Time-frequency plane splitting for the first order local polynomial Fourier transform

In this paper we present a time-frequency plane tiling (splitting) approach for the local polynomial Fourier transform. Comparison of the proposed approach with the one based on the short-time Fourier transform is given. Advantages of the first order local polynomial Fourier transform in the localization and analysis of LFM signals are shown. Signals that can locally be approximated by the LFM signals are also considered. Theory is illustrated by several examples.