3,036 research outputs found
Modern Methods of Time-Frequency Warping of Sound Signals
Tato práce se zabĂ˝vá reprezentacĂ nestacionárnĂch harmonickĂ˝ch signálĹŻ s ÄŤasovÄ› promÄ›nnĂ˝mi komponentami. PrimárnÄ› je zaměřena na Harmonickou transformaci a jeji variantu se subkvadratickou vĂ˝poÄŤetnĂ sloĹľitostĂ, Rychlou harmonickou transformaci. V tĂ©to práci jsou prezentovány dva algoritmy vyuĹľĂvajĂcĂ Rychlou harmonickou transformaci. Prvni pouĹľĂvá jako metodu odhadu zmÄ›ny základnĂho kmitoÄŤtu sbĂranĂ© logaritmickĂ© spektrum a druhá pouĹľĂvá metodu analĂ˝zy syntĂ©zou. Oba algoritmy jsou pouĹľity k analĂ˝ze Ĺ™eÄŤovĂ©ho segmentu pro porovnánĂ vystupĹŻ. Nakonec je algoritmus vyuĹľĂvajĂcĂ metody analĂ˝zy syntĂ©zou pouĹľit na reálnĂ© zvukovĂ© signály, aby bylo moĹľnĂ© změřit zlepšenĂ reprezentace kmitoÄŤtovÄ› modulovanĂ˝ch signálĹŻ za pouĹľitĂ HarmonickĂ© transformace.This thesis deals with representation of non-stationary harmonic signals with time-varying components. Its main focus is aimed at Harmonic Transform and its variant with subquadratic computational complexity, the Fast Harmonic Transform. Two algorithms using the Fast Harmonic Transform are presented. The first uses the gathered log-spectrum as fundamental frequency change estimation method, the second uses analysis-by-synthesis approach. Both algorithms are used on a speech segment to compare its output. Further the analysis-by-synthesis algorithm is applied on several real sound signals to measure the increase in the ability to represent real frequency-modulated signals using the Harmonic Transform.
Parametric Regression on the Grassmannian
We address the problem of fitting parametric curves on the Grassmann manifold
for the purpose of intrinsic parametric regression. As customary in the
literature, we start from the energy minimization formulation of linear
least-squares in Euclidean spaces and generalize this concept to general
nonflat Riemannian manifolds, following an optimal-control point of view. We
then specialize this idea to the Grassmann manifold and demonstrate that it
yields a simple, extensible and easy-to-implement solution to the parametric
regression problem. In fact, it allows us to extend the basic geodesic model to
(1) a time-warped variant and (2) cubic splines. We demonstrate the utility of
the proposed solution on different vision problems, such as shape regression as
a function of age, traffic-speed estimation and crowd-counting from
surveillance video clips. Most notably, these problems can be conveniently
solved within the same framework without any specifically-tailored steps along
the processing pipeline.Comment: 14 pages, 11 figure
Velocity estimation via registration-guided least-squares inversion
This paper introduces an iterative scheme for acoustic model inversion where
the notion of proximity of two traces is not the usual least-squares distance,
but instead involves registration as in image processing. Observed data are
matched to predicted waveforms via piecewise-polynomial warpings, obtained by
solving a nonconvex optimization problem in a multiscale fashion from low to
high frequencies. This multiscale process requires defining low-frequency
augmented signals in order to seed the frequency sweep at zero frequency.
Custom adjoint sources are then defined from the warped waveforms. The proposed
velocity updates are obtained as the migration of these adjoint sources, and
cannot be interpreted as the negative gradient of any given objective function.
The new method, referred to as RGLS, is successfully applied to a few scenarios
of model velocity estimation in the transmission setting. We show that the new
method can converge to the correct model in situations where conventional
least-squares inversion suffers from cycle-skipping and converges to a spurious
model.Comment: 20 pages, 13 figures, 1 tabl
Modeling Non-Stationary Processes Through Dimension Expansion
In this paper, we propose a novel approach to modeling nonstationary spatial
fields. The proposed method works by expanding the geographic plane over which
these processes evolve into higher dimensional spaces, transforming and
clarifying complex patterns in the physical plane. By combining aspects of
multi-dimensional scaling, group lasso, and latent variables models, a
dimensionally sparse projection is found in which the originally nonstationary
field exhibits stationarity. Following a comparison with existing methods in a
simulated environment, dimension expansion is studied on a classic test-bed
data set historically used to study nonstationary models. Following this, we
explore the use of dimension expansion in modeling air pollution in the United
Kingdom, a process known to be strongly influenced by rural/urban effects,
amongst others, which gives rise to a nonstationary field
- …