On generalized Walsh bases
Abstract
This paper continues the study of orthonormal bases (ONB) of $L^2[0,1]$ introduced in \cite{DPS14} by means of Cuntz algebra $\mathcal{O}_N$ representations on $L^2[0,1]$. For $N=2$, one obtains the classic Walsh system. We show that the ONB property holds precisely because the $\mathcal{O}_N$ representations are irreducible. We prove an uncertainty principle related to these bases. As an application to discrete signal processing we find a fast generalized transform and compare this generalized transform with the classic one with respect to compression and sparse signal recovery.
- Publication:
-
arXiv e-prints
- Pub Date:
- February 2018
- arXiv:
- arXiv:1803.00123
- Bibcode:
- 2018arXiv180300123E
- Keywords:
-
- Mathematics - Functional Analysis