Abstract -Orthogonal frequency division multiplexing is a scheme of encoding digital information on numerous carrier frequencies. The orthogonality permits an proficient modulator and demodulator realization by means of FFT algorithm resting on receiver side, and inverse FFT resting on sender side. A substitute technique for orthogonal transmission and reception of data using Rajan Transform an...

The terms Fast Fourier Transform (FFT) and Inverse Fast Fourier Transform (IFFT) are used to denote efficient and fast algorithms to compute the Discrete Fourier Transform (DFT) and the Inverse Discrete Fourier Transform (IDFT) respectively. The FFT/IFFT is widely used in many digital signal processing applications and the efficient implementation of the FFT/IFFT is a topic of continuous research.

where a(u, v) denotes the standard deviation of a coefficient. The inverse transform is given by The maximum coefficient value for the cosine transform can be derived from (1) as (3) (2) for w = <P for w = 1, 2, "', N-1. [ (2j + 1)U1T] [(2k + 1)V1T] • cos cos 2N 2N 1 !v' 2 I X I! p(x; u , v) = exp-Vi a(u, v) a(u, v) 1 C(w) = Vi N-1N-1 fO, k) = ~ ~ C(u)C(v)F(u, v) u=O v=O for i, k = 0, 1, "', N-...

Because the Radon transform is a smoothing transform, any noise in the Radon data becomes magnified when the inverse Radon transform is applied. Among the methods used to deal with this problem is the wavelet-vaguelette decomposition (WVD) coupled with wavelet shrinkage, as introduced by Donoho (1995). We extend several results of Donoho and others here. First, we introduce a new sufficient con...

(1.1) = inf f t > 0 j Bt g(t) g is exponentially distributed (i.e. has a density function f(t) = e t with t > 0 and > 0 ). This problem can be viewed as an inverse to the problem of finding a density function f of when g is given. Explicit solutions to the latter problem are known only in a limited number of special cases including linear or quadratic g . The law of is also known for a square-r...

We summarize a recently developed integral equation approach to tackling the long-time existence problem for smooth solution v(x, t) to the 3-D Navier-Stokes equation in the context of a periodic box problem with smooth time-independent forcing and initial condition v0. Using an inverse Laplace transform of v̂(k, t) − v̂0 in 1/t, we arrive at an integral equation for Û(k, p), where p is inverse-L...

All methods presented in textbooks for computing inverse -transforms of rational functions have some limitation: 1) the direct division method does not, in general, provide enough information to derive an analytical expression for the time-domain sequence whose -transform is ; 2) computation using the inversion integral method becomes labored when has poles at the origin of the complex plane; 3...

It is known that the Laplace transform is frequently used to solve fractional-order differential equations. Unlike integer-order differential equations, fractional-order differential equations always lead to difficulties in calculating inversion of Laplace transforms. Motivated by finding an easy way to numerically solve the fractional-order differential equations, we investigated the validity ...

and Applied Analysis 3 fractional order to distributed order fractional. In Section 4, we introduce the distributed order fractional evolution systems C doD α t x t A C doD β t x t Bu t , x 0 x0, 0 < β < α ≤ 1, 1.5 where u t is control vector, and generalize the results obtained in Section 3 for this case. Finally, the conclusions are given in the last section. 2. Elementary Definitions and The...

In this paper, we will illustrate the F-transform based on generalized fuzzy partitions as a tool for expectile smoothing. This allows to represent a time series in terms of a fuzzy-valued function whose level-cuts are modeled by F-transform and estimated by expectile regression. The proposed methodology is illustrated on real economic and …nancial time series. Keywords: Fuzzy Transform, Expect...