In this contribution, the F 1-transform of functions of two variables is introduced. It combines properties of the F-transform of functions of two variables and the F 1-transform of functions of one variable. The aim of this study is to prove approximation properties of the F 1-transform components and of the inverse F 1-transform in this particular case.

The connection between a Taylor series and a continued-fraction involves a nonlinear relation between the Taylor coefficients {an} and the continued-fraction coefficients {bn}. In many instances it turns out that this nonlinear relation transforms a complicated sequence {an} into a very simple one {bn}. We illustrate this simplification in the context of graph combinatorics. PACS numbers: 02.90...

The aim of this contribution is to show how the Ftransform technique can be generalized from the case of constant components to the case of polynomial components. For this purpose, we choose complete functional spaces with inner products. After a general presentation of Fm-transform where m ≥ 0, a detailed characterization of the F -transform is given. We applied a technique of numeric integrat...

The technique of direct and inverse fuzzy (F-)transforms of three different types is introduced and approximating properties of the inverse F-transforms are described. A method of lossy image compression and reconstruction on the basis of the F-transform is presented.

The technique of the direct and inverse fuzzy (F-) transform is introduced and approximating properties of the inverse F-transforms are described. A method of lossy image compression and reconstruction on the basis of F-transforms is illustrated on examples of pictures and music.

one of the common problems in reflective seismic records is the existence of coherent linear and random noises which cause covering of the most important parts of reflective signals; therefore, it is necessary to attenuate them by processing methods. several processing techniques have been devised for attenuation of coherent linear noises and linear radon or ?-? transform is a powerful techniqu...

This contribution focuses on inverse fuzzy transforms (shortly inverse F-transforms) over residuated lattices introduced by I. Perfilieva and their approximation properties. We will try to reduce some requirements used in the original work to prove Approximation theorem. Moreover, we show in which sense F-transforms are the best approximations. Keywords— Fuzzy transform, Approximation, Extensio...

and the inverse Fourier transform is f (x) = 1 2π ∫ ∞ −∞ F(ω)e dω Recall that i = √−1 and eiθ = cos θ+ i sin θ. Think of it as a transformation into a different set of basis functions. The Fourier transform uses complex exponentials (sinusoids) of various frequencies as its basis functions. (Other transforms, such as Z, Laplace, Cosine, Wavelet, and Hartley, use different basis functions). A Fo...

Abstract The fuzzy transform setting (F-transform) is proposed as a tool for representation and approximation of type-1 and type-2 fuzzy numbers; the inverse F-transform on appropriate fuzzy partition of the membership interval [0,1] is used to characterize spaces of fuzzy numbers in such a way that arithmetic operations are de…ned and expressed in terms of the F-transform of the results. A typ...

1 Review 1.1 Setup In the previous lecture, we considered an apparatus consisting of three planes: • an aperture plane. Coordinates on the aperture plane are denoted by x and y. • a transform plane. Coordinates on the transform plane are denoted by X and Y. • an image plane. Coordinates on the image plane are denoted by x and y. We defined the spatial frequencies, µ = k f X ν = k f Y where f is...