4 research outputs found
Frame Theory for Signal Processing in Psychoacoustics
This review chapter aims to strengthen the link between frame theory and
signal processing tasks in psychoacoustics. On the one side, the basic concepts
of frame theory are presented and some proofs are provided to explain those
concepts in some detail. The goal is to reveal to hearing scientists how this
mathematical theory could be relevant for their research. In particular, we
focus on frame theory in a filter bank approach, which is probably the most
relevant view-point for audio signal processing. On the other side, basic
psychoacoustic concepts are presented to stimulate mathematicians to apply
their knowledge in this field
Local signal decomposition based methods for the calculation of three-dimensional scalar optical diffraction field due to a field given on a curved surface
Ankara : The Department of Electrical and Electronics Engineering and the Graduate School of Engineering and Science of Bilkent University, 2013.Thesis (Ph. D.) -- Bilkent University, 2013.Includes bibliographical references leaves 122-130.A three-dimensional scene or object can be optically replicated via the threedimensional
imaging and display method holography. In computer-generated
holography, the scalar diffraction field due to a field given on an object (curved
surface) is calculated numerically. The source model approaches treat the building
elements of the object (such as points or planar polygons) independently to
simplify the calculation of diffraction field. However, as a tradeoff, the accuracies
of fields calculated by such methods are degraded. On the other hand,
field models provide exact field solutions but their computational complexities
make their application impractical for meaningful sizes of surfaces. By using
the practical setup of the integral imaging, we establish a space-frequency signal
decomposition based relation between the ray optics (more specifically the
light field representation) and the scalar wave optics. Then, by employing the
uncertainty principle inherent to this space-frequency decomposition, we derive an upper bound for the joint spatial and angular (spectral) resolution of a physically
realizable light field representation. We mainly propose two methods for
the problem of three-dimensional diffraction field calculation from fields given
on curved surfaces. In the first approach, we apply linear space-frequency signal
decomposition methods to the two-dimensional field given on the curved
surface and decompose it into a sum of local elementary functions. Then, we
write the diffraction field as a sum of local beams each of which corresponds to
such an elementary function on the curved surface. By this way, we increase
the accuracy provided by the source models while keeping the computational
complexity at comparable levels. In the second approach, we firstly decompose
the three-dimensional field into a sum of local beams, and then, we construct a
linear system of equations where we form the system matrix by calculating the
field patterns that the three-dimensional beams produce on the curved surface.
We find the coefficients of the beams by solving the linear system of equations
and thus specify the three-dimensional field. Since we use local beams in threedimensional
field decomposition, we end up with sparse system matrices. Hence,
by taking advantage of this sparsity, we achieve considerable reduction in computational
complexity and memory requirement compared to other field model
approaches that use global signal decompositions. The local Gaussian beams
used in both approaches actually correspond to physically realizable light rays.
Indeed, the upper joint resolution bound that we derive is obtained by such
Gaussian beams.Şahin, ErdemPh.D