In this paper, we develop some methods to save the bandwidth required in the fractional domain. The fractional domain is the transformed domain of the fractional Fourier transform (FRFT). It is the intermediate of the time domain and the frequency domain. We find that, with the aid of the fractional Hilbert transform and other techniques, we can save 112 or 314 of the bandwidth in the fractiona...

A known theorem, Nigam 2010 dealing with the degree of approximation of conjugate of a signal belonging to Lipξ t -class by E, 1 C, 1 product summability means of conjugate series of Fourier series has been generalized for the weighted W Lr, ξ t , r ≥ 1 , t > 0 -class, where ξ t is nonnegative and increasing function of t, by ̃ E1 nC n which is in more general form of Theorem 2 of Nigam and Shar...

Circulant embedding is a technique that has been used to generate realizations from certain real-valued Gaussian stationary processes. This technique has two potential advantages over competing methods for simulating time series. First, the statistical properties of the generating procedure are exactly the same as those of the target stationary process. Second, the technique is based upon the d...

This application note describes the basics of the Fast Fourier Transform and how to use a Digital Signal Processing Library. The library and design example use Microchip’s dsPIC30F Series Digital Signal Controller, specifically the dsPIC30F3013. The Transform Analysis discusses the differences between the Discrete Fourier Transform (DFT) and the Fast Fourier Transform (FFT), and how the FFT is ...

Algorithms for the rapid computation of the forward and inverse discrete Fourier transform for points which are nonequispaced or whose number is unrestricted are presented. The computational procedure is based on approximation using a local Taylor series expansion and the fast Fourier transform (FFT). The forward transform for nonequispaced points is computed as the solution of a linear system ...

This paper looks at one of the jewels of mathematics, the Fourier series / transform and briefly surveys its applications and looks at possible ways of enhancing the performance of the fast Fourier transform

Recently, regime shifts or structure breaks had acquired very high attention in analyzing financial time series data. Abrupt of changes in the government policy, financial crises and many of challenges lead to change in the behavior of the financial time series data. In addition, wavelet transform also becomes very famous in the financial sector and it has better advantages than the other filte...

We consider the problem of convergence of Fourier series when we make a change of variable. Under a certain reasonable hypothesis, we give a necessary and sufficient condition for a homeomorphism of the circle to transform absolutely convergent Fourier series into uniformly convergent Fourier series.

In the present work, a hybrid of Fourier transform and homotopy perturbation method is developed for solving the non-homogeneous partial differential equations with variable coefficients. The Fourier transform is employed with combination of homotopy perturbation method (HPM), the so called Fourier transform homotopy perturbation method (FTHPM) to solve the partial differential equations. The c...

magnetotelluric (mt) method is an important passive surface geophysical method which uses the earth’s natural electromagnetic fields to investigate the electrical resistivity structure of the subsurface. the depth of investigation of mt is much higher than that of other electromagnetic (em) methods (vozoff, 1991). for a general conductivity distribution in the earth, the horizontal electric fie...