Preconditioned iterative methods are described for the solution of an elliptic partial differential equation over an unit square region with Robbins boundary conditions. Transform based preconditioners are constructed and analyzed. The motivation is to exploit the fast inversion of transform based systems via the fast transform. We prove that transform based preconditioners can be chosen so tha...

Transient eddy current problem is solved in the present paper by the method of the Laplace transform for the case of a double conductor line located parallel to a conducting half-space. The Fourier sine and cosine integral transforms are used in order to find the Laplace transform of the solution. The inverse Laplace transform of the solution is found in closed form. The integrated electromotiv...

Discrete wavelet transform (DWT) is the one of the main approaches used for image compression. A new discrete wavelet transform (DWT) architecture is proposed in this paper to realize a memory-efficient 2D DWT unit. The main goal of the proposed system is to change the processing unit in the pipelined DWT. Processing unit is modified in such a way that total number of processing required in the...

The paper presents analysis of frame partitioning in the next generation video coding standard HEVC. Complex study on frequency of the particular coding unit, prediction unit and transform unit sizes selection made by the encoder compliant with HEVC technology is included. General conclusions based on extensive experiments for HD video sequences are presented. Such knowledge may be the first st...

We explain the orthogonal planes split (OPS) of quaternions based on the arbitrary choice of one or two linearly independent pure unit quaternions f ,g. Next we systematically generalize the quaternionic Fourier transform (QFT) applied to quaternion fields to conform with the OPS determined by f ,g, or by only one pure unit quaternion f , comment on their geometric meaning, and establish invers...

We study -length Abelian codes over Galois rings with characteristic , where and are relatively prime, having the additional structure of being closed under the following two permutations: i) permutation effected by multiplying the coordinates with a unit in the appropriate mixed-radix representation of the coordinate positions and ii) shifting the coordinates by positions. A code is -quasi-cyc...

Some systems of univariate orthogonal polynomials can be mapped into other families by the Fourier transform. The most-studied example is related to Hermite functions, which are eigenfunctions For multivariate case, using transform and Parseval’s identity, very recently, some examples this type have been introduced orthogonality relations discussed. In present paper, method applied for on unit ...

Speed and selectivity of DC fault protection are critical for High-Voltage (HVDC) grids present significant technical economic challenges. Therefore, this paper proposes a non-unit solution that detects discriminates faults based on frequency domain analysis the transient period faults. The representation generic HVDC grid section corresponding DC-side signatures in form basis generalized appro...

The Fourier Transform Sum-Product Algorithm (FT-SPA) used in non-binary Low-Density Parity-Check (LDPC) decoding makes extensive use of the Walsh-Hadamard Transform (WHT). We have developed a massively parallel Fast Walsh-Hadamard Transform (FWHT) which exploits the Graphics Processing Unit (GPU) pipeline and memory hierarchy, thereby minimizing the level of memory bank conflicts and maximizing...

An algorithm for computing the discrete Fourier transform of data with threefold symmetry axes is presented. This algorithm is straightforward and easily implemented. It reduces the computational complexity of such a Fourier transform by a factor of 3. There are no restrictive requirements imposed on the initial data. Explicit formulae and a scheme of computing the Fourier transform are given. ...