We investigate a problem of approximate non-linear sampling recovery of functions on the interval I:=[0,1] expressing the adaptive choice of n sampled values of a function to be recovered, and of n terms from a given family of functions Φ. More precisely, for each function f on I, we choose a sequence ξ = {ξs} s =1 n of n points in I, a sequence a = {as}s=1} n of n functions defined on n and a ...

We investigate the approximation properties of general polynomial preserving operators that approximate a function into some scaled subspace of L via an appropriate sequence of inner products. In particular, we consider integer shift-invariant approximations such as those provided by splines and wavelets, as well as finite elements and multi-wavelets which use multiple generators. We estimate t...

Following our previous work of Lachowicz & Czerny (2005), we explore further the application of the continuous wavelet transform to X-ray astronomical signals. Using the public archive of the XMM-Newton satellite, we analyze all available EPIC-pn observations for nearby Seyfert 1 galaxies MCG–6-30-15 and NGC 4051. We confine our analysis to 0.002–0.007 Hz frequency band in which, on the way of ...

Scale-discretised wavelets yield a directional wavelet framework on the sphere where a signal can be probed not only in scale and position but also in orientation. Furthermore, a signal can be synthesised from its wavelet coefficients exactly, in theory and practice (to machine precision). Scale-discretised wavelets are closely related to spherical needlets (both were developed independently at...

The trait of the ball mill is chaotic in nature due its complex dynamics associated during grinding. Grinding in ball mill generates high-intensity vibration and is too complex on account dependency of multiple variables. In this paper, the vibration signal is acquired using a low power ZigBee based three axes wireless MEMS accelerometer sensor mounted onto the mill shell. Firstly, the exact fr...

This paper investigates the use of dyadic wavelets for the control of multifrequency rotor vibration. A scheme for real-time control of rotor vibration using an adaptive wavelet decomposition and reconstruction of time-varying signals is proposed. Quasi-periodic control forces are constructed adaptively in real-time to optimally cancel vibration produced by nonsmooth disturbance forces. Control...

This paper provides a technique to investigate the solutions of generalized nonlinear singular Lane–Emden equations of first and second kinds by using a Haar wavelet quasi-linearization approach. The Lane–Emden equation is widely studied and is treated as a challenging equation in the theory of stellar structure for the gravitational potential of a self gravitating, spherically symmetric polytr...

In this article, we explore the effectiveness of different numerical techniques in the training of backpropaqgation neural networks (BPNN) which are fed with wavelet-transformed data to capture useful information on various time scales. The purpose is to predict S&P500 future prices using BPNN trained with conjugate gradient (Fletcher-Reeves update, Polak-Ribiére update, Powell-Beale restart), ...

We show that the nonlinear evolution of the cosmic gravitational clustering is approximately spatial local in the x-k (position-scale) phase space if the initial perturbations are Gaussian. That is, if viewing the mass field with modes in the phase space, the nonlinear evolution will cause strong coupling among modes with different scale k, but at the same spatial area x, while the modes at dif...

Nonlinear thresholding of wavelet coefficients is an efficient method for denoising signals with isolated singularities. The quasi-optimal value of the threshold depends on the sample size and on the variance of the noise, which is in many situations unknown. We present a recursive algorithm to estimate the variance of the noise, prove its convergence and investigate its mathematical properties...