Digital signal processing (3rd ed.): principles, algorithms, and applications
Digital signal processing (3rd ed.): principles, algorithms, and applications
Transform Coding of Images
Digital Signal Processing: A Computer-Based Approach
Digital Signal Processing: A Computer-Based Approach
Digital Signal Processing Handbook
Digital Signal Processing Handbook
Digital Methods for Signal Analysis
Digital Methods for Signal Analysis
Orthogonal Transforms for Digital Signal Processing
Orthogonal Transforms for Digital Signal Processing
Handbook of Image and Video Processing (Communications, Networking and Multimedia)
Handbook of Image and Video Processing (Communications, Networking and Multimedia)
Discrete Generalized Fresnel Functions and Transforms in an Arbitrary Discrete Basis
IEEE Transactions on Signal Processing
Hi-index | 0.00 |
In this paper the so-called generalized convolution, being in fact an adequate adaptation of the well known circular convolution concept to any invertible block-transform, is proposed, developed, and analysed. First the proposed idea is summarized for a one-dimensional case. Then it is extended to multidimensional problems. The presented generalized convolution concept is based on the earlier A-convolution. This idea is recalled at the beginning and a set of techniques for studying the dependence of the respective coefficients on the arbitrary transform, is suggested. The generalized convolution matrix, being an extension of that for the circular convolution, is introduced and adapted to an arbitrary invertible transform. The filtering problem is then defined and presented in the transform domain. The multidimensional analysis starts with two-dimensional problems, then it is continued with formulas for multidimensional filtering tasks. The paper is illustrated with examples computed for twenty carefully selected transforms. Among them are Haar, Hadamard, Hartley, Karhunen-Loeve and a family of 16 discrete trigonometric transforms.