Abstract: This paper proposes strategies in level crossing (LC) sampling and reconstruction that provide high fidelity signal reconstruction for speech signals; these strategies circumvent the problem of exponentially increasing number of samples as the bit-depth is increased and hence are highly efficient. Specifically, the results indicate that the distribution of the intervals between samples is one of the key factors in the quality of signal reconstruction; including samples with short intervals does not improve the accuracy of the signal reconstruction, whilst samples with large intervals lead to numerical instability. The proposed sampling method, termed reduced conventional level crossing (RCLC) sampling, exploits redundancy between samples to improve the efficiency of the sampling without compromising performance. A reconstruction technique is also proposed that enhances the numerical stability through linear interpolation of samples separated by large intervals. Interpolation is demonstrated to improve the accuracy of the signal reconstruction in addition to the numerical stability. We further demonstrate that the RCLC and interpolation methods can give useful levels of signal recovery even if the average sampling rate is less than the Nyquist rate.
Abstract: This paper is a numerical investigation of a laminar
isothermal plane two dimensional wall jet. Special attention has been
paid to the effect of the inlet conditions at the nozzle exit on the
hydrodynamic and thermal characteristics of the flow. The
behaviour of various fluids evolving in both forced and mixed
convection regimes near a vertical plate plane is carried out. The
system of governing equations is solved with an implicit finite
difference scheme. For numerical stability we use a staggered non
uniform grid. The obtained results show that the effect of the Prandtl
number is significant in the plume region in which the jet flow is
governed by buoyant forces. Further for ascending X values, the
buoyancy forces become dominating, and a certain agreement
between the temperature profiles are observed, which shows that the
velocity profile has no longer influence on the wall temperature
evolution in this region. Fluids with low Prandtl number warm up
more importantly, because for such fluids the effect of heat diffusion
is higher.
Abstract: Extended Kalman Filter (EKF) is probably the most
widely used estimation algorithm for nonlinear systems. However,
not only it has difficulties arising from linearization but also many
times it becomes numerically unstable because of computer round off
errors that occur in the process of its implementation. To overcome
linearization limitations, the unscented transformation (UT) was
developed as a method to propagate mean and covariance
information through nonlinear transformations. Kalman filter that
uses UT for calculation of the first two statistical moments is called
Unscented Kalman Filter (UKF). Square-root form of UKF (SRUKF)
developed by Rudolph van der Merwe and Eric Wan to
achieve numerical stability and guarantee positive semi-definiteness
of the Kalman filter covariances. This paper develops another
implementation of SR-UKF for sequential update measurement
equation, and also derives a new UD covariance factorization filter
for the implementation of UKF. This filter is equivalent to UKF but
is computationally more efficient.
Abstract: In this paper we improve the quasilinearization method by barycentric Lagrange interpolation because of its numerical stability and computation speed to achieve a stable semi analytical solution. Then we applied the improved method for solving the Fin problem which is a nonlinear equation that occurs in the heat transferring. In the quasilinearization approach the nonlinear differential equation is treated by approximating the nonlinear terms by a sequence of linear expressions. The modified QLM is iterative but not perturbative and gives stable semi analytical solutions to nonlinear problems without depending on the existence of a smallness parameter. Comparison with some numerical solutions shows that the present solution is applicable.
Abstract: Multi-dimensional principal component analysis
(PCA) is the extension of the PCA, which is used widely as the
dimensionality reduction technique in multivariate data analysis, to
handle multi-dimensional data. To calculate the PCA the singular
value decomposition (SVD) is commonly employed by the reason of
its numerical stability. The multi-dimensional PCA can be calculated
by using the higher-order SVD (HOSVD), which is proposed by
Lathauwer et al., similarly with the case of ordinary PCA. In this
paper, we apply the multi-dimensional PCA to the multi-dimensional
medical data including the functional independence measure (FIM)
score, and describe the results of experimental analysis.