A New Multi-Dimensional Transform for Digital Signal Processing Using Generalized Association Schemes
Abstract
Our research focused on the development of a multi-dimensional discrete transform using a new algebra of multi-dimensional arrays. The proposed transform for the n-dimensional can compute en block the transforms of a family of (n-1) dimensional arrays. Also, the number of multiplications is relatively low. The definition of the transform (for the 3-dimensional case) uses the concept of an inverse pair for a pair of 3-dimensional arrays. We have developed methods to compute such inverse pairs and it has been shown there is an abundant supplies of such pairs which could then profitably be used to define various types of 3-dimensional transforms. We have also investigated the properties of the ternary algebra associated with the 3-dimensional arrays. Further, the multi-dimensional approach has been used by us to the representation of uncertain information in conjunction with the Dempster-Schafer theory. It has been shown how to compute the information regarding the probability of occurrences of the variables as certain matrix products. Digital signal processing, Transforms, Multi-dimensional arrays.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 31, 1994
- Accession Number
- ADA284166
Entities
People
- Prabir Bhattacharya
Organizations
- University of Nebraska–Lincoln