Efficient Analysis of Time-Varying Multicomponent Signals with Modified LPTFT

Wei, Yongmei; Bi, Guoan

doi:10.1155/asp.2005.1261

Cited by 26 publications

(25 citation statements)

References 13 publications

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“…When M = 2, we can get the secondorder LPFT, which has achieved improved performance in many applications such as radar imaging [11,12], nonstationary interference excision in DSSS communications [13,14], chirp signal detection [15], and source localization and tracking in nonstationary environment [16]. A review on the developments and applications of the LPFT can be referred to [17,18]. In the following, we will focus on the uncertainty principles of the second-order LPFT and then generalize to those of the Mth-order LPFT.…”

Section: Uncertainty Principles Of the Second-order Lpftmentioning

confidence: 99%

Systematic analysis of uncertainty principles of the local polynomial Fourier transform

2014

EURASIP J. Adv. Signal Process.

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Section: Uncertainty Principles Of the Second-order Lpftmentioning

confidence: 99%

Systematic analysis of uncertainty principles of the local polynomial Fourier transform

2014

EURASIP J. Adv. Signal Process.

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“…If the second order LPFT is used to process higher-order PPSs, as shown in [27,28] for example, the number of polynomial coefficients to be estimated is reduced, which directly leads to the reduction of the PTFT order, or equivalently the reduction of the required computational complexity. We will discuss the side effects of this order mismatch, i.e., the order of the LPFT is smaller than the order of the PPSs, on the resolution of the signal representation in the time-frequency domain.…”

Section: The Lpftmentioning

confidence: 99%

“…Therefore, the window width for practical applications should be properly selected to achieve a compromise between the resolutions in both time and frequency. An adaptive procedure for window length selection has been provided in [28]. Similarly, an automated procedure for window width selection is possible and will be discussed in our future study.…”

Section: Order Mismatch Effectsmentioning

confidence: 99%

“…It was shown in [28] that when the second order LPFT is used to process the chirp signals, the length of overlap between the adjacent signal segments can be significantly reduced without obviously degrading the signal resolution in the time-frequency domain, which allows us to further minimize the required computational complexity. For example, the required number of complex multiplications in (4) is reduced as l increases.…”

Section: Effects Of Overlap Lengthsmentioning

confidence: 99%

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On uncertainty principle of the local polynomial Fourier transform

2012

EURASIP J. Adv. Signal Process.

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In this article, a comprehensive study on uncertainty principle of the local polynomial Fourier transform (LPFT) is presented. It shows that the uncertainty product of the LPFT of an arbitrary order is related to the parameters of the signal and the window function, in addition to the errors of estimating the polynomial coefficients. Important 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 discussed. The effects of minimizing computational complexities on signal representation by reducing the order of the transform and the overlap length between signal segments are also examined. In terms of the signal concentration, comparisons among the short-time Fourier transform, the Wigner-Ville distribution and the second order LPFT are presented. The LPFT is shown to be an excellent candidate providing better representations for time-varying signals.

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“…ATTENTION: The Singapore Copyright Act applies to the use of this document. Nanyang Technological University Library Furthermore, methods to reduce the overlap between adjacent segments are also presented to reduce the computational complexity [48]. In this way, the computational load of the LPFT can be greatly reduced.…”

Section: Motivationmentioning

confidence: 99%

Signal processing methods based on the local polynomial fourier transform

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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...

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Efficient Analysis of Time-Varying Multicomponent Signals with Modified LPTFT

Cited by 26 publications

References 13 publications

Systematic analysis of uncertainty principles of the local polynomial Fourier transform

Systematic analysis of uncertainty principles of the local polynomial Fourier transform

On uncertainty principle of the local polynomial Fourier transform

Signal processing methods based on the local polynomial fourier transform

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