Future wireless communication systems are demanding a more flexible physical layer. GFDM is a block filtered multicarrier modulation scheme proposed to add multiple degrees of freedom and to cover other waveforms in a single framework. In this paper, GFDM modulation and demodulation is presented as a frequency-domain circular convolution, allowing for a reduction of the implementation complexit...

This work deals with Hadamard Z2Z4Q8-codes, which are binary codes after a Gray map from a subgroup of a direct product of Z2, Z4 and Q8 groups, where Q8 is the quaternionic group. In a previous work, these kind of codes were classified in five shapes. In this paper we analyze the allowable range of values for the rank and dimension of the kernel, which depends on the particular shape of the co...

Abstract. Using a simple formula for conditional expectations over an analogue of Wiener space, we calculate a generalized analytic conditional Fourier-Feynman transform and convolution product of generalized cylinder functions which play important roles in Feynman integration theories and quantum mechanics. We then investigate their relationships, that is, the conditional Fourier-Feynman trans...

The Khatri-Rao and Tracy-Singh products for partitioned matrices are viewed as generalized Hadamard and generalized Kronecker products, respectively. We define the KhatriRao and Tracy-Singh sums for partitioned matrices as generalized Hadamard and generalized Kronecker sums and derive some results including matrix equalities and inequalities involving the two sums. Based on the connection betwe...

In this paper, assuming p/n → 0 as n → ∞, we will prove the weak and strong convergence to the semicircle law of the empirical spectral distribution of the Hadamard product of a normalized sample covariance matrix and a sparsing matrix, which is of the form Ap = 1 √ np (Xm,nX ∗ m,n − σnIm) ◦ Dm, where the matrices Xm,n and Dm are independent and the entries of Xm,n (m × n) are independent, the ...

Methods for extracting features and classifying textures in high resolution colour images are presented. The proposed features are directional texture features obtained from the convolution of the Walsh-Hadamard transform with different orientations of texture patches from high resolution images, as well as simple chromatic features that correspond to hue and saturation in the HLS colour space....

The Hadamard product features prominently in tensor-based algorithms in scientific computing and data analysis. Due to its tendency to significantly increase ranks, the Hadamard product can represent a major computational obstacle in algorithms based on low-rank tensor representations. It is therefore of interest to develop recompression techniques that mitigate the effects of this rank increas...

It is conjectured that binary cocyclic matrices are a uniform source of Hadamard matrices. In testing this conjecture, it is useful to have a general method of calculating cocyclic matrices. We present such a method in this paper. The method draws on standard cohomology theory of finite groups. In particular we employ the Universal Coefficient Theorem, which expresses the second cohomology grou...

We begin by introducing some function spaces Lcp(R+),Xcp(J) made up of integrable functions with exponent or power weights defined on infinite intervals, and then we investigate the properties Mellin convolution operators mapping these spaces, next, derive new boundedness continuity Hadamard integral Xcp(J) Xp(J). Based this, a class boundary value problems for fractional differential equations...