10,675 research outputs found
Fast Algorithms for the computation of Fourier Extensions of arbitrary length
Fourier series of smooth, non-periodic functions on are known to
exhibit the Gibbs phenomenon, and exhibit overall slow convergence. One way of
overcoming these problems is by using a Fourier series on a larger domain, say
with , a technique called Fourier extension or Fourier
continuation. When constructed as the discrete least squares minimizer in
equidistant points, the Fourier extension has been shown shown to converge
geometrically in the truncation parameter . A fast algorithm has been described to compute Fourier extensions for the case
where , compared to for solving the dense discrete
least squares problem. We present two algorithms for
the computation of these approximations for the case of general , made
possible by exploiting the connection between Fourier extensions and Prolate
Spheroidal Wave theory. The first algorithm is based on the explicit
computation of so-called periodic discrete prolate spheroidal sequences, while
the second algorithm is purely algebraic and only implicitly based on the
theory
Optimal-Dimensionality Sampling on the Sphere: Improvements and Variations
For the accurate representation and reconstruction of band-limited signals on
the sphere, an optimal-dimensionality sampling scheme has been recently
proposed which requires the optimal number of samples equal to the number of
degrees of freedom of the signal in the spectral (harmonic) domain. The
computation of the spherical harmonic transform (SHT) associated with the
optimal-dimensionality sampling requires the inversion of a series of linear
systems in an iterative manner. The stability of the inversion depends on the
placement of iso-latitude rings of samples along co-latitude. In this work, we
have developed a method to place these iso-latitude rings of samples with the
objective of improving the well-conditioning of the linear systems involved in
the computation of the SHT. We also propose a multi-pass SHT algorithm to
iteratively improve the accuracy of the SHT of band-limited signals.
Furthermore, we review the changes in the computational complexity and
improvement in accuracy of the SHT with the embedding of the proposed methods.
Through numerical experiments, we illustrate that the proposed variations and
improvements in the SHT algorithm corresponding to the optimal-dimensionality
sampling scheme significantly enhance the accuracy of the SHT.Comment: 5 Pages, 4 figure
FFT Interpolation from Nonuniform Samples Lying in a Regular Grid
This paper presents a method to interpolate a periodic band-limited signal
from its samples lying at nonuniform positions in a regular grid, which is
based on the FFT and has the same complexity order as this last algorithm. This
kind of interpolation is usually termed "the missing samples problem" in the
literature, and there exists a wide variety of iterative and direct methods for
its solution. The one presented in this paper is a direct method that exploits
the properties of the so-called erasure polynomial, and it provides a
significant improvement on the most efficient method in the literature, which
seems to be the burst error recovery (BER) technique of Marvasti's et al. The
numerical stability and complexity of the method are evaluated numerically and
compared with the pseudo-inverse and BER solutions.Comment: Submitted to the IEEE Transactions on Signal Processin
Eulerian method for multiphase interactions of soft solid bodies in fluids
We introduce an Eulerian approach for problems involving one or more soft
solids immersed in a fluid, which permits mechanical interactions between all
phases. The reference map variable is exploited to simulate finite-deformation
constitutive relations in the solid(s) on the same fixed grid as the fluid
phase, which greatly simplifies the coupling between phases. Our coupling
procedure, a key contribution in the current work, is shown to be
computationally faster and more stable than an earlier approach, and admits the
ability to simulate both fluid--solid and solid--solid interaction between
submerged bodies. The interface treatment is demonstrated with multiple
examples involving a weakly compressible Navier--Stokes fluid interacting with
a neo-Hookean solid, and we verify the method's convergence. The solid contact
method, which exploits distance-measures already existing on the grid, is
demonstrated with two examples. A new, general routine for cross-interface
extrapolation is introduced and used as part of the new interfacial treatment
ワイヤレス通信のための先進的な信号処理技術を用いた非線形補償法の研究
The inherit nonlinearity in analogue front-ends of transmitters and receivers have had primary impact on the overall performance of the wireless communication systems, as it gives arise of substantial distortion when transmitting and processing signals with such circuits. Therefore, the nonlinear compensation (linearization) techniques become essential to suppress the distortion to an acceptable extent in order to ensure sufficient low bit error rate. Furthermore, the increasing demands on higher data rate and ubiquitous interoperability between various multi-coverage protocols are two of the most important features of the contemporary communication system. The former demand pushes the communication system to use wider bandwidth and the latter one brings up severe coexistence problems. Having fully considered the problems raised above, the work in this Ph.D. thesis carries out extensive researches on the nonlinear compensations utilizing advanced digital signal processing techniques. The motivation behind this is to push more processing tasks to the digital domain, as it can potentially cut down the bill of materials (BOM) costs paid for the off-chip devices and reduce practical implementation difficulties. The work here is carried out using three approaches: numerical analysis & computer simulations; experimental tests using commercial instruments; actual implementation with FPGA. The primary contributions for this thesis are summarized as the following three points: 1) An adaptive digital predistortion (DPD) with fast convergence rate and low complexity for multi-carrier GSM system is presented. Albeit a legacy system, the GSM, however, has a very strict requirement on the out-of-band emission, thus it represents a much more difficult hurdle for DPD application. It is successfully implemented in an FPGA without using any other auxiliary processor. A simplified multiplier-free NLMS algorithm, especially suitable for FPGA implementation, for fast adapting the LUT is proposed. Many design methodologies and practical implementation issues are discussed in details. Experimental results have shown that the DPD performed robustly when it is involved in the multichannel transmitter. 2) The next generation system (5G) will unquestionably use wider bandwidth to support higher throughput, which poses stringent needs for using high-speed data converters. Herein the analog-to-digital converter (ADC) tends to be the most expensive single device in the whole transmitter/receiver systems. Therefore, conventional DPD utilizing high-speed ADC becomes unaffordable, especially for small base stations (micro, pico and femto). A digital predistortion technique utilizing spectral extrapolation is proposed in this thesis, wherein with band-limited feedback signal, the requirement on ADC speed can be significantly released. Experimental results have validated the feasibility of the proposed technique for coping with band-limited feedback signal. It has been shown that adequate linearization performance can be achieved even if the acquisition bandwidth is less than the original signal bandwidth. The experimental results obtained by using LTE-Advanced signal of 320 MHz bandwidth are quite satisfactory, and to the authors’ knowledge, this is the first high-performance wideband DPD ever been reported. 3) To address the predicament that mobile operators do not have enough contiguous usable bandwidth, carrier aggregation (CA) technique is developed and imported into 4G LTE-Advanced. This pushes the utilization of concurrent dual-band transmitter/receiver, which reduces the hardware expense by using a single front-end. Compensation techniques for the respective concurrent dual-band transmitter and receiver front-ends are proposed to combat the inter-band modulation distortion, and simultaneously reduce the distortion for the both lower-side band and upper-side band signals.電気通信大学201
Enhancing Compressed Sensing 4D Photoacoustic Tomography by Simultaneous Motion Estimation
A crucial limitation of current high-resolution 3D photoacoustic tomography
(PAT) devices that employ sequential scanning is their long acquisition time.
In previous work, we demonstrated how to use compressed sensing techniques to
improve upon this: images with good spatial resolution and contrast can be
obtained from suitably sub-sampled PAT data acquired by novel acoustic scanning
systems if sparsity-constrained image reconstruction techniques such as total
variation regularization are used. Now, we show how a further increase of image
quality can be achieved for imaging dynamic processes in living tissue (4D
PAT). The key idea is to exploit the additional temporal redundancy of the data
by coupling the previously used spatial image reconstruction models with
sparsity-constrained motion estimation models. While simulated data from a
two-dimensional numerical phantom will be used to illustrate the main
properties of this recently developed
joint-image-reconstruction-and-motion-estimation framework, measured data from
a dynamic experimental phantom will also be used to demonstrate their potential
for challenging, large-scale, real-world, three-dimensional scenarios. The
latter only becomes feasible if a carefully designed combination of tailored
optimization schemes is employed, which we describe and examine in more detail
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