Fractional Delayer Utilizing Hermite Interpolation with Caratheodory Representation

Fractional delay is indispensable for many sorts of circuits and signal processing applications. Fractional delay filter (FDF) utilizing Hermite interpolation with an analog differentiator is a straightforward way to delay discrete signals. This method has a low time-domain error, but a complicated sampling module than the Shannon sampling scheme. A simplified scheme, which is based on Shannon sampling and utilizing Hermite interpolation with a digital differentiator, will lead a much higher time-domain error when the signal frequency approaches the Nyquist rate. In this letter, we propose a novel fractional delayer utilizing Hermite interpolation with Caratheodory representation. The samples of differential signal are obtained by Caratheodory representation from the samples of the original signal only. So, only one sampler is needed and the sampling module is simple. Simulation results for four types of signals demonstrate that the proposed method has significantly higher interpolation accuracy than Hermite interpolation with digital differentiator

Efficient target-response interpolation for a graphic equalizer

Proceedings of the 41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP, held in Shanghai (China) during 20-25 March 2016.A graphic equalizer is an adjustable filter in which the command gain of each frequency band is practically independent of the gains of other bands. Designing a graphic equalizer with a high precision requires evaluating a target response that interpolates the magnitude response at several frequency points between the command gains. Good accuracy has been previously achieved by using polynomial interpolation methods such as cubic Hermite or spline interpolation. However, these methods require large computational resources, which is a limitation in real-time applications. This paper proposes an efficient way of computing the target response without sacrificing the approximation accuracy. This new approach called Linear Interpolation with Constant Segments (LICS) reduces the computing time of the target response by 55% and has an intrinsic parallel structure. Performance of the LICS method is assessed on an ARM Cortex-A7 core, which is commonly used in embedded systems.This work was conducted in spring 2015 when the first author was a visiting postdoctoral researcher at Aalto University. This research has been partly funded by the TIN2014-53495-R and TIN2011-23283 projects of the Ministerio de Economía y Competitividad and FEDER

Signal recovery from partial fractional fourier domain information and pulse shape design using iterative projections

Cataloged from PDF version of article.Signal design and recovery problems come up in a wide variety of applications in signal processing. In this thesis, we first investigate the problem of pulse shape design for use in communication settings with matched filtering where the rate of communication, intersymbol interference, and bandwidth of the signal constitute conflicting themes. In order to design pulse shapes that satisfy certain criteria such as bit rate, spectral characteristics, and worst case degradation due to intersymbol interference, we benefit from the wellknown Projections Onto Convex Sets. Secondly, we investigate the problem of signal recovery from partial information in fractional Fourier domains. Fractional Fourier transform is a mathematical generalization of the ordinary Fourier transform, the latter being a special case of the first. Here, we assume that low resolution or partial information in different fractional Fourier transform domains is available in different intervals. These information intervals define convex sets and can be combined within the Projections Onto Convex Sets framework. We present generic scenarios and simulation examples in order to illustrate the use of the method.Güven, H EmreM.S

Real-time Digital Simulation of Guitar Amplifiers as Audio Effects

Práce se zabývá číslicovou simulací kytarových zesilovačů, jakož to nelineárních analogových hudebních efektů, v reálném čase. Hlavním cílem práce je návrh algoritmů, které by umožnily simulaci složitých systémů v reálném čase. Tyto algoritmy jsou prevážně založeny na automatizované DK-metodě a aproximaci nelineárních funkcí. Kvalita navržených algoritmů je stanovana pomocí poslechových testů.The work deals with the real-time digital simulation of guitar amplifiers considered as nonlinear analog audio effects. The main aim is to design algorithms which are able to simulate complex systems in real-time. These algorithms are mainly based on the automated DK-method and the approximation of nonlinear functions. Quality of the designed algorithms is evaluated using listening tests.

From infinite dimensional modelling to parametric reduced-order approximation: Application to open-channel flow for hydroelectricity

International audienceIn this paper, it will be shown that open-channel hydraulic systems can be suitably represented for control purposes by using input delay linear parameter-varying (LPV) models. The physical equations on which this work is done are Saint-Venant equations applied to a non-rectangular cross section channel. These later are two coupled non-linear hyper-bolic partial differential equations which are linearized and transformed into irrational transfer functions. An accurate model approximation procedure, denoted IPTFA (Irrational Proper Transfer Function Algorithm) is developed in order to obtain a rational transfer function plus input delays which is then parameterized by one single parameter: the initial steady-state discharge. Frequency domain responses of the irrational and reduced-order transfer functions are shown to match for a large range of discharge

Two-Component Structure of the Hbeta Broad-Line Region in Quasars. I. Evidence from Spectral Principal Component Analysis

We report on a spectral principal component analysis (SPCA) of a sample of 816 quasars, selected to have small Fe II velocity shifts with spectral coverage in the rest wavelength range 3500--5500 \AA. The sample is explicitly designed to mitigate spurious effects on SPCA induced by Fe II velocity shifts. We improve the algorithm of SPCA in the literature and introduce a new quantity, \emph{the fractional-contribution spectrum}, that effectively identifies the emission features encoded in each eigenspectrum. The first eigenspectrum clearly records the power-law continuum and very broad Balmer emission lines. Narrow emission lines dominate the second eigenspectrum. The third eigenspectrum represents the Fe II emission and a component of the Balmer lines with kinematically similar intermediate velocity widths. Correlations between the weights of the eigenspectra and parametric measurements of line strength and continuum slope confirm the above interpretation for the eigenspectra. Monte Carlo simulations demonstrate the validity of our method to recognize cross talk in SPCA and firmly rule out a single-component model for broad Hbeta. We also present the results of SPCA for four other samples that contain quasars in bins of larger Fe II velocity shift; similar eigenspectra are obtained. We propose that the Hbeta-emitting region has two kinematically distinct components: one with very large velocities whose strength correlates with the continuum shape, and another with more modest, intermediate velocities that is closely coupled to the gas that gives rise to Fe II emission.Comment: 22 pages, 17 figures, accepted for publication in The Astrophysical Journa

Quantum wave modeling on highly parallel distributed memory machines

Parallel computers are finding major applications in almost all scientific and engineering disciplines. An interesting area that has received attention is quantum scattering. Algorithms for studying quantum scattering are computation intensive and hence suitable for parallel machines. The state-of-the-art methods developed for uniprocessors require the computation of two Fast Fourier Transforms (FFTs) at each time step. However, the communication overhead in implementing FFTs make them an expensive operation on distributed memory parallel machines;The focus of this dissertation is the development of efficient parallel methods for studying the phenomenon of time-dependent quantum-wave scattering. The methods described belong to the class of integral equation methods, which involve the application of a repeated sequence of very short time step propagations. Free propagation of a wavepacket is most easily handled in the so-called momentum representation whereas the effect of the potential is most easily obtained in the coordinate representation. The two representations are Fourier Transforms of each other. The algorithm presented eliminates the computation of FFTs by performing the propagation totally within the coordinate representation. The communication required is only with the nearest neighbors and is load balanced, thus making the algorithm suitable for distributed memory parallel machines. Implementation results on the nCUBE hypercube and comparison with standard FFT methods are also presented