In mathematical modeling of the non-squared frequency-dependent diffusions, also known as the anomalous diffusions, it is desirable to have a positive real Fourier transform for the time derivative of arbitrary fractional or odd integer order. The Fourier transform of the fractional time derivative in the Riemann-Liouville and Caputo senses, however, involves a complex power function of the fra...

This paper is concerned with the definition of the continuous fractional Hartley transform. First, a general theory of linear fractional transform is presented to provide a systematic procedure to define the fractional version of any well-known linear transforms. Then, the results of general theory are used to derive the definitions of fractional Fourier transform (FRFT) and fractional Hartley ...

The present paper deals with the wavelet transform of fractional integral operator (the RiemannLiouville operators) on Boehmian spaces. By virtue of the existing relation between the wavelet transform and the Fourier transform, we obtained integrable Boehmians defined on the Boehmian space for the wavelet transform of fractional integrals.

The rapid growth of digital imaging applications, including desktop publishing, multimedia, teleconferencing, and high-definition television (HDTV) has increased the need for effective and standardized image compression techniques. The purpose of image compression is to achieve a very low bit rate representation, while preserving a high visual quality of decompressed images. It has been recentl...

Image reconstruction from amplitude-only and phase-only data in the fractional Fourier domain applying the inverse fractional Fourier transform is analyzed on the examples of perfect edges of different contrasts and real-world image. © 2003 MAIK “Nauka/Interperiodica”. 1 The question of the importance of phase and amplitude in the Fourier domain has been studied in many publications [1–4]. Ther...

The Fourier transform can be successfully used in the field of signal processing, image processing, communications and data compression applications. The discrete fractional Fourier transform, generalization of the discrete Fourier transform, is used for compression of high resolution satellite images. With the extra degree of freedom provided by the DFrFT, its fractional order 'a', h...

The Fractional Fourier Transform is a generalized form of Fourier Transform, which can be interpreted as a rotation by angle ? in time-frequency plane or decomposition of signals in terms of chirps. However it fails in locating Fractional Fourier Domain Frequency contents. Short-time FRFT variants are suitable for analysis of multicomponent and non-linear chirp signals with improved time-freque...

An efficient algorithm for computing the one-dimensional partial fast Fourier transform fj = ∑c(j) k=0 e Fk is presented. Naive computation of the partial fast Fourier transform requires O(N) arithmetic operations for input data of length N . Unlike the standard fast Fourier transform, the partial fast Fourier transform imposes on the frequency variable k a cutoff function c(j) that depends on ...

This research paper describes an image change detection method based upon the Discrete Fractional Fourier transform (DFrFT) along with intensity normalization and thresholding. DFrFT is used as it provides extra degree of freedom to detect accurate changed regions. The use of intensity normalization and thresholding ensure that change is based on appearance or disappearance of objects only, wit...

The recent emergence of the discrete fractional Fourier transform (DFRFT) has caused a revived interest in the eigenanalysis of the discrete Fourier transform (DFT) matrix F with the objective of generating orthonormal Hermite-Gaussian-like eigenvectors. The Grünbaum tridiagonal matrix T – which commutes with matrix F – has only one repeated eigenvalue with multiplicity two and simple remaining...