Novel types of convolution operators for quaternion linear canonical transform (QLCT) are proposed. Type one and two defined in the spatial QLCT spectral domains, respectively. They distinct space consistent once complex or real space. Various formulas discussed. Consequently, quaternionic functions can be implemented by product their QLCTs, summation products QLCTs. As applications, correlatio...

In recent years there has been a renewed interest in finding fast algorithms to compute accurately the linear canonical transform (LCT) of a given function. This is driven by the large number of applications of the LCT in optics and signal processing. The well-known integral transforms: Fourier, fractional Fourier, bilateral Laplace and Fresnel transforms are special cases of the LCT. In this p...

The linear canonical transform(LCT) has become a very active area in signal processing community in recent years, with many applications in optics, radar system analysis, filter design, phase retrieval, pattern recognition, etc. Many 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...

In this paper, we employ the concept of the Generalized Discrete Fourier Transform, which in turn relies on the Hasse derivative of polynomials, to give a general construction of Reed-Solomon codes over Galois fields of characteristic not necessarily co-prime with the length of the code. The constructed linear codes  enjoy nice algebraic properties just as the classic one.

The linear canonical transform describes the effect of first-order quadratic phase optical systems on a wave field. Several recent papers have developed sampling rules for the numerical approximation of the transform. However, sampling an analog function according to existing rules will not generally permit the reconstruction of the analog linear canonical transform of that function from its sa...

As a generalization of the 2D Fourier transform (2D FT) and 2D fractional Fourier transform, the 2D nonseparable linear canonical transform (2D NsLCT) is useful in optics and signal and image processing. To reduce the digital implementation complexity of the 2D NsLCT, some previous works decomposed the 2D NsLCT into several low-complexity operations, including 2D FT, 2D chirp multiplication (2D...

In this paper, we present a new predictive hybrid model using discrete wavelet transform (DWT), and the artificial neural network (ANN) to reduce the bullwhip effect of demand in supply chain to obtain a real amount of final customer demand. Also, we compare our result with more comprehensive sample of previous research to extend the scope of our study. In this new research our methodology is c...

Linear canonical transforms (LCTs) are a family of integral transforms with wide application in optical, acoustical, electromagnetic, and other wave propagation problems. The Fourier and fractional Fourier transforms are special cases of LCTs. In this paper, we extend the uncertainty principle for hypercomplex signals in the linear canonical transform domains, giving the tighter lower bound on ...

For classical discrete systems under constant composition, we re-examine how linear-nonlinear boundary in canonical ensemble, connecting a set of potential energy surface and that microscopic configuration thermodynamic equilibrium, is characterized by underlying lattice, from tropical geometry. We here show applying suitable limit multiple coordinate transform to time evolution dynamical syste...