A four-stage algorithm for updating a Burrows–Wheeler transform

We present a four-stage algorithm that updates the Burrows–Wheeler Transform of a text T$T$, when this text is modified. The Burrows–Wheeler Transform is used by many text compression applications and some self-index data structures. It operates by reordering the letters of a text T$T$ to obtain a new text bwt(T)$bwt\left(T\right)$ which can be better compressed.     

Intrinsic time in Wheeler–DeWitt conformal superspace

Intrinsic time in geometrodynamics is obtained using a scaled Dirac mapping. By addition of a background metric, one can construct a scalar field which is suitable for the role of intrinsic time. The Cauchy problem was successfully solved in conformal variables because they are physical. Intrinsic time as a logarithm of the spatial metric determinant was first applied to a cosmological problem byMisner. Global time exists under the condition of a constant mean curvature slicing of spacetime. A coordinate volume of a hypersurface and the so-called York’s mean time are a canonical conjugated pair. So, the volume is intrinsic global time by its sense. The experimentally observed redshift in cosmology is an evidence of its existence.     

Spectral: Solving Schroedinger and Wheeler–DeWitt equations in the positive semi-axis by the spectral method

The Galerkin spectral method can be used for approximate calculation of eigenvalues and eigenfunctions of unidimensional Schroedinger-like equations such as the Wheeler–DeWitt equation. The criteria most commonly employed for checking the accuracy of results is the conservation of norm of the wave function, but some other criteria might be used, such as the orthogonality of eigenfunctions and the variation of the spectrum with varying computational parameters, e.g. the number of basis functions used in the approximation. The package Spectra, which implements the spectral method in Maple language together with a number of testing tools, is presented. Alternatively, Maple may interact with the Octave numerical system without the need of Octave programming by the user.     

Fuzzy measures and generalized Möbius transform

Generalized Möbius transform is recalled and applied in some special cases. The relationship with the standard Möbius transform is shown. By means of the generalized Möbius transform, a general concept of k -order additivity independent of the cardinality of the underlying space is introduced. The relationship of the Choquet integral and the Lebesgue integral by means of the generalized Möbius transform is clarified. Also possibilistic Möbius transform and k -order possibility measures are introduced. Finally, some examples are given, including the characterization of de Finetti's discrete lower probabilities.     

An unsupervised approach for co-channel speech separation using Hilbert–Huang transform and Fuzzy C-Means clustering

In this paper we discuss an unsupervised approach for co-channel speech separation where two speakers are speaking simultaneously over same channel. We propose a two stage separation process where the initial stage is based on empirical mode decomposition (EMD) and Hilbert transform generally known as Hilbert–Huang transform. EMD decomposes the mixed signal into oscillatory functions known as intrinsic mode functions. Hilbert transform is applied to find the instantaneous amplitudes and Fuzzy C-Means clustering is applied to group the speakers at initial stage. In second stage of separation speaker groups are transformed into time–frequency domain using short time Fourier transform (STFT). Time–frequency ratio’s are computed by dividing the STFT matrix of mixed speech signal and STFT matrix of stage1 recovered speech signals. Histogram of the ratios obtained can be used to estimate the ideal binary mask for each speaker. These masks are applied to the speech mixture and the underlying speakers are estimated. Masks are estimated from the speech mixture and helps in imputing the missing values after stage1 grouping of speakers. Results obtained show significant improvement in objective measures over other existing single-channel speech separation methods.     

Theory and algorithms for two-dimensional warped discrete Fourier transform

In this paper, the two-dimensional Warped Discrete Fourier Transform （2-D WDFT） is developed based on the concept of the 1-D WDFT. An exact computation algorithm is developed for 2-D WDFT based on matrix factorizing with special structure. A fast algorithm is then proposed to reduce greatly the computational complexity of the inverse 2-D WDFT. Finally, numerical examples are given to show the efficiency of the proposed approach.     

An improved method to calculate phase locking value based on Hilbert–Huang transform and its application

Phase synchronization analysis has been demonstrated to be a useful method to infer brain function and neural activity based on electroencephalography (EEG) signals. The phase locking value (PLV) is one of the most important tools for phase synchronization analysis. Although the traditional method (TM) to calculate PLV, which is based on the Hilbert transform, has been applied extensively, some of methodological problems of TM have not been solved. To address these problems, this paper proposes an improved method (IM) to calculate the PLV based on the Hilbert–Huang transform. For the IM, the Hilbert–Huang transform, instead of the Hilbert transform, is used to process non-stationary EEG signals and the empirical mode decomposition, not band-pass filter, is used to get target frequency band. The performance of the IM is evaluated by comparing normal and hypoxia EEG signals. The PLVs are used as features for a least squares support vector machine to recognize normal and hypoxia EEG. Experimental results show that the PLVs calculated by the IM can distinguish the EEG signals better than those calculated by TM.     

A new music-empirical wavelet transform methodology for time–frequency analysis of noisy nonlinear and non-stationary signals

The goal of signal processing is to estimate the contained frequencies and extract subtle changes in the signals. In this paper, a new adaptive multiple signal classification-empirical wavelet transform (MUSIC-EWT) methodology is presented for accurate time–frequency representation of noisy non-stationary and nonlinear signals. It uses the MUSIC algorithm to estimate the contained frequencies in the signal and build the appropriate boundaries to create the wavelet filter bank. Then, the EWT decomposes the time-series signal into a set of frequency bands according to the estimated boundaries. Finally, the Hilbert transform is applied to observe the evolution of calculated frequency bands over time. The usefulness and effectiveness of the proposed methodology are validated using two simulated signals and an ECG signal obtained experimentally. The results demonstrate clearly that the proposed methodology is immune to noise and capable of estimating the optimal boundaries to isolate the frequencies from noise and estimate the main frequencies with high accuracy, especially the closely-spaced frequencies.     

Feedback-free rate-allocation scheme for transform domain Wyner–Ziv video coding

In most existing Wyner–Ziv video coding schemes, a feedback channel (FC) is expected at the decoder in order to allocate a proper bit rate for each Wyner–Ziv frame. However, FC not only results in additional latency but also increases decoding complexity due to the several feedback-decoding iterations. Moreover, FC may be unavailable in many practical video applications. In this paper, we propose a novel feedback-free rate-allocation scheme for transform domain Wyner–Ziv video coding (TD-WZVC), which predicts the rate for each Wyner–Ziv frame at the encoder without significantly increasing the complexity of the encoder. First, a correlation estimation model is presented to characterize the relationship between the source frame and the reference frame estimated at the encoder in TD-WZVC. Then, an efficient FC-free rate-allocation algorithm is proposed and a linear model is built to avoid both overestimation and underestimation of the real rate and obtain an optimal rate-distortion performance. Experimental results show that the proposed scheme is able to achieve a good encoder rate allocation while still maintaining consistent coding efficiency.     

Signal-adaptive discrete evolutionary transform as a sparse time–frequency representation

Discrete evolutionary transform (DET) has usually been applied to signals in a blind-way without using any parameters to characterize the signal. For this reason, it is not optimal and needs improvement by using some information about the signal. In this paper, we propose an improvement for the discrete evolutionary transform in order to obtain a sparse representation and redefine the generalized time-bandwidth product optimal short-time Fourier transform as a special case of it. In case of linear FM-type signals, the optimized kernel function of the transform is determined according to signal parameters including the instantaneous frequency. The performance of the adaptive-DET is illustrated on three distinct cases. In case of multi-component LFM signals, when the concentration of the proposed distribution is compared to the ordinary sinusoidal-DET, the improvement is computed as 28% in terms of the ratio of norms. Furthermore we define a new and a general class of distribution functions named as the short-time generalized discrete Fourier transform (ST-GDFT) which is a larger set of signal representations including the adaptive-DET.     

Development of a fine-grained parallel Karhunen–Loève transform

A high-performance Karhunen–Loève transform for multi-spectral imagery suitable for remote sensing applications has been prototyped on a platform FPGA, through hardware compilation onto a PC-based development board. Performance estimates suggest that the design will outperform implementation on a high-end microprocessor, given due attention to I/O (input/output). Detailed analysis of the design steps taken to produce a successful prototype are given. A design that addresses the issue of data bandwidth is included. General conclusions are reached for the utility of this architecture and design method for fine-grained parallel processing.     

Convolution theorems for the linear canonical transform and their applications

As generalization of the fractional Fourier transform (FRFT), the linear canonical transform (LCT) has been used in several areas, including optics and signal processing. Many properties for this transform are already known, but the convolution theorems, similar to the version of the Fourier transform, are still to be determined. In this paper, the authors derive the convolution theorems for the LCT, and explore the sampling theorem and multiplicative filter for the band limited signal in the linear canonical domain. Finally, the sampling and reconstruction formulas are deduced, together with the construction methodology for the above mentioned multiplicative filter in the time domain based on fast Fourier transform (FFT), which has much lower computational load than the construction method in the linear canonical domain.     

Action recognition via bio-inspired features: The richness of center–surround interaction

Motion is a key feature for a wide class of computer vision approaches to recognize actions. In this article, we show how to define bio-inspired features for action recognition. To do so, we start from a well-established bio-inspired motion model of cortical areas V1 and MT. The primary visual cortex, designated as V1, is the first cortical area encountered in the visual stream processing and early responses of V1 cells consist in tiled sets of selective spatiotemporal filters. The second cortical area of interest in this article is area MT where MT cells pool incoming information from V1 according to the shape and characteristic of their receptive field. To go beyond the classical models and following the observations from Xiao et al. [61], we propose here to model different surround geometries for MT cells receptive fields. Then, we define the so-called bio-inspired features associated to an input video, based on the average activity of MT cells. Finally, we show how these features can be used in a standard classification method to perform action recognition. Results are given for the Weizmann and KTH databases. Interestingly, we show that the diversity of motion representation at the MT level (different surround geometries), is a major advantage for action recognition. On the Weizmann database, the inclusion of different MT surround geometries improved the recognition rate from 63.01 ± 2.07% up to 99.26 ± 1.66% in the best case. Similarly, on the KTH database, the recognition rate was significantly improved with the inclusion of MT different surround geometries (from 47.82 ± 2.71% up to 92.44 ± 0.01% in the best case). We also discussed the limitations of the current approach which are closely related to the input video duration. These promising results encourage us to further develop bio-inspired models incorporating other brain mechanisms and cortical areas in order to deal with more complex videos.     

Approximate analytical solutions of fractional Benney–Lin equation by reduced differential transform method and the homotopy perturbation method

In this paper, the approximate analytical solutions of Benney–Lin equation with fractional time derivative are obtained with the help of a general framework of the reduced differential transform method (RDTM) and the homotopy perturbation method (HPM). RDTM technique does not require any discretization, linearization or small perturbations and therefore it reduces significantly the numerical computation. Comparing the methodology (RDTM) with some known technique (HPM) shows that the present approach is effective and powerful. The numerical calculations are carried out when the initial conditions in the form of periodic functions and the results are depicted through graphs. The eight different cases have studied and proved that the method is extremely effective due to its simplistic approach and performance.     

Approximation of Laplace transform of fractional derivatives via Clenshaw–Curtis integration

In this paper, we approximate the Laplace transform of fractional derivatives via Clenshaw–Curtis integration. The idea of applying Chebyshev polynomial to the numerical computation of integrals is extended to Laplace transform of fractional derivatives. The numerical stability of forward recurrence relations is considered, which depends on the asymptotic behaviour of the coefficients. Error estimation for the Laplace approximation of the fractional derivatives is also considered. Finally, from the numerical examples, the method seems to be promising for approximation of the Laplace transform of fractional derivative.     

The training of Karhunen–Loève transform matrix and its application for H.264 intra coding

In H.264/AVC, 4 × 4 discrete cosine transform (DCT) is performed on the residual signals after intra prediction for decorrelation. Actually, residual blocks with different prediction modes exhibit different frequency characteristics. Therefore, the fixed transform matrix cannot match the energetic distribution of residual signals very well, which degrades the decorrelation performance. Fortunately, the energetic distributions of residual blocks with the same mode are relatively coincident, which makes it possible to train a universally good Karhunen–Loève transform (KLT) matrix for each mode. In this paper, an optimal frequency matching (OFM) algorithm is proposed to train KLT matrices for residual blocks and nine KLT matrices corresponding to nine prediction modes of 4 × 4 intra blocks are trained. Experimental results show that KLT with trained matrices yields a persistent gain over H.264 using 4 × 4 DCT with an average peak signal-to-noise ratio (PSNR) enhancement of 0.22dB and a maximum enhancement of 0.33dB.

Laplace transform finite volume modeling of water hammer along fluid–structure interaction

Water hammer or propagation of pressure waves generates profound forces through pipelines of industrial high pressure processes which causes structural vibration of the pipe in both radial and axial directions. To model the sudden rupture of a pipeline system the fluid–structure interaction, FSI, is taken into account by coupling the structural vibration equations to the fluid dynamic equation. In this paper, Laplace transform finite volume, LTFV, which is a new technique along the finite element method is developed to treat fluid transient and the structural vibration equations respectively.To evaluate the numerical results, a Thermal Hydraulic Test Loop (THTL facility) which has been designed and constructed for experimental research on the physical phenomena, characteristics and performance of the safety systems involved in plants is used. To conduct tests for representing a sudden break condition in the loop, the THTL facility has been equipped by devices and sensors to record pressure and vibration signals during simulated accidents. Under steady condition, by an electrical signal an electric valve, Break valve, is opened and simultaneously pressure along pipe vibration signals close to valve is recorded. Comparing the experimental data to results from numerical modeling validated the implemented method.