3,175 research outputs found
Higher-Order Properties of Analytic Wavelets
The influence of higher-order wavelet properties on the analytic wavelet
transform behavior is investigated, and wavelet functions offering advantageous
performance are identified. This is accomplished through detailed investigation
of the generalized Morse wavelets, a two-parameter family of exactly analytic
continuous wavelets. The degree of time/frequency localization, the existence
of a mapping between scale and frequency, and the bias involved in estimating
properties of modulated oscillatory signals, are proposed as important
considerations. Wavelet behavior is found to be strongly impacted by the degree
of asymmetry of the wavelet in both the frequency and the time domain, as
quantified by the third central moments. A particular subset of the generalized
Morse wavelets, recognized as deriving from an inhomogeneous Airy function,
emerge as having particularly desirable properties. These "Airy wavelets"
substantially outperform the only approximately analytic Morlet wavelets for
high time localization. Special cases of the generalized Morse wavelets are
examined, revealing a broad range of behaviors which can be matched to the
characteristics of a signal.Comment: 15 pages, 6 Postscript figure
Generalized Morse Wavelets as a Superfamily of Analytic Wavelets
The generalized Morse wavelets are shown to constitute a superfamily that
essentially encompasses all other commonly used analytic wavelets, subsuming
eight apparently distinct types of analysis filters into a single common form.
This superfamily of analytic wavelets provides a framework for systematically
investigating wavelet suitability for various applications. In addition to a
parameter controlling the time-domain duration or Fourier-domain bandwidth, the
wavelet {\em shape} with fixed bandwidth may be modified by varying a second
parameter, called . For integer values of , the most symmetric,
most nearly Gaussian, and generally most time-frequency concentrated member of
the superfamily is found to occur for . These wavelets, known as
"Airy wavelets," capture the essential idea of popular Morlet wavelet, while
avoiding its deficiencies. They may be recommended as an ideal starting point
for general purpose use
On the Analytic Wavelet Transform
An exact and general expression for the analytic wavelet transform of a
real-valued signal is constructed, resolving the time-dependent effects of
non-negligible amplitude and frequency modulation. The analytic signal is first
locally represented as a modulated oscillation, demodulated by its own
instantaneous frequency, and then Taylor-expanded at each point in time. The
terms in this expansion, called the instantaneous modulation functions, are
time-varying functions which quantify, at increasingly higher orders, the local
departures of the signal from a uniform sinusoidal oscillation. Closed-form
expressions for these functions are found in terms of Bell polynomials and
derivatives of the signal's instantaneous frequency and bandwidth. The analytic
wavelet transform is shown to depend upon the interaction between the signal's
instantaneous modulation functions and frequency-domain derivatives of the
wavelet, inducing a hierarchy of departures of the transform away from a
perfect representation of the signal. The form of these deviation terms
suggests a set of conditions for matching the wavelet properties to suit the
variability of the signal, in which case our expressions simplify considerably.
One may then quantify the time-varying bias associated with signal estimation
via wavelet ridge analysis, and choose wavelets to minimize this bias
Analysis of Modulated Multivariate Oscillations
The concept of a common modulated oscillation spanning multiple time series
is formalized, a method for the recovery of such a signal from potentially
noisy observations is proposed, and the time-varying bias properties of the
recovery method are derived. The method, an extension of wavelet ridge analysis
to the multivariate case, identifies the common oscillation by seeking, at each
point in time, a frequency for which a bandpassed version of the signal obtains
a local maximum in power. The lowest-order bias is shown to involve a quantity,
termed the instantaneous curvature, which measures the strength of local
quadratic modulation of the signal after demodulation by the common oscillation
frequency. The bias can be made to be small if the analysis filter, or wavelet,
can be chosen such that the signal's instantaneous curvature changes little
over the filter time scale. An application is presented to the detection of
vortex motions in a set of freely-drifting oceanographic instruments tracking
the ocean currents
On the relation between sSFR and metallicity
In this paper we present an exact general analytic expression
linking the gas metallicity Z to the specific
star formation rate (sSFR), that validates and extends the approximate relation
put forward by Lilly et al. (2013, L13), where is the yield per stellar
generation, is the instantaneous ratio between inflow and star
formation rate expressed as a function of the sSFR, and is the integral of
the past enrichment history, respectively. We then demonstrate that the
instantaneous metallicity of a self-regulating system, such that its sSFR
decreases with decreasing redshift, can be well approximated by the first term
on the right-hand side in the above formula, which provides an upper bound to
the metallicity. The metallicity is well approximated also by the L13 ideal
regulator case, which provides a lower bound to the actual metallicity. We
compare these approximate analytic formulae to numerical results and infer a
discrepancy <0.1 dex in a range of metallicities and almost three orders of
magnitude in the sSFR. We explore the consequences of the L13 model on the
mass-weighted metallicity in the stellar component of the galaxies. We find
that the stellar average metallicity lags 0.1-0.2 dex behind the gas-phase
metallicity relation, in agreement with the data. (abridged)Comment: 14 pages, 6 figures, MNRAS accepte
Frequency-Domain Stochastic Modeling of Stationary Bivariate or Complex-Valued Signals
There are three equivalent ways of representing two jointly observed
real-valued signals: as a bivariate vector signal, as a single complex-valued
signal, or as two analytic signals known as the rotary components. Each
representation has unique advantages depending on the system of interest and
the application goals. In this paper we provide a joint framework for all three
representations in the context of frequency-domain stochastic modeling. This
framework allows us to extend many established statistical procedures for
bivariate vector time series to complex-valued and rotary representations.
These include procedures for parametrically modeling signal coherence,
estimating model parameters using the Whittle likelihood, performing
semi-parametric modeling, and choosing between classes of nested models using
model choice. We also provide a new method of testing for impropriety in
complex-valued signals, which tests for noncircular or anisotropic second-order
statistical structure when the signal is represented in the complex plane.
Finally, we demonstrate the usefulness of our methodology in capturing the
anisotropic structure of signals observed from fluid dynamic simulations of
turbulence.Comment: To appear in IEEE Transactions on Signal Processin
Oxygen Gas Abundances at 0.4<z<1.5: Implications for the Chemical Evolution History of Galaxies
We report VLT-ISAAC and Keck-NIRSPEC near-infrared spectroscopy for a sample
of 30 0.47<z<0.92 CFRS galaxies and five [OII]-selected, M_B,AB<-21.5, z~1.4
galaxies. We have measured Halpha and [NII] line fluxes for the CFRS galaxies
which have [OII], Hbeta and [OIII] line fluxes available from optical
spectroscopy. For the z~1.4 objects we measured Hbeta and [OIII] emission line
fluxes from J-band spectra, and Halpha line fluxes plus upper limits for [NII]
fluxes from H-band spectra. We derive the extinction and oxygen abundances for
the sample using a method based on a set of ionisation parameter and oxygen
abundance diagnostics, simultaneously fitting the [OII], Hbeta, [OIII], Halpha
and [NII] line fluxes. Our most salient conclusions are: a) the source of gas
ionisation in the 30 CFRS and in all z~1.4 galaxies is not due to AGN activity;
b) about one third of the 0.47<z<0.92 CFRS galaxies in our sample have
substantially lower metallicities than local galaxies with similar luminosities
and star formation rates; c) comparison with a chemical evolution model
indicates that these low metallicity galaxies are unlikely to be the
progenitors of metal-poor dwarf galaxies at z~0, but more likely the
progenitors of massive spirals; d) the z~1.4 galaxies are characterized by the
high [OIII]/[OII] line ratios, low extinction and low metallicity that are
typical of lower luminosity CADIS galaxies at 0.4<z<0.7, and of more luminous
Lyman Break Galaxies at z~3.1, but not seen in CFRS galaxies at 0.4<z<1.0; e)
the properties of the z~1.4 galaxies suggest that the period of rapid chemical
evolution takes place progressively in lower mass systems as the universe ages,
and thus provides further support for a downsizing picture of galaxy formation,
at least from z~1.4 to today.Comment: Proceedings contribution for "The Fabulous Destiny of Galaxies;
Bridging Past and Present", Marseille, 200
A Power Variance Test for Nonstationarity in Complex-Valued Signals
We propose a novel algorithm for testing the hypothesis of nonstationarity in
complex-valued signals. The implementation uses both the bootstrap and the Fast
Fourier Transform such that the algorithm can be efficiently implemented in
O(NlogN) time, where N is the length of the observed signal. The test procedure
examines the second-order structure and contrasts the observed power variance -
i.e. the variability of the instantaneous variance over time - with the
expected characteristics of stationary signals generated via the bootstrap
method. Our algorithmic procedure is capable of learning different types of
nonstationarity, such as jumps or strong sinusoidal components. We illustrate
the utility of our test and algorithm through application to turbulent flow
data from fluid dynamics
Near-Infrared Spectroscopy of 0.4<z<1.0 CFRS Galaxies: Oxygen Abundances, SFRs and Dust
Using new J-band VLT-ISAAC and Keck-NIRSPEC spectroscopy, we have measured
Halpha and [NII] line fluxes for 0.47<z<0.92 CFRS galaxies which have [OII],
Hbeta and [OIII]a line fluxes available from optical spectroscopy, to
investigate how the properties of the star forming gas in galaxies evolve with
redshift. We derive the extinction and oxygen abundances for the sample using a
method based on a set of ionisation parameter and oxygen abundance diagnostics,
simultaneously fitting the [OII], Hbeta,[OIII], Halpha, and [NII] line fluxes.
The individual reddening measurements allow us to accurately correct the
Halpha-based star formation rate (SFR) estimates for extinction. Our most
salient conclusions are: a) in all 30 CFRS galaxies the source of gas
ionisation is not due to AGN activity; b) we find a range of 0<AV<3, suggesting
that it is important to determine the extinction for every single galaxy in
order to reliably measure SFRs and oxygen abundances in high redshift galaxies;
c) high values of [NII]/Halpha >0.1 for most (but not all) of the CFRS galaxies
indicate that they lie on the high-metallicity branch of the R23 calibration;
d) about one third of the 0.47<z<0.92 CFRS galaxies in our sample have lower
metallicities than local galaxies with similar luminosities and star formation
rates; e) comparison with a chemical evolution model indicates that these low
metallicity galaxies are unlikely to be the progenitors of metal-poor dwarf
galaxies at z~0.Comment: Accepted for publication in the Astrophysical Journa
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