Pascal Matrices and Discrete Pascal Transform: Theory and Related Applications
Date Issued
2008
Date
2008
Author(s)
Liu, Wan-Lin
Abstract
Pascal triangle was researched by mathematicians ago. It has many mathematical properties. In this article, we apply Pascal triangle in digital signal processing and image processing.y Pascal triangle, we define two types of the lower triangular Pascal matrices which we denote as type I and type II Pascal matrix respectively, and furthermore introduce a kind of Pascal matrix which we denote as type III Pascal matrix. The lower triangular Pascal matrices, i.e., type I and type II Pascal matrix which we define consist of the rows of Pascal triangle. e discuss three types of Pascal matrices and their relative applications in digital signal processing and image processing, including unification several discrete transforms, edge detection, interpolation, and digital filter design.n particular, we introduce the discrete Pascal transform. The discrete Pascal transform (DPT) was proposed by Aburdene and Goodman. It belongs to the family of the discrete polynomial transforms. Such transform finds numerous applications in signal and image processing, as well as in communication and control systems. We perform how to use the discrete Pascal transform to make an edge detector, and to do interpolations.
Subjects
Pascal triangle
digital signal processing
digital image processing
edge detection
interpolation
digital filter design
discrete Pascal transform
Type
thesis
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