Wide-Sense Translinear Systems

Abstract

The principle of additive superposition, which characterizes linear systems, was extended by Oppenheim to the principle of homomorphic superposition, which characterizes generalized linear systems, which form a class of nonlinear systems. The advantage of additive or homomorphic superposition is that the output corresponding to any particular input can be deducted from outputs to simpler inputs in terms of which that particular input can be synthesized. A new class of systems, which has the same advantage, is defined and illustrated with examples. One of the examples establishes a new property of the discrete Fourier transforms.

Indexing Terms:

• Systems
• DFT
• Signal Design