determined distribution of orbital eccentricities and thus employing it naturally incorporates an observer’s prior experience of what types of orbits are probable or improbable. The default parameters in the code are currently set to the Beta distribution which best describes the entire population of exoplanets with well-constrained orbits.
InversionKit is an interactive Java program that performs rotational and structural linear inversions from frequency data.
ionFR calculates the amount of ionospheric Faraday rotation for a specific epoch, geographic location, and line-of-sight. The code uses a number of publicly available, GPS-derived total electron content maps and the most recent release of the International Geomagnetic Reference Field. ionFR can be used for the calibration of radio polarimetric observations; its accuracy had been demonstrated using LOFAR pulsar observations.
ipole is a ray-tracing code for covariant, polarized radiative transport particularly useful for modeling Event Horizon Telescope sources, though may also be used for other relativistic transport problems. The code extends the ibothros scheme for covariant, unpolarized transport using two representations of the polarized radiation field: in the coordinate frame, it parallel transports the coherency tensor, and in the frame of the plasma, it evolves the Stokes parameters under emission, absorption, and Faraday conversion. The transport step is as spacetime- and coordinate- independent as possible; the emission, absorption, and Faraday conversion step is implemented using an analytic solution to the polarized transport equation with constant coefficients. As a result, ipole is stable, efficient, and produces a physically reasonable solution even for a step with high optical depth and Faraday depth.
The IRACpm R package applies a 7-8 order distortion correction to IRAC astrometric data from the Spitzer Space Telescope and includes a function for measuring apparent proper motions between different Epochs. These corrections are applicable only to positions measured by APEX; cryogenic images benefit from a correction for varying intra-pixel sensitivity prior to the application of the distortion.
IRACproc is a software suite that facilitates the co-addition of dithered or mapped Spitzer/IRAC data to make them ready for further analysis with application to a wide variety of IRAC observing programs. The software runs within PDL, a numeric extension for Perl available from pdl.perl.org, and as stand alone perl scripts. In acting as a wrapper for the Spitzer Science Center's MOPEX software, IRACproc improves the rejection of cosmic rays and other transients in the co-added data. In addition, IRACproc performs (optional) Point Spread Function (PSF) fitting, subtraction, and masking of saturated stars.
IRAF includes a broad selection of programs for general image processing and graphics, plus a large number of programs for the reduction and analysis of optical and IR astronomy data. Other external or layered packages are available for applications such as data acquisition or handling data from other observatories and wavelength regimes such as the Hubble Space Telescope (optical), EUVE (extreme ultra-violet), or ROSAT and AXAF (X-ray). These external packages are distributed separately from the main IRAF distribution but can be easily installed. The IRAF system also includes a complete programming environment for scientific applications, which includes a programmable Command Language scripting facility, the IMFORT Fortran/C programming interface, and the full SPP/VOS programming environment in which the portable IRAF system and all applications are written.
IRAS90 is a suite of programs for processing IRAS data. It takes advantage of Starlink's (ascl:1110.012) ADAM environment, which provides multi-platform availability of both data and the programs to process it, and the user friendly interface of the parameter entry system. The suite can determine positions in astrometric coordinates, draw grids, and offers other functions for standard astronomical measurement and standard projections.
The UKIRT IRCAM3 data reduction and analysis software package, IRCAMDR (formerly ircam_clred) analyzes and displays any 2D data image stored in the standard Starlink (ascl:1110.012) NDF data format. It reduces and analyzes IRCAM1/2 data images of 62x58 pixels and IRCAM3 images of 256x256 size. Most of the applications will work on NDF images of any physical (pixel) dimensions, for example, 1024x1024 CCD images can be processed.
IRDAP (IRDIS Data reduction for Accurate Polarimetry) accurately reduces SPHERE-IRDIS polarimetric data. It is a highly-automated end-to-end pipeline; its core feature is model-based correction of the instrumental polarization effects. IRDAP handles data taken both in field- and pupil-tracking mode and using the broadband filters Y, J, H and Ks. Data taken with the narrowband filters can be reduced as well, although with a somewhat worse accuracy. For pupil-tracking observations IRDAP can additionally apply angular differential imaging.
We describe the InfraRed Data Reduction (IRDR) software package, a small ANSI C library of fast image processing routines for automated pipeline reduction of infrared (dithered) observations. We developed the software to satisfy certain design requirements not met in existing packages (e.g., full weight map handling) and to optimize the software for large data sets (non-interactive tasks that are CPU and disk efficient). The software includes stand-alone C programs for tasks such as running sky frame subtraction with object masking, image registration and coaddition with weight maps, dither offset measurement using cross-correlation, and object mask dilation. Although we currently use the software to process data taken with CIRSI (a near-IR mosaic imager), the software is modular and concise and should be easy to adapt/reuse for other work.
Iris is a downloadable Graphical User Interface (GUI) application which allows the astronomer to build and analyze wide-band Spectral Energy Distributions (SEDs). The components of Iris have been contributed by members of the VAO. Specview, contributed by STScI, provides a GUI for reading, editing, and displaying SEDs, as well as defining models and parameter values. Sherpa, contributed by the Chandra project at SAO, provides a library of models, fit statistics, and optimization methods; the underlying I/O library, SEDLib, is a VAO product written by SAO to current IVOA (International Virtual Observatory Alliance) data model standards. NED is a service provided by IPAC for easy location of data for a given extragalactic source, including SEDs. SedImporter converts non-standard SED data files into a format supported by Iris.
IRSFRINGE is an IDL-based GUI package that allows observers to interactively remove fringes from IRS spectra. Fringes that originate from the detector subtrates are observed in the IRS Short-High (SH) and Long-High (LH) modules. In the Long-Low (LL) module, another fringe component is seen as a result of the pre-launch change in one of the LL filters. The fringes in the Short-Low (SL) module are not spectrally resolved. the fringes are already largely removed in the pipeline processing when the flat field is applied. However, this correction is not perfect and remaining fringes can be removed with IRSFRINGE from data in each module. IRSFRINGE is available as a stand-alone package and is also part of the Spectroscopic Modeling, Analysis and Reduction Tool (SMART, ascl:1210.021).
iSAP consists of three programs, written in IDL, which together are useful for spherical data analysis. MR/S (MultiResolution on the Sphere) contains routines for wavelet, ridgelet and curvelet transform on the sphere, and applications such denoising on the sphere using wavelets and/or curvelets, Gaussianity tests and Independent Component Analysis on the Sphere. MR/S has been designed for the PLANCK project, but can be used for many other applications. SparsePol (Polarized Spherical Wavelets and Curvelets) has routines for polarized wavelet, polarized ridgelet and polarized curvelet transform on the sphere, and applications such denoising on the sphere using wavelets and/or curvelets, Gaussianity tests and blind source separation on the Sphere. SparsePol has been designed for the PLANCK project. MS-VSTS (Multi-Scale Variance Stabilizing Transform on the Sphere), designed initially for the FERMI project, is useful for spherical mono-channel and multi-channel data analysis when the data are contaminated by a Poisson noise. It contains routines for wavelet/curvelet denoising, wavelet deconvolution, multichannel wavelet denoising and deconvolution.
ISAP, written in IDL, simplifies the process of visualizing, subsetting, shifting, rebinning, masking, combining scans with weighted means or medians, filtering, and smoothing Auto Analysis Results (AARs) from post-pipeline processing of the Infrared Space Observatory's (ISO) Short Wavelength Spectrometer (SWS) and Long Wavelength Spectrometer (LWS) data. It can also be applied to PHOT-S and CAM-CVF data, and data from practically any spectrometer. The result of a typical ISAP session is expected to be a "simple spectrum" (single-valued spectrum which may be resampled to a uniform wavelength separation if desired) that can be further analyzed and measured either with other ISAP functions, native IDL functions, or exported to other analysis package (e.g., IRAF, MIDAS) if desired. ISAP provides many tools for further analysis, line-fitting, and continuum measurements, such as routines for unit conversions, conversions from wavelength space to frequency space, line and continuum fitting, flux measurement, synthetic photometry and models such as a zodiacal light model to predict and subtract the dominant foreground at some wavelengths.
Isca provides a framework for the idealized modeling of the global circulation of planetary atmospheres at varying levels of complexity and realism. Though Isca is an outgrowth of models designed for Earth's atmosphere, it may readily be extended into other planetary regimes. Various forcing and radiation options are available. At the simple end of the spectrum a Held-Suarez case is available. An idealized grey radiation scheme, a grey scheme with moisture feedback, a two-band scheme and a multi-band scheme are also available, all with simple moist effects and astronomically-based solar forcing. At the complex end of the spectrum the framework provides a direct connection to comprehensive atmospheric general circulation models.
iSEDfit uses Bayesian inference to extract the physical properties of galaxies from their observed broadband photometric spectral energy distribution (SED). In its default mode, the inputs to iSEDfit are the measured photometry (fluxes and corresponding inverse variances) and a measurement of the galaxy redshift. Alternatively, iSEDfit can be used to estimate photometric redshifts from the input photometry alone.
After the priors have been specified, iSEDfit calculates the marginalized posterior probability distributions for the physical parameters of interest, including the stellar mass, star-formation rate, dust content, star formation history, and stellar metallicity. iSEDfit also optionally computes K-corrections and produces multiple "quality assurance" (QA) plots at each stage of the modeling procedure to aid in the interpretation of the prior parameter choices and subsequent fitting results. The software is distributed as part of the impro IDL suite.
ISIS is a complete package to process CCD images using the image Optimal subtraction method (Alard & Lupton 1998, Alard 1999). The ISIS package can find the best kernel solution even in case of kernel variations as a function of position in the image. The relevant computing time is minimal in this case and is only slightly different from finding constant kernel solutions. ISIS includes as well a number of facilities to compute the light curves of variables objects from the subtracted images. The basic routines required to build the reference frame and make the image registration are also provided in the package.
ISIS, the Interactive Spectral Interpretation System, is designed to facilitate the interpretation and analysis of high resolution X-ray spectra. It is being developed as a programmable, interactive tool for studying the physics of X-ray spectrum formation, supporting measurement and identification of spectral features, and interaction with a database of atomic structure parameters and plasma emission models.
ISO transforms MESA history files into a uniform basis for interpolation and then constructs new stellar evolution tracks and isochrones from that basis. It is written in Fortran and requires MESA (ascl:1010.083), primarily for interpolation. Though designed to ingest MESA star history files, tracks from other stellar evolution codes can be incorporated by loading the tracks into the data structures used in the codes.
Isochrones, written in Python, simplifies common tasks often done with stellar model grids, such as simulating synthetic stellar populations, plotting evolution tracks or isochrones, or estimating the physical properties of a star given photometric and/or spectroscopic observations.
iSpec is an integrated software framework written in Python for the treatment and analysis of stellar spectra and abundances. Spectra treatment functions include cosmic rays removal, continuum normalization, resolution degradation, and telluric lines identification. It can also perform radial velocity determination and correction and resampling. iSpec can also determine atmospheric parameters (i.e effective temperature, surface gravity, metallicity, micro/macroturbulence, rotation) and individual chemical abundances by using either the synthetic spectra fitting technique or equivalent widths method. The synthesis is performed with SPECTRUM (ascl:9910.002).
ISPy3 is a collection of Python routines that can be used to model and analyse integrated-light spectra of stars and stellar populations. The actual spectral modelling and related tasks (setting up model atmospheres, etc) is done via external codes. Currently, the Kurucz codes (ATLAS/SYNTHE) and MARCS/TurboSpectrum are supported.
ISW and Weak Lensing Likelihood code is the likelihood code that calculates the likelihood of Integrated Sachs Wolfe and Weak Lensing of Cosmic Microwave Background using the WMAP 3year CMB maps with mass tracers such as 2MASS (2-Micron All Sky Survey), SDSS LRG (Sloan Digital Sky Survey Luminous Red Galaxies), SDSS QSOs (Sloan Digital Sky Survey Quasars) and NVSS (NRAO VLA All Sky Survey) radio sources. The details of the analysis (*thus the likelihood code) can be understood by reading the papers ISW paper and Weak lensing paper. The code does brute force theoretical matter power spectrum and calculations with CAMB. See the paper for an introduction, descriptions, and typical results from some pre-WMAP data. The code is designed to be integrated into CosmoMC. For further information concerning the integration, see Code Modification for integration into COSMOMC.
ITERA, the IDL Tool for Emission-line Ratio Analysis, is an IDL widget tool that allows you to plot ratios of any strong atomic and ionized emission lines as determined by standard photoionization and shock models. These "line ratio diagrams" can then be used to determine diagnostics for nebulae excitation mechanisms or nebulae parameters such as density, temperature, metallicity, etc. ITERA can also be used to determine line sensitivities to such parameters, compare observations with the models, or even estimate unobserved line fluxes.
IUEDR reduces IUE data. It addresses the problem of working from the IUE Guest Observer tape or disk file through to a calibrated spectrum that can be used in scientific analysis and is a complete system for IUE data reduction. IUEDR was distributed as part of the Starlink software collection (ascl:1110.012).
iWander assesses the origin of interstellar small bodies such as asteroids and comets. It includes a series of databases and tools that can be used in general for studying the dynamics of an interstellar vagabond object (small−body, interstellar spaceship and even stars).
Large-scale surveys have brought about a revolution in astronomy. To analyse the resulting wealth of data, we need automated tools to identify, classify, and quantify the important underlying structures. J plots can classify and quantify a pixelated structure, based on its principal moments of inertia. This enables us to automatically detect, and objectively compare, centrally condensed cores, elongated filaments, and hollow rings. A Python code is available on GitHub with examples of how to analyse 2D or 3D datasets, enabling an unbiased analysis and comparison of simulated and observed structures.
JAGS analyzes Bayesian hierarchical models using Markov Chain Monte Carlo (MCMC) simulation not wholly unlike BUGS. JAGS has three aims:
The Jeans Anisotropic MGE (JAM) modeling method uses the Multi-Gaussian Expansion parameterization for the galaxy surface brightness. The code allows for orbital anisotropy (three-integrals distribution function) and also provides the full second moment tensor, including proper motions and radial velocities.
JAVELIN (formerly known as SPEAR) is an approach to reverberation mapping that computes the lags between the AGN continuum and emission line light curves and their statistical confidence limits. It uses a damped random walk model to describe the quasar continuum variability and the ansatz that emission line variability is a scaled, smoothed and displaced version of the continuum. While currently configured only to simultaneously fit light curve means, it includes a general linear parameters formalism to fit more complex trends or calibration offsets. The noise matrix can be modified to allow for correlated errors, and the correlation matrix can be modified to use a different stochastic process. The transfer function model is presently a tophat, but this can be altered by changing the line-continuum covariance matrices. It is also able to cope with some problems in traditional reverberation mapping, such as irregular sampling, correlated errors and seasonal gaps.
JB2008 (Jacchia-Bowman 2008) is an empirical thermospheric density model developed as an improved revision to the Jacchia-Bowman 2006 model, based on Jacchia’s diffusion equations. Driving solar indices are computed from on-orbit sensor data, which are used for the solar irradiances in the extreme through far ultraviolet, including x-ray and Lyman-α wavelengths. Exospheric temperature equations are developed to represent the thermospheric EUV and FUV heating. Semiannual density equations based on multiple 81-day average solar indices are used to represent the variations in the semiannual density cycle that result from EUV heating, and geomagnetic storm effects are modeled using the Dst index as the driver of global density changes.
COADD was used to reduce photometry and continuum data from the UKT14 instrument on the James Clerk Maxwell Telescope in the 1990s. The software can co-add multiple observations and perform sigma clipping and Kolmogorov-Smirnov statistical analysis. Additional information on the software is available in the JCMT Spring 1993 newsletter (large PDF).
JCMTDR reduces continuum on-the-fly mapping data obtained with UKT14 or the heterodyne instruments using the IFD on the James Clerk Maxwell Telescope. This program reduces archive data and heterodyne beam maps and was distributed as part of the Starlink software collection (ascl:1110.012).
Written in Python, JetCurry models the 3D geometry of jets from 2-D images. JetCurry requires NumPy and SciPy and incorporates emcee (ascl:1303.002) and AstroPy (ascl:1304.002), and optionally uses VPython. From a defined initial part of the jet that serves as a reference point, JetCurry finds the position of highest flux within a bin of data in the image matrix and fits along the x axis for the general location of the bends in the jet. A spline fitting is used to smooth out the resulted jet stream.
JETGET accesses, visualizes, and analyses (magnetized-)fluid dynamics data stored in Hierarchical Data Format (HDF) and ASCII files. Although JETGET has been optimized to handle data output from jet simulations using the Zeus code (ascl:1306.014) from NCSA, it is also capable of analyzing other data output from simulations using other codes. JETGET can select variables from the data files, render both two- and three-dimensional graphics and analyze and plot important physical quantities. Graphics can be saved in encapsulated Postscript, JPEG, VRML, or saved into an MPEG for later visualization and/or presentations. The strength of JETGET in extracting the physics underlying such phenomena is demonstrated as well as its capabilities in visualizing the 3-dimensional features of the simulated magneto-hydrodynamic jets. The JETGET tool is written in Interactive Data Language (IDL) and uses a graphical user interface to manipulate the data. The tool was developed on a LINUX platform and can be run on any platform that supports IDL.
JetSeT is an open source C/Python framework to reproduce radiative and accelerative processes acting in relativistic jets, allowing to fit the numerical models to observed data. The main features of this framework are:
- Handling observed data: re-binning, definition of data sets, bindings to astropy tables and quantities
definition of complex numerical radiative scenarios: Synchrotron Self-Compton (SSC), external Compton
(EC) and EC against the CMB
- Constraining of the model in the pre-fitting stage, based on accurate and already published
phenomenological trends. In particular, starting from phenomenological parameters, such as spectral indices,
peak fluxes and frequencies, and spectral curvatures, that the code evaluates automatically, the pre-fitting
algorithm is able to provide a good starting model, following the phenomenological trends that I have
implemented. fitting of multiwavelength SEDs using both frequentist approach (iminuit) and bayesian MCMC
- Self-consistent temporal evolution of the plasma under the effect of radiative and accelerative processes,
both first order and second order (stochastic acceleration) processes.
JHelioview is open source visualization software for solar physics data. The JHelioviewer client application enables users to browse petabyte-scale image archives; the JHelioviewer server integrates a JPIP server, metadata catalog, and an event server. JHelioview uses the JPEG 2000 image compression standard, which provides efficient access to petabyte-scale image archives; JHelioviewer also allows users to locate and manipulate specific data sets.
The JKTEBOP code is used to fit a model to the light curves of detached eclipsing binary stars in order to derive the radii of the stars as well as various other quantities. It is very stable and includes extensive Monte Carlo or bootstrapping error analysis algorithms. It is also excellent for transiting extrasolar planetary systems. All input and output is done by text files; JKTEBOP is written in almost-standard FORTRAN 77 using first the g77 compiler and now the ifort compiler.
JKTLD outputs theoretically-calculated limb darkening (LD) strengths for equations (LD laws) which predict the amount of LD as a function of the part of the star being observed. The coefficients of these laws are obtained by bilinear interpolation (in effective temperature and surface gravity) in published tables of coefficients calculated from stellar model atmospheres by several researchers. Many observations of stars require the strength of limb darkening (LD) to be estimated, which can be done using theoretical models of stellar atmospheres; JKTLD can help in these circumstances.
JoXSZ jointly fits the thermodynamic profiles of galaxy clusters from both SZ and X-ray data using a Markov chain Monte Carlo fitting algorithm. It is an enhanced version of preprofit (ascl:1910.002), which fits only SZ data. JoXSZ parameterizes the pressure and electron density profile of a galaxy cluster with a given center and derives the temperature profile as the ratio of these quantities through the ideal gas law. The X-ray and SZ-based temperatures can be similar or different, which allows study of the cluster elongation along line of sight, gas clumping, or calibration uncertainties.
JPLephem loads and uses standard Jet Propulsion Laboratory (JPL) ephemerides for predicting the position and velocity of a planet or other Solar System body. It is one of the foundations of the Skyfield (ascl:1907.024) astronomy library for Python, and can also be used as a standalone package to generate raw vectors.
JSPAM models galaxy collisions using a restricted n-body approach to speed up computation. Instead of using a softened point-mass potential, the software supports a modified version of the three component potential created by Hernquist (1994, ApJS 86, 389). Although spherically symmetric gravitationally potentials and a Gaussian model for the bulge are used to increase computational efficiency, the potential mimics that of a fully consistent n-body model of a galaxy. Dynamical friction has been implemented in the code to improve the accuracy of close approaches between galaxies. Simulations using this code using thousands of particles over the typical interaction times of a galaxy interaction take a few seconds on modern desktop workstations, making it ideal for rapidly prototyping the dynamics of colliding galaxies. Extensive testing of the code has shown that it produces nearly identical tidal features to those from hierarchical tree codes such as Gadget but using a fraction of the computational resources. This code was used in the Galaxy Zoo: Mergers project and is very well suited for automated fitting of galaxy mergers with automated pattern fitting approaches such as genetic algorithms. Java and Fortran versions of the code are available.
JUDE (Jayant's UVIT Data Explorer) converts the Level 1 data (FITS binary table) from the Ultraviolet Imaging Telescope (UVIT) on ASTROSAT into three output files: a photon event list as a function of frame number (FITS binary table); a FITS image file with two extensions; and a PNG file created from the FITS image file with an automated scaling.
Juliet essentially serves as a wrapper of other tools, including Batman (ascl:1510.002), George (ascl:1511.015), Dynesty (ascl:1809.013) and AstroPy (ascl:1304.002), to analyze and model transits, radial-velocities, or both from multiple instruments at the same time. Using nested sampling algorithms, it performs a thorough sampling of the parameter space and a model comparison via Bayesian evidences. Juliet also fits transiting and non-transiting multi-planetary systems, and Gaussian Processes (GPs) which might share hyperparameters between the photometry and radial-velocities simultaneously (e.g., stellar rotation periods).
Jupiter is a multidimensional astrophysical hydrocode. It is based on a Godunov method, and it is parallelized with MPI. The mesh geometry can either be cartesian, cylindrical or spherical. It allows mesh refinement and includes special features adapted to the description of planets embedded in disks and nearly steady states.
Juwvid performs time-frequency analysis. Written in Julia, it uses a modified version of the Wigner distribution, the pseudo Wigner distribution, and the short-time Fourier transform from MATLAB GPL programs, tftb-0.2. The modification includes the zero-padding FFT, the non-uniform FFT, the adaptive algorithm by Stankovic, Dakovic, Thayaparan 2013, the S-method, the L-Wigner distribution, and the polynomial Wigner-Ville distribution.
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