In this article, we establish theory of Parseval framelets associated to generalized multiresolution analysis (GMRA) in the setting of reducing subspace for the local field of positive characterist...

Construction of Parseval Framelets Associated with GMRA on Local Fields of Positive Characteristic

For the discrete Fourier transform with respect to the system of characters of a local field with positive characteristic, we propose a fast algorithm. We find the complexity of the algorithm.

Fast discrete Fourier transform on local fields of positive characteristic

In view of the problems of low recognition rate, slow detection speed and poor generalization of existing traditional detection methods, a DCNN-based method for detecting the solder joint qualification of cable joints is proposed. Firstly, the method corrects the tilted image by Discrete Fourier Transformation, Hough Line Detection and Affine Transformation to extract the solder joint area. Secondly, the features of the solder joint area are extracted by establishing a deep convolutional neural network. Finally, the solder joints are classified by the Softmax classifier. Experiments show that the recognition rate of the method reaches 98.6% and the detection speed is 0.078 sec/sheet, which has higher practical application value than other traditional algorithms.

The Research of Qualification Detection of Cable Joint Solder Joint Based on DCNN

For the discrete Fourier transform with respect to the system of characters of a local field with zero characteristic, we propose a fast algorithm. We find the complexity of the algorithm.

Fast Discrete Fourier Transform on Local Fields of Zero Characteristic

We present an algorithm for construction step wavelets on local fields of positive characteristic.

How to construct wavelets on local fields of positive characteristic

Non-Haar MRA on local fields of positive characteristic

We propose a simple method to construct integral periodic mask and corresponding scaling step functions that generate non-Haar orthogonal MRA on the local field $ F^{(s)}$ of positive characteristic $p$. To construct this mask we use two new ideas. First, we consider local field as vector space over the finite field $GF(p^s)$. Second, we construct scaling function by arbitrary tree that has $p^s$ vertices. By fixed prime number $p$ there exist $p^{s(p^s-2)}$ such trees.

The problem of constructing L2 integrable functions on a local field of zero characteristic, whose shifts form an orthonormal system, is considered.

Alexander Vodolazov

Papers

Non-Haar MRA on local fields of positive characteristic

Fast discrete Fourier transform on local fields of positive characteristic

Non-Haar MRA on local fields of positive characteristic

Shift Systems in Local Fields of Zero Characteristic