In this paper, a two-dimensional multi-wavelet is constructed in terms of Chebyshev polynomials. The constructed multi-wavelet is an orthonormal basis for space. By discretizing two-dimensional Fredholm integral equation reduce to a algebraic system. The obtained system is solved by the Galerkin method in the subspace of by using two-dimensional multi-wavelet bases. Because the bases of subs...

The main purpose of this paper is to propose a new numerical method for solving the optimal control problems based on state parameterization. Here, the boundary conditions and the performance index are first converted into an algebraic equation or in other words into an optimization problem. In this case, state variables will be approximated by a new hybrid technique based on new second kind Ch...

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We construct an orthogonal wavelet basis for the interval using a linear combination of Legendre polynomial functions. The coefficients are taken as appropriate roots of Chebyshev polynomials of the second kind, as has been proposed in reference [1]. A multi-resolution analysis is implemented and illustrated with analytical data and real-life signals from turbulent flow fields.

Design/methodology/approach – Two tests were performed, one on Acoustic Emission artificial signals generated on a CFRP plate and one on an Acousto Ultrasonic setup used for actively detecting impact damage. The waveforms were represented using a data reduction technique based on the Daubechies wavelet and an image processing technique using Chebyshev moments approximation, to get 32 descriptor...

We study the compression performance of the quincunx discrete wavelet transform (DWT) and we compare it with the dyadic DWT in terms of ratedistortion. The 2D non-separable quincunx wavelet filters are designed by making use of the ‘transformations of variables’ technique of Tay & Kingsbury starting from the 1D biorthogonal (9,7)-taps filters. The applied transformation functions are respective...

We study the compression performance of the quincunx discrete wavelet transform (DWT) and we compare it with the dyadic DWT in terms of PSNR and bit rate. The 2D non-separable quincunx wavelet filters are designed by making use of the ‘transformations of variables’ technique of Tay & Kingsbury starting from the 1D biorthogonal (9,7)-taps filters. The applied transformation functions are respect...