The properties of higher-order reassigned local polynomial periodogram

Reassigned operation is a technique to improve the representation quality of time-varying signals in the time-frequency domain. This paper presents the arbitrary higher-order reassigned local polynomial periodograms (LPPs) and their properties. The modified Wigner-Ville distribution is defined and its properties are discussed as a basis to derive the properties of the higher-order reassigned LPPs. The higher-order reassigned LPPs are shown to have desirable properties such as the non-negativity, non-bilinearity, time and frequency shifts invariance, time-scaling property and energy conservation. The property to perfectly localize the corresponding order polynomial phase signals is also shown to obtain improved signal concentration in the time-frequency domain.