1,800 research outputs found
ESPRIT for multidimensional general grids
We present a new method for complex frequency estimation in several
variables, extending the classical (1d) ESPRIT-algorithm. We also consider how
to work with data sampled on non-standard domains (i.e going beyond
multi-rectangles)
High-resolution sinusoidal analysis for resolving harmonic collisions in music audio signal processing
Many music signals can largely be considered an additive combination of
multiple sources, such as musical instruments or voice. If the musical sources
are pitched instruments, the spectra they produce are predominantly harmonic,
and are thus well suited to an additive sinusoidal model. However,
due to resolution limits inherent in time-frequency analyses, when the harmonics
of multiple sources occupy equivalent time-frequency regions, their
individual properties are additively combined in the time-frequency representation
of the mixed signal. Any such time-frequency point in a mixture
where multiple harmonics overlap produces a single observation from which
the contributions owed to each of the individual harmonics cannot be trivially
deduced. These overlaps are referred to as overlapping partials or harmonic
collisions. If one wishes to infer some information about individual sources in
music mixtures, the information carried in regions where collided harmonics
exist becomes unreliable due to interference from other sources. This interference
has ramifications in a variety of music signal processing applications
such as multiple fundamental frequency estimation, source separation, and
instrumentation identification.
This thesis addresses harmonic collisions in music signal processing applications.
As a solution to the harmonic collision problem, a class of signal
subspace-based high-resolution sinusoidal parameter estimators is explored.
Specifically, the direct matrix pencil method, or equivalently, the Estimation
of Signal Parameters via Rotational Invariance Techniques (ESPRIT)
method, is used with the goal of producing estimates of the salient parameters
of individual harmonics that occupy equivalent time-frequency regions. This
estimation method is adapted here to be applicable to time-varying signals
such as musical audio. While high-resolution methods have been previously
explored in the context of music signal processing, previous work has not
addressed whether or not such methods truly produce high-resolution sinusoidal parameter estimates in real-world music audio signals. Therefore, this
thesis answers the question of whether high-resolution sinusoidal parameter
estimators are really high-resolution for real music signals.
This work directly explores the capabilities of this form of sinusoidal parameter
estimation to resolve collided harmonics. The capabilities of this
analysis method are also explored in the context of music signal processing
applications. Potential benefits of high-resolution sinusoidal analysis are
examined in experiments involving multiple fundamental frequency estimation
and audio source separation. This work shows that there are indeed
benefits to high-resolution sinusoidal analysis in music signal processing applications,
especially when compared to methods that produce sinusoidal
parameter estimates based on more traditional time-frequency representations.
The benefits of this form of sinusoidal analysis are made most evident
in multiple fundamental frequency estimation applications, where substantial
performance gains are seen. High-resolution analysis in the context of
computational auditory scene analysis-based source separation shows similar
performance to existing comparable methods
Super-resolution, Extremal Functions and the Condition Number of Vandermonde Matrices
Super-resolution is a fundamental task in imaging, where the goal is to
extract fine-grained structure from coarse-grained measurements. Here we are
interested in a popular mathematical abstraction of this problem that has been
widely studied in the statistics, signal processing and machine learning
communities. We exactly resolve the threshold at which noisy super-resolution
is possible. In particular, we establish a sharp phase transition for the
relationship between the cutoff frequency () and the separation ().
If , our estimator converges to the true values at an inverse
polynomial rate in terms of the magnitude of the noise. And when no estimator can distinguish between a particular pair of
-separated signals even if the magnitude of the noise is exponentially
small.
Our results involve making novel connections between {\em extremal functions}
and the spectral properties of Vandermonde matrices. We establish a sharp phase
transition for their condition number which in turn allows us to give the first
noise tolerance bounds for the matrix pencil method. Moreover we show that our
methods can be interpreted as giving preconditioners for Vandermonde matrices,
and we use this observation to design faster algorithms for super-resolution.
We believe that these ideas may have other applications in designing faster
algorithms for other basic tasks in signal processing.Comment: 19 page
State Space-Based Method for the DOA Estimation by the Forward-Backward Data Matrix Using Small Snapshots
In this presentation, a new low computational burden method for the direction of arrival (DOA) estimation from noisy signal using small snapshots is presented. The approach introduces State Space-based Method (SSM) to represent the received array signal, and uses small snapshots directly to form the Hankel data matrix. Those Hankel data matrices are then utilized to construct forward-backward data matrix that is used to estimate the state space model parameters from which the DOA of the incident signals can be extracted. In contrast to existing methods, such as MUSIC, Root-MUSIC that use the covariance data matrix to estimate the DOA and the sparse representation (SR) based DOA which is obtained by solving the sparsest representation of the snapshots, the SSM algorithm employs forward-backward data matrix formed only using small snapshots and doesn't need additional spatial smoothing method to process coherent signals. Three numerical experiments are employed to compare the performance among the SSM, Root-MUSIC and SR-based method as well as Cramér–Rao bound (CRB). The simulation results demonstrate that when a small number of snapshots, even a single one, are used, the SSM always performs better than the other two method no matter under the circumstance of uncorrelated or correlated signal. The simulation results also show that the computational burden is reduced significantly and the number of antenna elements is saved greatly
Graph Spectral Image Processing
Recent advent of graph signal processing (GSP) has spurred intensive studies
of signals that live naturally on irregular data kernels described by graphs
(e.g., social networks, wireless sensor networks). Though a digital image
contains pixels that reside on a regularly sampled 2D grid, if one can design
an appropriate underlying graph connecting pixels with weights that reflect the
image structure, then one can interpret the image (or image patch) as a signal
on a graph, and apply GSP tools for processing and analysis of the signal in
graph spectral domain. In this article, we overview recent graph spectral
techniques in GSP specifically for image / video processing. The topics covered
include image compression, image restoration, image filtering and image
segmentation
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