Local polynomial-time–frequency transform formulation of the pseudo-L-Wigner distribution

Hory, C.; Mellet, C.; Valière, Jean-Christophe; Dépollier, Claude

doi:10.1016/s0165-1684(00)00223-1

Cited by 4 publications

(1 citation statement)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Moreover, the LPFT can be used as an IF estimator, and the corresponding asymptotic covariance matrix and bias of the estimates are studied in [38,49]. The concept of the LPFT is also implemented for the polynomial WVD to produce high signal concentration along the IF [119], and it is also extended to the L-Wigner distribution in [120].…”

Section: Local Polynomial Fourier Transform (Lpft)mentioning

confidence: 99%

Signal processing methods based on the local polynomial fourier transform

Li¹

View full text Add to dashboard Cite

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 ATTENTION: The Singapore Copyright Act applies to the use of this document. Nanyang Technological University Library Contents viii reassignment technique is employed to further increase the concentration of the local polynomial periodogram (LPP), which is the square of the LPFT. First, the uncertainty principle of the LPFT is investigated. It is shown that the uncertainty product of the LPFT of an arbitrary order is related to the signal parameters, the window function, and the errors of estimating the polynomial coefficients. The uncertainty principle of the LPFT becomes time-independent when the Gaussian window is used to segment the signal and the parameters of the LPFT kernel are estimated correctly. Factors that affect resolutions of signal representation, such as the window width, the length of overlap between signal segments, order mismatch and estimation errors of polynomial coefficients, are also discussed. Examples in speech and bat sound processing are demonstrated to show the advantage of the LPFT, compared with the STFT and the WVD. Second, the quantitative signal-to-noise ratio (SNR) analysis of the LPFT is derived based on the relationship between the LPFT and the WVD. The quantitative SNR analysis of the pseudo WVD (PWVD) in continuous-time form is presented as well. Comparisons are made among the SNRs achieved by using the LPFT, the FT, the STFT and the PWVD. Both the theoretical analysis and simulations have shown that the LPFT can provide higher SNR improvement than the FT, the STFT and the PWVD. Third, applications in radar imaging...

show abstract