Nonnegative time-frequency distributions for parametric time-frequency representations using semi-affine transformation group

Authors:
Hongxing Zou;Dianjun Wang;Xianda Zhang;Yanda Li
Affiliations:
Dept. of Autom., Tsinghua Univ., and State Key Lab. of Intelligent Technology and Systems, Tsinghua Univ. and Natl. Lab. of Pat. Recog., Inst. of Autom., The Chinese Acad. of Sci., Beijing, China;Department of Mathematical Sciences, Tsinghua University, Beijing, China;Department of Automation, Tsinghua University, Beijing, China;Department of Automation, Tsinghua University, Beijing, China
Venue:
Signal Processing
Year:
2005

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Abstract

This paper proposes a method for calculating a nonnegative time-frequency distribution (TFD) whose concentration is identical to that of Wigner-Ville distribution (WVD) when instantaneous frequencies (IFs) of the best-matched elementary functions of the signal under analysis are pre-estimated. This method is based on a special class of transformation group, referred to as semi-affine transformation (SAT) group. The essence of this method is to create a joint distribution by translating the values of WVDs of Morlet wavelet to the positions around IFs of the best-matched elementary functions. Theoretical predictions and numerical results indicate that the proposed strategy can result in the most visually appealing TFDs for highly nonstationary signals.