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.

The IFTAC is a special purpose analog computer designed to take the direct Fourier transform of a recorded function C(t). The system uses a recorded time base generated by a monochromatic source in the interferometer to correct for any changes in velocity of motion of the movable mirror, and to compensate for wow and flutter and changes in velocity of the tape transport drive system. Introducti...

Per temporal frequency component, the (least squares) Parabo-lic Radon Transform (PRT) is equivalent to the (least squares) Nonuniform Discrete Fourier Transform (NDFT). This can be used in two ways. Firstly, the efficiency of the PRT can be improved by using very fast algorithms for the calculation of the direct nonuniform Fourier transform. Secondly, comparing the PRT to the NDFT provides use...

In this paper we study Hyers-Ulam stability of Euler’s equation in the calculus variations two special cases: when F=F(x,y′) and F=F(y,y′). For first case use direct method for second Laplace transform. Theorem Example corresponding estimations Jyx−Jy0x are given. We mention that it is time problem Ulam-stability extremals functionals represented integral form studied.

Let $T$ be a bounded linear operator on a Hilbert space $mathscr{H}$. We say that $T$ has the hyponormal property if there exists a function $f$, continuous on an appropriate set so that $f(|T|)geq f(|T^ast|)$. We investigate the properties of such operators considering certain classes of functions on which our definition is constructed. For such a function $f$ we introduce the $f$-Aluthge tran...

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...

Let P = fP 0 ; : : : ; P n?1 g denote a set of polynomials with complex coeecients. Let Z = fz 0 ; : : : ; z n?1 g C denote any set of sample points. For any f = (f 0 ; : : : ; f n?1) 2 C n the discrete polynomial transform of f (with respect to P and Z) is deened as the collection i=0 f i P j (z i)w(i) for some associated weight function w. These sorts of transforms nd important applications i...

Nanoparticles of ytterbium tungstate prepared through the direct addition of an Yb3+ solution to a tungstate solution, were computed through Fourier transform infrared spectroscopy (FTIR), scanning electron microscopy (SEM), energy-dispersive X-ray spectroscopy (EDS). Further the supercapacitive characteristics of the nanoparticles, as a potential material for constructing electrodes, were eval...