Edge detection with trigonometric polynomial shearlets

In this paper we show that certain trigonometric polynomial shearlets which are special cases of directional de la Vall\'{e}e Poussin type wavelets able to detect singularities along boundary curves periodic characteristic functions. Motivated by recent results for discrete in two dimensions, provide lower and upper estimates the magnitude corresponding inner products. proof use localization properties time frequency domain and, among other things, bounds Fresnel integrals. Moreover, give numerical examples underline theoretical results.