Efficient Analysis of Time-Varying Multicomponent Signals with Modified LPTFT
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Efficient Analysis of Time-Varying Multicomponent Signals with Modified LPTFT Yongmei Wei School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798 Email: [email protected]
Guoan Bi School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798 Email: [email protected] Received 19 May 2004; Revised 13 October 2004; Recommended for Publication by Yuan-Pei Lin This paper presents efficient algorithms for the analysis of nonstationary multicomponent signals based on modified local polynomial time-frequency transform. The signals to be analyzed are divided into a number of segments and the desired parameters for computing the modified local polynomial time-frequency transform in each segment are estimated from polynomial Fourier transform in the frequency domain. Compared to other reported algorithms, the length of overlap between consecutive segments is reduced to minimize the overall computational complexity. The concept of adaptive window lengths is also employed to achieve a better time-frequency resolution for each component. Numerical simulations with synthesized multicomponent signals show that the proposed ones achieve better performance on instantaneous frequency estimation with greatly reduced computational complexity. Keywords and phrases: time-frequency analysis, time varying, multicomponent, modified LPTFT, impulse noise.
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INTRODUCTION
Due to their superior performance in dealing with nonstationary signals, time-frequency transforms (TFTs) have found various applications in many areas including communications, multimedia, mechanics, and biology [1]. The most popular and simplest TFT is short-time Fourier transform (STFT) that has been widely used for many practical applications [1, 2]. Nevertheless, the STFT suffers from low resolution when the analyzed signal is highly nonstationary. Local polynomial time-frequency transform (LPTFT), referred to as the generalization of STFT, was reported to provide high resolution for nonstationary signals [3, 4] with a local polynomial function approximating to the frequency characteristics. Unfortunately, the estimation of a number of extra parameters required by LPTFT computation results in a heavy computational load. This is mainly due to the long overlap between consecutive signal segments for which the estimation process is implemented [4]. In order to reduce the computational complexity, attempts can be made to reduce the length of overlap between the consecutive segments. However, problems of reduced resolution in the time-frequency domain have to be solved by using more effective methods of window length selection.
This paper presents analysis algorithms for time-varying multicomponent signals containing white Gaussian and/or impulse noises. Different from previously reported algorithms, the proposed modified local polynomial timefrequency transform (MLPTFT) reduces the overlap length between consecutive segments to minimize the number of segments to be processed. Effective meth
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