A NEW ADAPTIVE FILTERING SCHEME BASED ON WAVELET TRANSFORM

Based on the scale function representation for a function in L2(R), a new wavelet transform based adaptive system identification scheme is proposed. It can reduce the amount of computation by exploiting the decimation properties and keep the advantage of quasi-orthogonal transform of the discrete wavelet, transform (DWT). The issue has been supported by computer simulations.

COMPUTATION OF CONTINUOUS WAVELET TRANSFORM AT DYADIC SCALES BY SUBDIVISION SCHEME

A new algorithm to compute continuous wavelet transforms at dyadic scales is proposed here. Our approach has a similar implementation with the standard algorithme a trous and can coincide with it in the one dimensional lower order spline case.Our algorithm can have arbitrary order of approximation and is applicable to the multidimensional case.We present this algorithm in a general case with emphasis on splines anti quast in terpolations.Numerical examples are included to justify our theorerical discussion.

Speech compression scheme based on wavelet transform and vector quantization

A coding method of speech compression, which is based on Wavlet Transform and Vector Quantization (VQ), is developed and studied. The Wavlet Thansform or Wavlet Packet Thansform is used to process the speech signal, then VQ is used to compress the coefficients of Wavlet Thansform, and the entropy coding is used to decrease the bit rate. The experimental results show that the speech signal, sampled by 8 kHz sampling rate and 8 bit quatisation,i.e., 64 kbit/s bit rate, can be compressed to 6 - 8 kbit/s, and still have high speech quality,and the low-delay, only 8 ms.

Linearized Transformed L1 Galerkin FEMs with Unconditional Convergence for Nonlinear Time Fractional Schr¨odinger Equations

A linearized transformed L1 Galerkin finite element method(FEM)is presented for numerically solving the multi-dimensional time fractional Schr¨odinger equations.Unconditionally optimal error estimates of the fully-discrete scheme are proved.Such error estimates are obtained by combining a new discrete fractional Gr¨onwall inequality,the corresponding Sobolev embedding theorems and some inverse inequalities.While the previous unconditional convergence results are usually obtained by using the temporal-spatial error spitting approaches.Numerical examples are presented to confirm the theoretical results.

An efficient hybrid computational technique for the time dependent Lane-Emden equation of arbitrary order

The study of dynamic behaviour of nonlinear models that arise in ocean engineering play a vital role in our daily life.There are many examples of ocean water waves which are nonlinear in nature.In shallow water,the linearization of the equations imposes severe conditions on wave amplitude than it does in deep water,and the strong nonlinear effects are observed.In this paper,q-homotopy analysis Laplace transform scheme is used to inspect time dependent nonlinear Lane-Emden type equation of arbitrary order.It offers the solution in a fast converging series.The uniqueness and convergence analysis of the considered model is presented.The given examples confirm the competency as well as accuracy of the presented scheme.The behavior of obtained solution for distinct orders of fractional derivative is dis-cussed through graphs.The auxiliary parameter¯h offers a suitable mode of handling the region of con-vergence.The outcomes reveal that the q-HATM is attractive,reliable,efficient and very effective.

An efficient analytical technique for fractional partial differential equations occurring in ion acoustic waves in plasma

In this work,we apply an efficient analytical algorithm namely homotopy perturbation Sumudu transform method(HPSTM)to find the exact and approximate solutions of linear and nonlinear time-fractional regularized long wave(RLW)equations.The RLW equations describe the nature of ion acoustic waves in plasma and shallow water waves in oceans.The derived results are very significant and imperative for explaining various physical phenomenons.The suggested method basically demonstrates how two efficient techniques,the Sumudu transform scheme and the homotopy perturbation technique can be integrated and applied to find exact and approximate solutions of linear and nonlinear time-fractional RLW equations.The nonlinear expressions can be simply managed by application of He’s polynomials.The result shows that the HPSTM is very powerful,efficient,and simple and it eliminates the round-off errors.It has been observed that the proposed technique can be widely employed to examine other real world problems.