this article is devoted to study of the autoconvolution equations and generalized mittag-leffler functions. these types of equations are given in terms of the laplace transform convolution of a function with itself. we state new classes of the autoconvolution equations of the first kind and show that the generalized mittag-leffler functions are solutions of these types of equations. in view of ...

In this short note, we study all-or-nothing transforms, which were recently proposed by Rivest as a mode of operation for block ciphers. We study transforms of this type that provide unconditional security. A simple construction for linear transforms is given, and some existence and non-existence results for general transforms are derived from a combinatorial characterization of these objects.

Weighted (L, L) inequalities are studied for a variety of integral transforms of Fourier type. In particular, weighted norm inequalities for the Fourier, Hankel, and Jacobi transforms are derived from Calderón type rearrangement estimates. The obtained results keep their novelty even in the simplest cases of the studied transforms, the cosine and sine Fourier transforms. Sharpness of the condit...

We show how periodized wavelet packet transforms and periodized wavelet transforms can be implemented on a quantum computer. Surprisingly, we find that the implementation of wavelet packet transforms is less costly than the implementation of wavelet transforms on a quantum computer.

New classes of Linearly Independent Ternary Arithmetic (LITA) transforms being the bases of ternary arithmetic polynomial expansions are introduced here. Recursive equations defining the LITA transforms and the corresponding butterfly diagrams are shown. Various properties and relations between introduced classes of new transforms are discussed. Computational costs to calculate LITA transforms ...

A general f ramework is presented for constructing transforms in the field of the input which have a convolutionlike property. The construction is carried out over finite fields, but is shown to be valid over the real and complex fields as well. It is shown that these basefield transforms can be v iewed as “projections” of the discrete Fourier transform @IT) and that they exist for all lengths ...

Discrete transforms are introduced and are defined in a ring of polynomials. These polynomial transforms are shown to have the convolution property and can be computed in ordinary arithmetic, without multiplications. Polynomial transforms are particularly well suited for computing discrete two-dimensional convolutions with a minimum number of operations. Efficient algorithms for computing one-d...

Abstract In this paper, we study the nonuniform fast Fourier transform with nonequispaced spatial and frequency data (NNFFT) sinc as its application. The computation of NNFFT is mainly based on nodes equispaced frequencies (NFFT). employs two compactly supported, continuous window functions. For fixed nonharmonic bandwidth, show that error $$\sinh$$ <mml:math xmlns:mml="http://www.w3.org/1998/M...

Near-best and best wavelet packet transforms were compared with wavelet transforms for the compression of polysomnograms in a low bitrate telemonitoring application. Near-best wavelet packet transforms provided better overall performance with respect to efficiency of computation and compression, and amenability for use in more sophisticated quality-on-demand algorithms. Keywords— near-best base...

New continuous group transforms, together with their discretization over a lattice of any density and admissible symmetry, are defined for a general compact simple Lie groups of rank 2 ≤ n < ∞. Rank 1 transforms are known. Rank 2 exposition of Cand S-transforms is in the literature. The E-transforms appear here for the first time.