The higher-order reassigned local polynomial periodogram and its properties

Recently the second order reassigned local polynomial periodogram (LPP) has been reported to show some desirable properties for signal representation in the time–frequency domain. In this paper, the higher-order reassigned LPPs and their properties are discussed. With the definition of the modified Wigner–Ville distribution, the reassignment operators of the third, fourth and the arbitrary higher-order reassigned LPP are defined and derived. It is shown that the higher-order reassigned LPPs share the properties with the second order reassigned LPP, such as the non-negativity, non-bilinearity, time and frequency shifts invariance, time-scaling property and energy conservation. The property of the higher-order reassigned LPP to perfectly localize the corresponding order polynomial phase signals is also investigated to obtain improved signal concentration in the time–frequency domain.

► The higher-order reassigned LPP is defined and mathematically proved.
► Properties of the higher-order reassigned LPP are discussed.
► The generalization complements our previous work on the second order reassigned LPP.