28,174 research outputs found
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
Sparse Vector Autoregressive Modeling
The vector autoregressive (VAR) model has been widely used for modeling
temporal dependence in a multivariate time series. For large (and even
moderate) dimensions, the number of AR coefficients can be prohibitively large,
resulting in noisy estimates, unstable predictions and difficult-to-interpret
temporal dependence. To overcome such drawbacks, we propose a 2-stage approach
for fitting sparse VAR (sVAR) models in which many of the AR coefficients are
zero. The first stage selects non-zero AR coefficients based on an estimate of
the partial spectral coherence (PSC) together with the use of BIC. The PSC is
useful for quantifying the conditional relationship between marginal series in
a multivariate process. A refinement second stage is then applied to further
reduce the number of parameters. The performance of this 2-stage approach is
illustrated with simulation results. The 2-stage approach is also applied to
two real data examples: the first is the Google Flu Trends data and the second
is a time series of concentration levels of air pollutants.Comment: 39 pages, 7 figure
Compressive Parameter Estimation for Sparse Translation-Invariant Signals Using Polar Interpolation
We propose new compressive parameter estimation algorithms that make use of
polar interpolation to improve the estimator precision. Our work extends
previous approaches involving polar interpolation for compressive parameter
estimation in two aspects: (i) we extend the formulation from real non-negative
amplitude parameters to arbitrary complex ones, and (ii) we allow for mismatch
between the manifold described by the parameters and its polar approximation.
To quantify the improvements afforded by the proposed extensions, we evaluate
six algorithms for estimation of parameters in sparse translation-invariant
signals, exemplified with the time delay estimation problem. The evaluation is
based on three performance metrics: estimator precision, sampling rate and
computational complexity. We use compressive sensing with all the algorithms to
lower the necessary sampling rate and show that it is still possible to attain
good estimation precision and keep the computational complexity low. Our
numerical experiments show that the proposed algorithms outperform existing
approaches that either leverage polynomial interpolation or are based on a
conversion to a frequency-estimation problem followed by a super-resolution
algorithm. The algorithms studied here provide various tradeoffs between
computational complexity, estimation precision, and necessary sampling rate.
The work shows that compressive sensing for the class of sparse
translation-invariant signals allows for a decrease in sampling rate and that
the use of polar interpolation increases the estimation precision.Comment: 13 pages, 5 figures, to appear in IEEE Transactions on Signal
Processing; minor edits and correction
Interpolation of nonstationary high frequency spatial-temporal temperature data
The Atmospheric Radiation Measurement program is a U.S. Department of Energy
project that collects meteorological observations at several locations around
the world in order to study how weather processes affect global climate change.
As one of its initiatives, it operates a set of fixed but irregularly-spaced
monitoring facilities in the Southern Great Plains region of the U.S. We
describe methods for interpolating temperature records from these fixed
facilities to locations at which no observations were made, which can be useful
when values are required on a spatial grid. We interpolate by conditionally
simulating from a fitted nonstationary Gaussian process model that accounts for
the time-varying statistical characteristics of the temperatures, as well as
the dependence on solar radiation. The model is fit by maximizing an
approximate likelihood, and the conditional simulations result in
well-calibrated confidence intervals for the predicted temperatures. We also
describe methods for handling spatial-temporal jumps in the data to interpolate
a slow-moving cold front.Comment: Published in at http://dx.doi.org/10.1214/13-AOAS633 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Recommended from our members
The role of HG in the analysis of temporal iteration and interaural correlation
An evaluation of intrusive instrumental intelligibility metrics
Instrumental intelligibility metrics are commonly used as an alternative to
listening tests. This paper evaluates 12 monaural intrusive intelligibility
metrics: SII, HEGP, CSII, HASPI, NCM, QSTI, STOI, ESTOI, MIKNN, SIMI, SIIB, and
. In addition, this paper investigates the ability of
intelligibility metrics to generalize to new types of distortions and analyzes
why the top performing metrics have high performance. The intelligibility data
were obtained from 11 listening tests described in the literature. The stimuli
included Dutch, Danish, and English speech that was distorted by additive
noise, reverberation, competing talkers, pre-processing enhancement, and
post-processing enhancement. SIIB and HASPI had the highest performance
achieving a correlation with listening test scores on average of
and , respectively. The high performance of SIIB may, in part, be
the result of SIIBs developers having access to all the intelligibility data
considered in the evaluation. The results show that intelligibility metrics
tend to perform poorly on data sets that were not used during their
development. By modifying the original implementations of SIIB and STOI, the
advantage of reducing statistical dependencies between input features is
demonstrated. Additionally, the paper presents a new version of SIIB called
, which has similar performance to SIIB and HASPI,
but takes less time to compute by two orders of magnitude.Comment: Published in IEEE/ACM Transactions on Audio, Speech, and Language
Processing, 201
- …