In this paper, we consider a q-analogue of the Dunkl operator on R, we define and study its associated Fourier transform which is a q-analogue of the Dunkl transform. In addition to several properties, we establish an inversion formula and prove a Plancherel theorem for this q-Dunkl transform. Next, we study the q-Dunkl intertwining operator and its dual via the q-analogues of the Riemann-Liouv...

The fractional cosine and sine transforms – closely related to the fractional Fourier transform, which is now actively used in optics and signal processing – are introduced and their main properties and possible applications are discussed.

The fractional Fourier transform (FrFT) can be thought of as a generalization of the Fourier transform to rotate a signal representation by an arbitrary angle in the time–frequency plane. A lower bound on the uncertainty product of signal representations in two FrFT domains for real signals is obtained, and it is shown that a Gaussian signal achieves the lower bound. The effect of shifting and ...

Filtering in a single time domain or in a single frequency domain has recently been generalized to filtering in a single fractional Fourier domain. In this correspondence, we further generalize this to repeated filtering in consecutive fractional Fourier domains and discuss its applications to signal restoration through an illustrative example.

A theorem characterizing fractional Brownian motion by Index Terms -Wavelet transform, fractional Brownian motion.the covariance structure of its wavelet transform is established.

We present a fractional Gabor expansion on a general, nonrectangular time-frequency lattice. The traditional Gabor expansion represents a signal in terms of time and frequency shifted basis functions, called Gabor logons. This constantbandwidth analysis results in a fixed, rectangular time frequency plane tiling. Many of the practical signals require a more flexible, non-rectangular time-freque...

In this paper, some properties of pseudo-differential operators, SG-elliptic partial differential equations with polynomial coefficients and localization operators on space S ν (R), are studied by using fractional Fourier transform. AMS Mathematics Subject Classification (2010): 35S05, 46F12, 47G30.