In this paper, some properties of pseudo-differential operators, SG-elliptic partial differential equations with polynomial coefficients and localization operators on space S ν (R), are studied by using fractional Fourier transform. AMS Mathematics Subject Classification (2010): 35S05, 46F12, 47G30.

We use the recent comprehensive research [17, 19] on the manifolds of square roots of −1 in real Clifford’s geometric algebras Cl(p,q) in order to construct the Clifford Fourier transform. Basically in the kernel of the complex Fourier transform the imaginary unit j ∈ C is replaced by a square root of−1 in Cl(p,q). The Clifford Fourier transform (CFT) thus obtained generalizes previously known ...

Introduction: The fractional Fourier transform (FRT) has received significant interest since the early 1990s [1, 2]. The ath order FRT operation corresponds to the ath power of the ordinary Fourier transform operation. The zeroth-order FRT of a function is the function itself and the first-order FRT is equal to the ordinary Fourier transform. For additional properties and references, see [3]. I...

in the present work we study the use of fourier transform near infrared spectroscopy (ftnirs)technique to analysis the calcium (ca), phosphorus (p) and copper (cu) contents offish meal. the regression methods employed were partial least squares (pls) and kernelpartial least squares (kpls). the results showed that the efficiency of kpls was better thanpls. as a whole, the application of ft-nirs ...

in this article, vibration analysis of an euler-bernoulli beam resting on a pasternak-type foundation is studied. the governing equation is solved by using a spectral finite element model (sfem). the solution involves calculating wave and time responses of the beam. the fast fourier transform function is used for temporal discretization of the governing partial differential equation into a set ...

In this chapter we show how to compute the Discrete Fourier Transform using a Fast Fourier Transform (FFT) algorithm, including not-so special case situations such as when the data to be transformed are real. In those situations, we speed up the transforms by about a factor of two by exploiting symmetries in the data and the coefficients. We end this chapter by showing how to approximate the de...

PURPOSE: Non-Cartesian imaging is essential in applications such as ultra-short time-echo imaging and realtime cardiac imaging. However, reconstruction speed becomes a limitation when iterative reconstruction is desired for parallel imaging, compressed sensing or artifact correction. In this work, we propose using pruned Fast Fourier Transform (pruned FFT) to accelerate almost all fast non-Cart...

In this chapter we show how to compute the Discrete Fourier Transform using a Fast Fourier Transform (FFT) algorithm, including not-so special case situations such as when the data to be transformed are real. In those situations, we speed up the transforms by about a factor of two by exploiting symmetries in the data and the coefficients. We end this chapter by showing how to approximate the de...

In this chapter we show how to compute the Discrete Fourier Transform using a Fast Fourier Transform (FFT) algorithm, including not-so special case situations such as when the data to be transformed are real. In those situations, we speed up the transforms by about a factor of two by exploiting symmetries in the data and the coefficients. We end this chapter by showing how to approximate the de...