Polynomial order reducing property of lattice filters for FM signals with polynomial phases

The behaviour of the optimal and adaptive reflection coefficients of lattice filters for FM signals with polynomial phases of order p is investigated. It is theoretically shown that the optimal reflection coefficients form FM signals with lower order polynomial phases p-1. This new characteristic which is correspondingly held for the adaptive reflection coefficients is introduced as the polynomial order reducing (POR) property of the reflection coefficients. Using the POR property, by inputting the signal produced by one adaptive coefficient to the next adaptive lattice filter, the input polynomial order can frequently be reduced so that a sinusoid is obtained. More interestingly, the phases of these signals are related to each other. While, the POR property is heuristically worthwhile, it may potentially be used in several signal processing applications. As an example, this property is applied to the instantaneous frequency (IF) estimation of a linear FM signal.