On Higher Order Positive Differential Energy Operator

TL;DR

This paper introduces the Positive Differential Energy Operator (PDEO), a higher order operator that addresses the positivity issue of traditional DEOs, improving AM/FM demodulation performance.

Contribution

The paper proposes PDEO, a novel higher order energy operator that ensures positivity and enhances demodulation accuracy over existing DEOs.

Findings

PDEO outperforms traditional DEOs in ASER for AM/FM demodulation.

PDEO resolves the energy sign problem inherent in higher order DEOs.

Simulations confirm improved signal energy measurement accuracy.

Abstract

The higher order differential energy operator (DEO), denoted via $\Upsilon_k(x)$, is an extension to the second order famous Teager-Kaiser operator. The DEO helps measuring the higher order gauge of energy of a signal which is useful for AM-FM demodulation. However, the energy criterion defined by the DEO is not compliant with the presumption of positivity of energy. In this paper we introduce a higher order operator called Positive Differential Energy Operator (PDEO). This operator which can be obtained using alternative recursive relations, resolves the energy sign problem. The simulations demonstrate that the proposed operator can outperform DEOs in terms of Average Signal to Error Ratio (ASER) in AM/FM demodulation.