Although versions of Poisson’s Summation Formula (PSF) have already been studied extensively, there seems to be no theorem that relates discretization to periodization and periodization to discretization in a simple manner. In this study, we show that two complementary formulas, both closely related to the classical Poisson Summation Formula, are needed to form a reciprocal Discretization-Perio...

Filters in a Convolutional Neural Network (CNN) contain model parameters learned from enormous amounts of data. In this paper, we suggest to decompose convolutional filters in CNN as a truncated expansion with pre-fixed bases, namely the Decomposed Convolutional Filters network (DCFNet), where the expansion coefficients remain learned from data. Such a structure not only reduces the number of t...

We present a face verification system inspired by known properties of the human visual system. In the proposed algorithm the face is normalized for geometry and luminance, and Fourier–Bessel (FB) descriptors are extracted from three locations in the eyes region (local analysis). The resulting representations are embedded in a dissimilarity space, where each image is represented by its distance ...

To study the impact of fundamental flow and background harmonics on harmonic and resonance characteristics of high-speed train-network coupling systems, harmonic admittance matrix model for four quadrant converter is deduced with the method of FFT and Bessel function. Equivalent load of train and chain network model of multiple conductors was established to conduct the calculation of fundamenta...

The spherical tensor gradient operator Y l (∇), which is obtained by replacing the Cartesian components of r by the Cartesian components of ∇ in the regular solid harmonic Y l (r), is an irreducible spherical tensor of rank l. Accordingly, its application to a scalar function produces an irreducible spherical tensor of rank l. Thus, it is in principle sufficient to consider only multicenter int...

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In this section, we consider approximative methods for the fast computation of multivariate discrete Fourier transforms for nonequi-spaced data (NDFT) in the time domain and in the frequency domain. In particular, we are interested in the approximation error as function of the arithmetic complexity of the algorithm. We discuss the robustness of NDFT{algorithms with respect to roundoo errors and...

We prove generalized Strichartz estimates for wave and massless Dirac equations in Aharonov-Bohm magnetic fields. Following a well established strategy to deal with scaling critical perturbations of dispersive PDEs, we make use Hankel transform rely on some precise Bessel functions. As complementary result, local smoothing estimate the Klein-Gordon equation same field.

The uncertainty principles of the 1-D fractional Fourier transform and the 1-D linear canonical transform have been derived. We extend the previous works and discuss the uncertainty principle for the two-dimensional affine generalized Fourier transform (2-D AGFFT). We find that derived uncertainty principle of the 2-D AGFFT can also be used for determining the uncertainty principles of many 2-D...