The continuous fractional wavelet transform (CFrWT) is a nontrivial generalization of the classical wavelet transform (WT) in the fractional Fourier transform (FrFT) domain. Firstly, the RiemannLebesgue lemma for the FrFT is derived, and secondly, the CFrWT in terms of the FrFT is introduced. Based on the CFrWT, a different proof of the inner product relation and the inversion formula of the CF...

First, this study obtained the fields of an Airy beam (AiB) with optical vortex (OV) for a Fourier transform (FT) system and a fractional Fourier transform (fractional FT) system; thereafter, their intensity and phase patterns were simulated numerically. The splitting on each line of the phase pattern indicates the position of an OV. The results show that the OV position will change when the po...

The performance of Orthogonal Frequency Division Multiple Access (OFDMA) system degrades significantly in doubly dispersive channels. This is due to the fact that exponential sub-carriers do not match the singular functions of this type of channels. To solve this problem, we develop a system whose sub-carriers are chirp functions. This is equivalent to exploiting Fractional Fourier Transform (F...

Determining orthonormal eigenvectors of the DFT matrix, which is closer to the samples of Hermite-Gaussian functions, is crucial in the definition of the discrete fractional Fourier transform. In this work, we disclose eigenvectors of the DFT matrix inspired by the ideas behind bilinear transform. The bilinear transform maps the analog space to the discrete sample space. As jω in the analog s-d...

The fractional Fourier transform (FRFT) is a useful tool for signal processing. It is the generalization of the Fourier transform. Many fractional operations, such as fractional convolution, fractional correlation, and the fractional Hilbert transform, are defined from it. In fact, the FRFT can be further generalized into the linear canonical transform (LCT), and we can also use the LCT to defi...

Linear canonical transforms play an important role in many fields of optics and signal processing. Well-known transforms such as the Fourier transform, the fractional Fourier transform, and the Fresnel transform can be seen as special cases of the linear canonical transform. In this paper we develop a sampling theorem for linear canonical transformed signals. The well-known Shannon sampling the...

Recently, the special kind of near-regular texture has drawn significant attention from researchers in the field of texture synthesis. Near-regular textures contain global regular structures that pose significant problems to the popular sample-based approaches, and irregular stochastic structures that can not be reproduced by simple tiling. Existing work tries to overcome this problem by user a...

This paper proposes color local binary pattern and fractional Fourier Transform features for face recognition. The YCbCr Color space model is used in this approach. Fractional Fourier Transform features and local binary pattern features are used for face recognition. kNN classifier is applied to face recognition phase.

The external description of a system [A,B,C,D] is given by its transfer function W(h). Classically in designing a system with given transfer function the key step is to express W(h) as a linear functional combination of simpler functions. Naturally such a decomposition of a transfer function must correspond to some type of decomposition of the system [A,B,C,D] into smaller subsystems. In this a...

We study properties of β-numeration systems, where β > 1 is the real root of the polynomial x −mx − x−1, m ∈ N, m ≥ 1. We consider arithmetic operations on the set of β-integers, i.e., on the set of numbers whose greedy expansion in base β has no fractional part. We show that the number of fractional digits arising under addition of β-integers is at most 5 for m ≥ 3 and 6 for m = 2, whereas und...