The higher-order reassigned local polynomial periodogram and its properties

Authors:
Xiumei Li;Guoan Bi;Gang Li
Affiliations:
School of Information Science and Engineering, Hangzhou Normal University, China;School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore;College of Information Engineering, Zhejiang University of Technology, China
Venue:
Signal Processing
Year:
2012

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Abstract

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.