A Class of High Pass Filters Derived From Elliptic Differential Operators

Subject Areas : International Journal of Industrial Mathematics

K. Dabighi ¹ , A. Nazari ² , S. Saryazdi ³ , V. Momenaei ⁴

1 - Department of mathematic, Kerman Branch, Islamic Azad University, Kerman, Iran.
2 - Department of Mathematics, Faculty of Mathematics and Computer Sciences, Shahid Bahonar University, Kerman, Iran.
3 - Department of Electrical Engineering, Shahid Bahonar University, Kerman, Iran.
4 - Department of Mathematic, Kerman Branch, Islamic Azad University, Kerman, Iran.

Received: 2019-02-21 Accepted : 2019-06-01 Published : 2020-04-01

Keywords: Elliptic ‎operators.‎, filters, differential operator, high pass filter, principal symbol,

Abstract :

In this study, we review the elliptic differential operators and filters, and due to a wide range of elliptic operators, focus on a batch of elliptic operators with constant coefficients second order and then generalizing them to a higher order. Finally by discretization of the elliptic operators, we express and prove two theorems and show that the obtained filters are the high pass.