Uncertainty principle of the second-order LPFT

This paper studies the uncertainty principle of the second-order local polynomial Fourier transform (LPFT). It shows that the uncertainty product of the LPFT is time-independent when the Gaussian window is used to segment the signal. Meanwhile when the extra parameter is estimated correctly, the uncertainty product of the LPFT becomes a constant. Compared to the short-time Fourier transform and the Wigner-Ville distribution, it shows that the LPFT provides a better resolution of signal presentation in the time-frequency domain. Simulation for a speech signal is also given to confirm that the LPFT is capable of revealing more spectrum details when the frequency contents change dramatically.