In this article, by using a partial on locally compact semi-direct product groups, we present a compatible extension of the Fourier transform. As a consequence, we extend the fundamental theorems of Abelian Fourier transform to non-Abelian case.

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...

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...

A new method, called the matrix enhancement and matrix pencil (MEMP) method, is presented for estimating twodimensional (2-D) frequencies. The MEMP method first constructs an enhanced matrix from the data samples, and then uses the matrix pencil approach to extract out the 2-D sinusoids from the principal eigenvectors of the enhanced matrix. The MEMP method yields the estimates of the 2-D frequ...