An interesting problem of algebraic computation is the computation of the greatest common divisor (GCD) of a set of polynomials. The GCD is usually linked with the characterisation of zeros of a polynomial matrix description of a system. The problem of finding the GCD of a set of n polynomials on R[x] of a maximal degree q is a classical problem that has been considered before (Karcanias et al....

a novel podand based anion receptor bearing benzimidazole motifs as recognition sites was designed and synthesized by reaction of 1,7-bis(2'-methylbenzoate)-1,4,7-trioxaheptane and phenylenediamine. the binding properties of anionic guest with this receptor were studied using uv-vis and fluorescence spectroscopy. these studies revealed that this receptor exhibit selective recognition towards f- ...

Image computation is a fundamental tool for performance assessment of astronomical instrumentation, usually implemented by Fourier transform techniques. We review the numerical implementation, evaluating a direct implementation of the discrete Fourier transform (DFT) algorithm, compared with fast Fourier transform (FFT) tools. Simulations show that the precision is quite comparable, but in the ...

The problem of constructing an orthogonal set of eigenvectors for a DFT matrix is well studied. An elegant solution is mentioned by Matveev in [1]. In this paper, we present a distilled form of his solution including some steps unexplained in his paper, along with correction of typos and errors using more consistent notation. Then we compare the computational complexity of his method with the m...

The novel methods for binary discrete Fourier transform (DFT) computation over the finite field have been proposed. are based on a trace calculation and use cyclotomic DFT. direct DFT computational complexity has reduced due to using function functions of which stored in small tables. inverse representation elements with respect normal basis. proposed can be used encoding/decoding subfield subc...

Recently, a novel systolic structure has been proposed for the computation of DFT for transform length N = 4 M , M being prime to 4. In this paper, we have proposed a similar structure for the computation of DHT by prime factor decomposition. A new recursive algorithm is also proposed for computing DHT using a linear systolic array of cordic processing elements. The proposed structure has nearl...

This paper describes an implementation of the Discrete Fourier Transform (DFT) and the Inverse Discrete Fourier Transform (IDFT). We show how the computation of the DFT and IDFT may be performed in Java and show why such operations are typically considered slow. This is a multi-part paper, in part 2, we discuss a speed up of the DFT and IDFT using a class of algorithms known as the FFT (Fast Fo...

In this paper we have presented a transcoding algorithm to perform super-resolution of sub-sampled images. First of all we used 1D case in the fourier domain (DFT). Then we extended the same approach for the 2D case. After presenting the results for this we looked at the possibility of improving the performance of our algorithm. This was done by removing the need to perform matrix inversions (h...

Optical-computing technology offers new challenges to algorithm designers since it can perform an n-point discrete Fourier transform (DFT) computation in only unit time. Note that the DFT is a nontrivial computation in the parallel random-access machine model, a model of computing commonly used by parallel-algorithm designers. We develop two new models, the DFT-VLSIO (very-large-scale integrate...

The classical method of numerically computing Fourier transforms of digitized functions in one or in -dimensions is the so-called discrete Fourier transform (DFT) efficiently implemented as fast Fourier transform (FFT) algorithms. In many cases, the DFT is not an adequate approximation to the continuous Fourier transform, and because the DFT is periodical, spectrum aliasing may occur. The metho...