Generalization of Convolution
Abstract
We generalize the concept of convolution to basis sets other than the Fourier basis. The basis set is defined by the eigenfunctions of a self-adjoint operator, which in turn defines the generalized transform. Several special cases are considered, including the scale transform and the chirplet transform, among others. We also generalize the concept of correlation between two functions. Examples are given to illustrate each result.
Fields of Study & Subjects
Mathematical Analysis and Transform Methods
Numerical methods in inverse problems
Sparse and Compressive Sensing Techniques
Publication details
- Journal / source
- Preprints.org
- Publication date
- 11 March 2026
- Language
- EN
- Document type
- Preprint