67,619 research outputs found
Analysis, Visualization, and Transformation of Audio Signals Using Dictionary-based Methods
date-added: 2014-01-07 09:15:58 +0000 date-modified: 2014-01-07 09:15:58 +0000date-added: 2014-01-07 09:15:58 +0000 date-modified: 2014-01-07 09:15:58 +000
Data-Driven Time-Frequency Analysis
In this paper, we introduce a new adaptive data analysis method to study
trend and instantaneous frequency of nonlinear and non-stationary data. This
method is inspired by the Empirical Mode Decomposition method (EMD) and the
recently developed compressed (compressive) sensing theory. The main idea is to
look for the sparsest representation of multiscale data within the largest
possible dictionary consisting of intrinsic mode functions of the form , where , consists of the
functions smoother than and . This problem can
be formulated as a nonlinear optimization problem. In order to solve this
optimization problem, we propose a nonlinear matching pursuit method by
generalizing the classical matching pursuit for the optimization problem.
One important advantage of this nonlinear matching pursuit method is it can be
implemented very efficiently and is very stable to noise. Further, we provide a
convergence analysis of our nonlinear matching pursuit method under certain
scale separation assumptions. Extensive numerical examples will be given to
demonstrate the robustness of our method and comparison will be made with the
EMD/EEMD method. We also apply our method to study data without scale
separation, data with intra-wave frequency modulation, and data with incomplete
or under-sampled data
Nonlinear approximation with nonstationary Gabor frames
We consider sparseness properties of adaptive time-frequency representations
obtained using nonstationary Gabor frames (NSGFs). NSGFs generalize classical
Gabor frames by allowing for adaptivity in either time or frequency. It is
known that the concept of painless nonorthogonal expansions generalizes to the
nonstationary case, providing perfect reconstruction and an FFT based
implementation for compactly supported window functions sampled at a certain
density. It is also known that for some signal classes, NSGFs with flexible
time resolution tend to provide sparser expansions than can be obtained with
classical Gabor frames. In this article we show, for the continuous case, that
sparseness of a nonstationary Gabor expansion is equivalent to smoothness in an
associated decomposition space. In this way we characterize signals with sparse
expansions relative to NSGFs with flexible time resolution. Based on this
characterization we prove an upper bound on the approximation error occurring
when thresholding the coefficients of the corresponding frame expansions. We
complement the theoretical results with numerical experiments, estimating the
rate of approximation obtained from thresholding the coefficients of both
stationary and nonstationary Gabor expansions.Comment: 19 pages, 2 figure
Fast Dictionary Learning for Sparse Representations of Speech Signals
© 2011 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. Published version: IEEE Journal of Selected Topics in Signal Processing 5(5): 1025-1031, Sep 2011. DOI: 10.1109/JSTSP.2011.2157892
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