Generalized Walsh functions and permutation-invariant systems
Abstract
This paper gives a representation of discrete version of Levy's generalized Walsh functions and characterizes finite discrete linear systems having these functions as their eigensignals. A basic property of the systems studied is the invariance of output signals to appropriately chosen sets of permutations of input signals. In view of this property these systems are designated 'permutation-invariant' (P-I) systems. The familiar cyclic and dyadic convolution systems are shown to be special classes of P-I systems.
- Publication:
-
Electromagnetic Compatibility
- Pub Date:
- 1977
- Bibcode:
- 1977elco.proc...43S
- Keywords:
-
- Invariance;
- Linear Systems;
- Permutations;
- Signal Analysis;
- Systems Analysis;
- Walsh Function;
- Convolution Integrals;
- Digital Systems;
- Discrete Functions;
- Dyadics;
- Eigenvectors;
- Electromagnetic Compatibility;
- Image Processing;
- Communications and Radar