Signal processing methods based on the local polynomial fourier transform
Li, Xiu Mei
Date of Issue2010
School of Electrical and Electronic Engineering
Nanyang Technological University
The majority of signals encountered in real applications, such as radar, sonar, speech, and communications, are often characterized by time-varying spectral contents. For this type of signals whose frequency contents evolve with time, signal representation in time or frequency domain alone cannot fully describe its time-varying characteristics. It would be far more useful to describe the signals with the time-frequency representations (TFRs). The TFRs for processing signals with time-varying frequencies can be generally categorized as linear and nonlinear transforms. The widely used linear transform is the short-time Fourier transform (STFT). The nonlinear transforms include the Wigner-Ville distribution (WVD) and various classes of quadratic time-frequency transforms. During the studies of various signal processing methods, it is found that the local polynomial Fourier transform (LPFT) is an important and effective processing tool for many practical applications, mainly because the LPFT is a linear transform and free from the cross terms that exist in the WVD. Furthermore, the LPFT uses extra parameters to approximate the phase of the signal into a polynomial form to describe time-varying signals with a much better accuracy than the STFT. This thesis focuses on the theoretical analysis of the LPFT, such as its uncertainty principle and SNR analysis, followed by applications to demonstrate its advantages and verify the theoretical analysis of the LPFT. Moreover, the reassignment technique is employed to further increase the concentration of the local polynomial periodogram (LPP), which is the square of the LPFT.
DRNTU::Engineering::Electrical and electronic engineering::Electronic systems::Signal processing