Suppose we have a function s(t) that measures the sound level at time t of an analog audio signal. We assume that s(t) is piecewise-continuous and of finite duration: s(t) = 0 when t is outside some interval a ≤ t ≤ b. Make a change of variable x = (t− a)/(b− a) and set f(x) = s(t). Then 0 ≤ x ≤ 1 when a ≤ t ≤ b, and f(x) is a piecewise continuous function of x. We convert f(x) into a digital s...

This paper investigates the performance of the digital symbol timing recovery schemes for 16QAM upstream transmission of DOCSIS Standard. Two forms of nonlinearity are considered: the magnitude square operation and the delay multiplication operation, both of which generate the output signal that contains the symbol timing information. The detailed analysis for the magnitude square timing recove...

in this work we synthesized of mesoporous silica nanoparticles and functionalized with 3-aminopropyltriethoxysilane to improve the loading and release of ibuprofen bonded to 3-aminopropyltriethoxysilane. sample were characterized by fourier transform infrared spectroscopy, scanning electron microscopy , x-ray diffraction, and ultraviolet-visible. the fourier transform infrared spectroscopy resu...

A method for the calculation of the fractional Fourier transform (FRT) by means of the fast Fourier transform (FFT) algorithm is presented. The process involves mainly two FFT's in cascade; thus the process has the same complexity as this algorithm. The method is valid for fractional orders varying from -1 to 1. Scaling factors for the FRT and Fresnel diffraction when calculated through the FFT...

We study the random variable Yn representing the number of occurrences of a symbol a in a word of length n chosen at random in a regular language L ⊆ {a; b}∗, where the random choice is de4ned via a non-negative rational formal series r of support L. Assuming that the transition matrix associated with r is primitive we obtain asymptotic estimates for the mean value and the variance of Yn and pr...

The ABCD matrix formalism, the Collins formula and the complex amplitude distributions on two spherical surfaces of given curvature and spacing are adapted to the mathematical expression of fractional order Fourier transform. This result provides a general expression as a tool for analyzing complicated systems involving several lenses and mirrors separated by arbitrary distances; for this class...