a Nearly Tridiagonal Matrix Magdy Tawfik Hanna1 ABSTRACT A fully-fledged definition for the fractional discrete Fourier transform of type IV (FDFT-IV) is presented and shown to outperform the simple definition of the FDFT-IV which is proved to be just a linear combination of the signal, its DFT-IV and their flipped versions. This definition heavily depends on the availability of orthonormal eig...

Discrete Sine Transforms of types VI and VII (DST-VI/VII) have recently received considerable interest in video coding. In particular, it was shown that DST-VII offers good approximation for KLT of residual signals produced by spatial (Intra) prediction process. In this paper, we offer an additional argument for use of such transforms by showing that they allow fast computation. Specifically, w...

The paper analyses effect of windowing a multi-frequency signal on the result of calculating signal parameters based on DFT. Influence of window side-lobes of nearby harmonic signals on the result of computation depends on the on the used window and on the difference in the two components magnitudes and frequencies. There are several other sources of resulting bias and uncertainty of measuremen...

Introduction: The discrete Hartley transform (DHT) is an attractive alternative to the discrete Fourier transform (DFT) because of its real-valued computation and properties similar to those of the DFT [1]. Another interesting property of the DHT is that the same kernel is used for both the transform and its inverse transform. Consequently, since its introduction the DHT has found its way to ma...

Energy bandstructure in silicon nanowires with [100] crystal orientation is calculated using the Tight-Binding (TB) model with supercell approach. Numerical methods are designed according to the physical model to reach an optimal computational performance. Computation results show that the bandstructures of silicon nanowires deviate from that of bulk silicon. The efficiency and accuracy of the ...

The Fast Fourier Transform (FFT) is an efficient computation of the Discrete Fourier Transform (DFT) and one of the most important tools used in digital signal processing applications. Because of its well-structured form, the FFT is a benchmark in assessing digital signal processor (DSP) performance. The development of FFT algorithms has assumed an input sequence consisting of complex numbers. ...

Utilizing tender resonant X-ray scattering, resonance effects in twist bend nematic phase were deciphered quantitatively. Distinct helical pitch variation trend between symmetric/asymmetric dimers was further analysed by DFT computation.

This paper is part 3 in a series of papers about the Discrete Fourier Transform (DFT) and the Inverse Discrete Fourier Transform (IDFT). The focus of this paper is on computing the Power Spectral Density (PSD) of the FFT (Fast Fourier Transform) and the IFFT (Inverse Fast Fourier Transform). The implementation is based on a well-known algorithm, called the decimation in time Radix 2 FFT, and re...

[NMe4 ]2 [As4 0 2 Clio] • 2 CH3CN was recovered by the reaction of [NMe4][N3] with AsCh in CH3CN under aerobic conditions. This compound was also obtained directly by the reaction of AsCb, AS2O3 and [NMe4][Cl] in acetonitrile. The structure was determined by X-ray diffraction. [NMe4 ]2 [As4 0 2Clio] • 2 CH3CN crystallizes in theoorthorhombic space group Fmmm with a = 11.4144(8), b = 14.732(1) a...

—Real-valued block codes are introduced, which are derived from Discrete Fourier Transforms (DFT) and Discrete Hartley Transforms (DHT). These algebraic structures are built from the eigensequences of the transforms. Generator and parity check matrices were computed for codes up to block length N=24. They can be viewed as lattices codes so the main parameters (dimension, minimal norm, area of t...